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Stress distribution in some common welded beam-to-column connections Nicholls, Jack Ivan 1960

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STRESS DISTRIBUTION IN SOME COMMON WELDED BEAM-TO-COLUMN CONNECTIONS by JACK IVAN NICHOLLS B.E., UNIVERSITY OF NEW ZEALAND, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M. A. Sc. IN THE DEPARTMENT of CIVIL ENGINEERING WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARDS. THE UNIVERSITY OF BRITISH COLUMBIA APRIL I960 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f SKJ<5T[^fLsE*>K-is$&. The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. U i ; ABSTRACT This i s a report on t e s t s of welded beam-to-column connections c a r r i e d out i n the Materials Testing Laboratory, Department of C i v i l Engineer-ing, U n i v e r s i t y of B r i t i s h Columbia. The t e s t s e r i e s included four basic types of connection commonly used i n p r a c t i c e , and f o r each type, a set of stress d i s t r i b u t i o n curves has been given f o r each part of the connection. R e a l i z i n g also, that f o r a con-nection to be of any p r a c t i c a l use, i t must have adequate r o t a t i o n capacity, moment-rotation curves have a l s o been given. From the various stress curves given, an attempt has been made to tabulate magnification f a c t o r s , which are described i n the text, and i n t h i s way c o r r e l a t e the peak stress values obtained with the t h e o r e t i c a l l i n e a r stresses assumed. In order to do t h i s f o r the column of each connection, a l i n e a r s t r e s s d i s t r i b u t i o n was assumed, using information obtained from the tests c a r r i e d out. F i n a l l y , the c a l c u l a t e d values f o r each connection are compared i n the concluding s e c t i o n . v i i i CONTENTS SECTION A Page INTRODUCTION ( i ) GENERAL 1 ( i i ) SOME FACTORS AFFECTING STRESS DISTRIBUTIONS 3 1. Residual Stresses 3 2. Beam not Welded at Right Angles to Column 3 3. Allowable Tolerances i n R o l l e d Sections U ( i i i ) STRESS MEASUREMENT CONSIDERATIONS 6 SECTION B THEORY 7 ( i ) MODIFIED STRESS-STRAIN CURVE 7 ( i i ) FAILURE THEORY 8 1. Beam F a i l u r e 9 2. Column F a i l u r e 11 3. Weld F a i l u r e 12 SECTION C TEST APPARATUS 14 ( i ) GENERAL 14 ( i i ) THE TEST SPECIMEN 14 ( i i i ) LOAD ANALYSIS FOR STIFFENING BEAM 16 ( i v ) LOAD APPLICATION AND MEASUREMENT 18 (v) ANGULAR MEASUREMENT 19 ( v i ) STRAIN MEASUREMENT 20 i v SECTION D TEST PROCEDURE 22 ( i ) CALIBRATION OF TURNBUCKLES 2 2 ( i i ) PROCEDURE FOR TESTING 2 3 SECTION E TEST RESULTS 2 4 ( i ) GENERAL 2 4 ( i i ) CONNECTION A - l 32 A. DESCRIPTION OF CONNECTION 3 2 B. FAILURE MECHANISM 3 3 C. MOMENT ROTATION CHARACTERISTICS 3 3 D. DISTRIBUTION OF STRESS 3 3 a) Gauge Layout 3 3 b) Discussion 3 5 1 . Tension Beam Flange 3 5 2 . Beam Web 3 5 3 . Column Web 3 6 c) F a i l u r e Moment 3 6 E. CALCULATIONS 3 8 a) Check on S t a t i c s 3 8 b) Mo d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stress 4 0 c) F a i l u r e Moment i n Column Web 4 1 d) Web C r i p p l i n g 4 2 ( i i i ) CONNECTION A - 2 4 4 A. DESCRIPTION OF CONNECTION 4 4 B. FAILURE MECHANISM 4 4 C. MOMENT ROTATION CHARACTERISTICS 4 4 V D. DISTRIBUTION OF STRESS 44 a) Gauge Layout 44 b) Discussion 45 1. Tension Beam Flange 45 2. Beam Web 46 3. Column Web 46 c) F a i l u r e Moment 46 E. CALCULATIONS 48 a) Check on S t a t i c s 48 b) M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses 50 c) F a i l u r e Moment i n Column Web 51 d) Web C r i p p l i n g 52 ( i v ) CONNECTION B 53 A. DESCRIPTION OF CONNECTION 53 B. FAILURE MECHANISM | 54 C. MOMENT ROTATION CHARACTERISTICS 55 D. DISTRIBUTION OF STRESS 55 a) Gauge Layout 55 b) Discussion 56 1. Beam Flanges 56 2. Beam Web 57 3. Column Web 57 4. Boxing Plates 57 c) F a i l u r e Moment 58 E. CALCULATIONS 60 a) Check on S t a t i c s 60 b) M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses 62 v i (v) CONNECTION C 65 A. DESCRIPTION OF CONNECTION 65 B. FAILURE MECHANISM 65 C. MOMENT ROTATION CHARACTERISTICS 65 D. DISTRIBUTION OF STRESS 66 a) Gauge Layout 66 b) Discussion 67 1. Moment Plates 67 2. Web Connecting Plate 68 3. Column Web 68 c) F a i l u r e Moment 68 E. CALCULATIONS 70 a) Check on S t a t i c s 70 b) M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses 71 c) F a i l u r e Moment i n Column Web 73 d) Web C r i p p l i n g 73 ( v i ) CONNECTION D 74 A. DESCRIPTION OF CONNECTION 74 B. FAILURE MECHANISM 75 C. MOMENT ROTATION CHARACTERISTICS 76 D. DISTRIBUTION OF STRESS 76 a) Gauge Layout 76 b) Discussion 78 1. Moment Plates 78 2. Web Connecting Plate 79 3. Column Web 79 4. Boxing Plates 80 E. CALCULATIONS 81 a) Check on S t a t i c s 81 b) Mo d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses 83 v i i CONCLUSIONS 85 ( i ) GENERAL 85 ( i i ) COMPARISON OF TEST VALUES 86 1. Connections A - l , A-2 and B 86 2. Connections C and D 88 ( i i i ) EFFECT OF POSITION OF BOXING PLATES 89 ( i v ) FACTORS OF SAFETY 92 (v) CONCLUDING REMARKS 92 BIBLIOGRAPHY i PHOTOGRAPHIC SUPPLEMENT i i i v i i i STRESS DISTRIBUTIONS Graph No. To follow page CONNECTION A-l 37 4 - Tension Beam Flange 5 - Beam Web 7 - Column Web CONNECTION A-2 47 9 - Tension Beam Flange 10 - Beam Web 11 - Column Web CONNECTION B 59 13 - Tension Beam Flange 14 - Compression Beam Flange 15 - Beam Web 16 - Column Web 17 - Tension Boxing Plates 18 - Compression Boxing Plates CONNECTION C 69 20 - Tension Moment Plate 21 - Compression Moment Plate 22 - Beam Web Connecting Plate 23 - Column Web CONNECTION D 80 25 - Tension Moment Plate 26 - Compression Moment Plate Ix Graph No. To follow page CONNECTION D (cont.) 80 27 - Web Connecting Plate 28 - Column Web 29 - Tension Boxing Plates 30 - Compression Boxing Plates CONNECTIONS A - l , A-2 $ B 87 31 - I d e a l i z e d Curves f o r Stress at Outer Surface of Tension Beam Flange CONNECTIONS C f D 89 33 - I d e a l i z e d Curves f o r Stress at Outer Surface of Tension Moment Plates X ACKNOWLEDGEMENT The w r i t e r wishes to express appreciation to the Canadian I n s t i t u t e of S t e e l Construction f o r f i n a n c i a l assistance i n the preparation of t h i s t h e s i s . He also expresses h i s thanks to the Dominion and Western Bridge Com-panies for t h e i r cooperation at the time of f a b r i c a t i o n of the t e s t specimens. He also expresses h i s thanks to his supervisor, Dr. A. Hrennikoff, who donated much of his time, not only to the formulation of basic requirements, but also to the guiding of the project to a conclusion with help and encouragement. NOTATIONS applied moment r e s i s t i n g moment at the connection s e c t i o n modulus normal stress normal t e n s i l e and compressive stresses allowable design stress modulus of e l a s t i c i t y normal s t r a i n d e f l e c t i o n or elongation t e n s i l e force (6^A) compressive force ($•A) applied loads area of cross-section areas of web and flange of s t r u c t u r a l section depth of beam and column sections breadth of beam and column sections flange thickness of beam and column sections web thickness of beam and column sections k-distance of beam and column sections SECTION A INTRODUCTION ( i ) General; From the design viewpoint, welded connections are c l a s s i f i e d as " r i g i d " , as opposed to " f l e x i b l e " or "pinned" connections which have l i t t l e or no resis t a n c e to end r o t a t i o n . Due to t h i s resistance to end r o t a t i o n i n r i g i d connections, a r e s i s t i n g moment i s developed, which manifests i t s e l f i n the beam i n the form of d i r e c t stress i n the flanges and web, with the flanges more highly stressed than the web. Providing t h i s stress i s within the e l a s -t i c range and assuming plane sections to remain plane, a l i n e a r stress d i s t r i -bution, as shown i n f i g u r e 1 i s assumed to e x i s t across the beam web and flanges. This stress d i s t r i b u t i o n w i l l not n e c e s s a r i l y be obtained under p r a c t i c a l conditions, and i t i s the object of t h i s paper to determine the d i s t r i b u t i o n of these stresses i n both the beam and column sections under s t a t i c loading. The four basic types of connection tested are those shown i n fi g u r e 2 . In a l l four connections, the beam was welded to the column flange. To follow p. 1 / w — i \ • ) y M O M E N T D I A G R A M (a.) T h e o r e t i c a l Linear Stress D i s t r i b u t i o n i n Beam Flanges and Web 2 Connection A: Here the beams were welded d i r e c t l y to the column flanges. Two connections were tested. A - l - F i g . 2(a): had a continuous f i l l e t weld around the periphery of the beam sect i o n . A-2 - F i g . 2(b): had 1/4" s i n g l e butt welds across a l l the beam flanges, and 6" of 1/4" f i l l e t weld on both sides of the beam web. Connection B: F i g . 2 ( c ) : had l / 4 M s i n g l e butt welds across a l l beam flanges, and 1/4" f i l l e t welds on both sides of the beam web. This connection also had boxing plates i n the column section, which were welded into place with 1/4" f i l l e t welds on both sides of the boxing pl a t e s . Connection C: F i g . 2(d): here the beams were welded to the column flanges through moment plates. The tension moment plate was welded to the column flange with a 5/16" s i n g l e butt weld, and to the beam tension flange with 1/4" f i l l e t weld. The compression moment plate was welded to the column flange with 1/4" f i l l e t welds on both sides of the moment pl a t e , and to the compres-sion beam flange with 1/4" f i l l e t welds on each edge of the moment plate as shown i n the f i g u r e . The "web connecting plate" was welded to t h e column flange with 1/4" f i l l e t welds on both sides of t h i s p l a t e , and to the beam web by 1/4" f i l l e t welds. Connection D: F i g . 2(e): b a s i c a l l y t h i s connection was the same as connection C . Here, however, there were boxing plates welded into the column section using arcund beam periphery. V.ErW A - A . To follow p. 2 COUMECTIOU A-2. i " f . k f welds boVh sides web. "^ single welds across beam flanges. tiHef weld bol-K sides o f beam web. 4 single, buH welds across all beam f l a n a e s i " fillet- weld* o f boxing boVh sides places. Vi&w C-C. C O N N E C T I O N C To follow p. 2 J WE.& COMWECTIMG PuT&r on one side onlg of j Warn web. 7 fillet welds on 4. sides o f comp? m o r n i n r p\atc / K _ < — £ — £ — £ — £ _ £ £—i—^^ J^** , | f / TESISIOM ; / / M^MEWT PUTfc. / ' i i / & single butt wield connecting tension m o t w n l plates to column flanges filled welds connecting plate" c o n n i z c f 1 mg web to beam web, ( d ) 4 filled welds connecting tension moment plate to beam Aanges. COMWE-CTIOM D . j^ " single butt weld connecting tension moment" plates to column flanges.  ^ fillet- welds connecting web * connecting plate to column flange., beam web. 3* fillet- weld connecting comph moment" plo.hr to beam flange. fillet" weld both sides of compn moment" plahz,. ^" fillet weld connecting tension m o m i n t plate to beam flange. VIEW 3 1/4" f i l l e t welds on both sides of the boxing plates as shown. There are, of course, many factors which can a f f e c t the stress d i s t r i b u t i o n s i n both the beam and column sections. The fo l l o w i n g i s a d i s -cussion of some of these. ( i i ) Some Factors A f f e c t i n g Stress D i s t r i b u t i o n : 1. Residual Stresses: Residual stresses are those present i n a s o l i d body when no ex-t e r n a l forces are a c t i n g on the body, or they may be considered as the s t r e s -ses that remain i n a structure as a r e s u l t of l o c a l i z e d deformations. Residual stresses introduced by welding are caused by l o c a l i z e d heating associated with the welding process, and to a l e s s e r degree by shrinkage of the weld material. In measuring the applied stresses with e l e c t r i c a l r esistance s t r a i n gauges, i t has been assumed that under 2 e r o external loading no stress e x i s t s i n the specimen, and hence the r e s i d u a l stresses have been neglected completely. The e f f e c t of neglecting these r e s i d u a l stresses does not seem to have been very consequential, since, f o r each t e s t c a r r i e d out, s t r a i n gauges i n s i m i l a r positions on both beams of the same connection, have i n d i c a * ted s i m i l a r stress values. In p a r t i c u l a r , the r e s u l t i n g stress d i s t r i b u t i o n curves show a f a i r l y symmetrical form f o r a l l applied moments. 2. Beam Not Welded at Right Angles to Column: This i s a very common occurrence i n welding p r a c t i c e , and one which has s i g n i f i c a n t features under the t e s t conditions. To understand f u l l y the r e s u l t i n g d i s t o r t i o n o f the str e s s pattern, f i g u r e 3 has been drawn. To follow p. 3 4 Figure 3, part (a) shows the beam framing i n t o the column, and the applied moment M acting on the connection. Part (b) shows the beam i n true se c t i o n , twisted through an angle a with respect to the column c e n t r e - l i n e and part (c) shows the components of M, the applied moment, p a r a l l e l to and at r i g h t angles to the beam web. These components may be stated as: (a) = M cos a - i n plane at beam web (b) a M s i n a - at r i g h t angles to beam web and they induce the following e f f e c t s : gives the l i n e a r t h e o r e t i c a l diagram which normally e x i s t s i n the I-beam section when subjected to a moment i n the plane of the web. M2 tends to cause a r o t a t i o n of the beam i n the d i r e c t i o n as shown, and hence the stresses i n the section are now modified. Consider the points A^, A^, and B^. Due to - tension at B^ and B^ ; compression at A^ and A^ Due to - tension at A^ and B^ ; compression at and B^. I t can be seen now that i n the compression zone of the beam, A^ and the h a l f flange on that side of the web w i l l have a reduced s t r e s s , whereas A^ and the h a l f flange on that side of the web w i l l have an increased s t r e s s . S i m i l a r conditions e x i s t i n the tension zone. This then accounts f o r the trapezoidal stress diagram shown at the two flanges. Using t h i s same argument, a d i s t o r t i o n of the p r a c t i c a l stress d i s t r i b u t i o n s due to t h i s twist i n welded p o s i t i o n of the beam, can also be deduced. 3. 'Allowable Tolerances i n R o l l e d Sections: A l l r o l l e d s t r u c t u r a l sections must pass a tolerance t e s t before 5 being supplied to the s t e e l f a b r i c a t o r . Having passed these t e s t s , however, does not n e c e s s a r i l y mean that the se c t i o n i s not d i s t o r t e d , quite the con-t r a r y . Apart from v a r i a t i o n s i n weight, length and thickness of cross-s e c t i o n a l d e t a i l , a flange d i s t o r t i o n as shown i n f i g u r e 4 can e x i s t . Fig„ L D i s t o r t i o n of Beam Flanges i n R o l l i n g This type of d i s t o r t i o n would lead to a t r a p e z o i d a l flange s t r e s s pattern s i m i l a r to that shown above i n f i g u r e 3, and once again, a d i r e c t i n -fluence on the str e s s pattern f o r the section. The above three features are perhaps the most s i g n i f i c a n t i n d i s t o r t i n g the stress patterns from t h e i r true shapes. There are others a l s o , such as discontinuous welds, which can introduce these stress concentrations.'" R.F.Pray e C.Jensen, "Welded Top Plate Beam-Column Connections," The Welding Journal Research Supplement, J u l y 1956. 6 ( i i i ) Stress Measurement Considerations: Since "welded" connections are dealt with in this test series, the stresses required are those actually developed in the weld sections. In order to do this e l e c t r i c a l resistance strain gauges were proposed, and used success-i f u l l y . These strain gauges, however, require a smooth surface to be glued to, such that accurate results can be obtained. Now any weld surface is very irregular, and since any action, such as f i l i n g , or grinding a section to the required surface conditions is l i a b l e to change the stress characteristics, placing gauges on the weld section was thus eliminated. This l e f t the other possibility of placing small gauges directly opposite the weld section. Small gauges, such that the stress measured would be extremely close, i f not equal, to that actually existing in the weld i t s e l f . Two types of gauge were used, (a) SR4 type A8 (b) Phillips type PR9214 these gauges, have c o i l dimensions of approximately 1/8" x 3/l6"• Another major feature to be considered was range of the gauges. Maximum strain measurement required for the test, was that of yield stress i.e. in the case of steel this value is 0.1$ to 0.2$ strain. Since the gauges are linear up to approximately 1.0% strain, then strain measurements on steel could be accomplished with these gauges. Yield stress was required for a l l steel sections, for which stress curves were to be drawn. In order to obtain these values, tension test speci-mens, 18 in number, were sele'cted from the various specimens after testing, and the yield point established by tensile tests. The values obtained varied widely, and generally were quite high, therefore a standard value of 35 kip/in." was adopted as yield stress, for a l l specimens. The actual values indicated by the tension tests were above this value. 7 SECTION B THEORY ( i ) Modified S t r e s s - S t r a i n Diagram: Subjecting a s t e e l t e s t specimen to a tension t e s t reveals a graph of stress versus s t r a i n as shown by the curve OABCDE i n f i g u r e 5(a). I n i t i a l l y there i s a steep l i n e a r section c a l l e d the " E l a s t i c Region," up to point B which i s the "Upper Y i e l d Point." Then the curve drops abruptly to point C, the "Lower Y i e l d Point," and from here continues i n a s t r a i g h t l i n e without stress increase to point D, t h i s range now being c a l l e d the " P l a s t i c Region." A f t e r point D, the stress begins to increase once again, u n t i l "Ultimate Stress" i s reached, point E, and f i n a l l y f a i l u r e at point F. This l a t t e r range DE i s generally c a l l e d the " S t r a i n Hardening Region." As with these tension specimens, so too, do the f i b r e s of a s t r u c -t u r a l element act, under t e n s i l e or compressive forces. Figure 5(b) shows an I-beam subjected to a moment M, and three s t r e s s diagrams developed i n the beam, f o r three d i f f e r e n t magnitudes of M. Figure 5b(i) indicates that y i e l d s t r e s s has developed at the outer beam f i b r e s , i . e . a s t r a i n i n the outer f i b r e s corresponding to point A i n 5(a). Figure 5b(ii) i n d i c a t e s a y i e l d To follow p. 7 4 8 s t r e s s developed over a greater s e c t i o n of the beam due to an increased moment, and hence a s t r a i n increase i n the outer f i b r e s , with no increase i n stress accompanying i t . T h i s , then, would correspond to a s t r a i n i n the outer f i b r e s , i n the region CD. I f now the s t r a i n i n the outer f i b r e s was allowed to increase u n t i l i t reached a value i n the s t r a i n hardening region, the stress i n the outer f i b r e s would increase once again, but In the theory of "Limi t Design," these s t r a i n hardening stresses are u s u a l l y neglected, and t h i s being so, the str e s s i s assumed to remain at the y i e l d value u n t i l ultimate f a i l u r e , at which stage a " P l a s t i c Hinge" i s sa i d to form. This condition has been shown i n 5 b ( i i i ) , the whole se c t i o n having now developed y i e l d s t r e s s , and an increase i n moment over and above t h i s condition cannot be equalized by a stress increase, hence f a i l u r e . Usually, as we l l as the s t r a i n hardening stresses, the peak at A i s neglected, and f i n a l l y the modified s t r e s s - s t r a i n curve OACDG i s l e f t . The moment corresponding to collapse conditions i s u s u a l l y designated or " P l a s t i c Moment". In the following chapters where str e s s diagrams have been drawn, the modified curve has been used as a basis f o r stress a n a l y s i s , s t r a i n hard-ening stresses have been neglected. ( i i ) F a i l u r e Theory: Having developed the theory of stress build-up i n the I-section, i t is now possible to in v e s t i g a t e the f a i l u r e modes of the connection, from the point of view of both beam and column f a i l u r e s . A p p l i c a t i o n of moment to the connection r e s u l t s i n the formation of s t r e s s e s , as shown above, which w i l l be greatest i n the beam flanges, and d i r e c t l y opposite these flanges, i n the column sec t i o n . These hig h l y stressed To follow p. 8. c Compression Flanqe. F i g . 6 Beam F a i l u r e T C j r 1 L Tension Flonqc. ( o. ) ^ •J ii 1 •U Compression Flange. (*) F i g . 8 Column F a i l u r e 9 sections then, lead to the possibility of three types of failure: 1. Beam Failure 2. Column Failure 3. Weld Failure. Consider the mechanism of each i n turn. 1. Beam Failure: In this failure mechanism, the applied moment i s increased u n t i l a plastic hinge i s formed i n the beam section, at which time, theoretically, yield stress ( Bt j ) , is developed over the total beam section. In practice, however, due to the fact that without boxing plates the column flanges are not completely r i g i d , but w i l l deflect as cantilevers, there w i l l be a stress r e l i e f at the outside edges of the beam flanges. It seems l i k e l y then that f u l l theoretical plastic moment need not necessarily be developed i n the beam of this connection for a beam failure to occur. Consider figure 6 above. Diagram (a) shows the connection with a moment applied to one of the beams, producing tensile and compressive forces in the beam flanges of T and C respectively. Diagram (b) represents the position of the beam at failure, with a rotation during loading of a as a result of plastic yielding in the beam. Diagrams (c) and (d) represent sections through the beam showing tension and compression column flanges respectively, at the point of formation of f u l l plastic moment i n the beam. The column flanges in (c) and (d) are bowed inwards and outwards respect-ively, opposite the compression and tension flanges of the beam, indicating the possible stress r e l i e f mentioned earlier. This possible stress r e l i e f would induce plastic stresses only in the central section of the beam flanges, and would produce stresses in the beam 10 s e c t i o n as shown i n f i g u r e 7(a). From t h i s , only a section of the beam as shown cross-hatched i n f i g u r e 7(b) would have y i e l d stresses induced. 4-6y Beam Flange 6Vres*. beam Stresses. Ic- distance. Fig. 7 as: Possible Stress R e l i e f f o r Connections Without  Boxing Plates The width "x" shown i n f i g u r e 7)b) would depend upon such features (a) thickness of column webj (b) k • k-distance f o r column section, c where the k-distance of an I-beam i s defined as the thickness of the flange plus the length of web which contains the f i l l e t s . The k-distance f o r the beam section has been dimensioned i n f i g u r e 7(b). Generally f o r the two sections of the connection: k^ = k-distance f o r the beam k • k-distance f o r the column, c 11 2. Column F a i l u r e : In a column f a i l u r e , the applied moment i s increased u n t i l the p l a s t i c hinge i s formed i n the web of the column. The formation of t h i s p l a s t i c hinge induces y i e l d stress over a length of the column web d i r e c t l y op-posite the beam. The t o t a l length of the column web stressed to y i e l d stress i n a f a i l u r e of t h i s type, includes a length equal t o the t o t a l depth of the beam,plus a length of column web e i t h e r side of t h i s which Has been deduced by Beedle as three times the k-distance of the column section ( r e f e r f i g u r e 9). This p l a s t i c hinge formation i s accompanied by t e n s i l e y i e l d i n g , and compressive buckling of the column web opposite the tension and compression beam flanges r e s p e c t i v e l y . Figure 8 represents the f a i l u r e mode encountered. Diagram (a) shows the connection with a moment applied producing compressive and t e n s i l e forces of C and T r e s p e c t i v e l y i n the beam flanges. Diagram (b) represents the p o s i t i o n of the beam at f a i l u r e , with a r o t a t i o n of "a" caused by the p l a s t i c deformations i n the column web. Diagrams (c) and (d) represent sections through the beam showing the tension and compression beam flanges at f a i l u r e , and i n p a r t i c u l a r the t e n s i l e y i e l d i n g of the column web opposite the tension flange of the beam, and the buckling of the column web opposite the compression flange of the beam. This type of f a i l u r e would be exhibited by connections without boxing plates i n the column section. 3 From the l i m i t design viewpoint, Beedle has formulated a c r i t e r i o n f o r the collapse condition i n a column s e c t i o n under applied moment. This con-d i t i o n i s shown i n f i g u r e 9. L.S.Beedle, " P l a s t i c Design of S t e e l Frames". John Wiley e Sons, New York, 1958, p.177-178. I b i d . To follow p. 11 1 'j^Jisi; vS + • w.V" /-fo^^U. Vi-'.'- / , ' A j ; « T ; -! ™ V • ' # • ' 5 ' / S Beedle*8 C r i t e r i o n f o r Column F a i l u r e 12 Neglecting s t r a i n hardening str e s s e s , Beedle has s p e c i f i e d the length of column web over which y i e l d stress i s induced at f a i l u r e to be + 6k where d^ » depth of beam section k-distance f o r the column section. For t h i s condition, the collapse moment can be c a l c u l a t e d as P — J — \ + 6 k c where t • thickness of the column web. w 3. Weld F a i l u r e : This t h i r d type of f a i l u r e occurs at points where a high s t r e s s concentration e x i s t s . I t i s regarded, however, as the most serious of a l l three, because once a f r a c t u r e i s i n i t i a t e d i n the weld material, there i s an immediate r e d i s t r i b u t i o n of s t r e s s which w i l l allow the f r a c t u r e to enlarge u n t i l complete rupture of the weld becomes possi b l e . The material of the weld indicates a b r i t -t l e nature under a t e n s i l e t e s t , and hence t h i s rupturing process can be very rapid indeed. In the beam and column f a i l u r e s described e a r l i e r , t h i s abruptness of collapse would not be expected. This i s so, since the sections which are highly stressed and deform to define the f a i l u r e mode, do not e x h i b i t a b r i t t l e nature under the t e n s i l e t e s t , but have a s t r e s s - s t r a i n curve of the type shown Ibid.p.177-178 13 i n f i g u r e 5. From t h i s then, the stresses produced due to s t r a i n hardening would allow the connection to deform slowly under increasing applied momenti. 14 SECTION C TEST APPARATUS ( i ) General: A l l specimens were fabricated with the same beam and column s i z e s , so that a d i r e c t comparison of the measured te s t values could be made, f o r the four d i f f e r e n t connections. The q u a n t i t i e s measured during the te s t were: 1. Applied load 2. Connection r o t a t i o n 3. S t r a i n at predetermined points. From these measured values moment-rotation curves have been drawn, which i n d i c a t e a r i g i d i t y comparison, and from the measured s t r a i n s , a d i s t r i b u -t i o n of stress has been computed and plotted. These r e s u l t s then, comprise the basis f o r comparison of the four connections tested. ( i i ) The Test Specimen: Figure 10 shows the basic t e s t specimen. I t consisted p r i m a r i l y of 4 beams, 8" x 5 1/4" W.F. at 17.0#/ft, welded to the flanges of a c e n t r a l column To follow p , 14 Head o f 0\sa,n f t 6 D-O 111 ^ holes, & <8 x I f L -D a ^ c o f CMsa-n 0 _ i CN M I e> Q CM £OLUMM: GWO>" VJr aV l&.&t F i g . 10 The Test Specimen 15 6" x 6" W.F. at 15.0///ft. There were two loads applied to the specimen: 1. Compression load "Q" applied by the t e s t i n g machine, causing d i r e c t compression stress i n the column. 2 . Loads "P" applied at the ends of the beam by turnbuckles, causing a moment M to develop at each connection. To avoid scoring the machined surfaces of the Olsen t e s t e r , 8" x 8" x 1" plates were welded t o the ends of the c e n t r a l column. Also, at the end of each beam two 5 1/4" x 3s" x ^" bearing plates were welded, one on each side of the beam web, to provide bearing resistance against the applied P-loads. I n i t i a l l y , due to the l i m i t e d amount of e l e c t r i c a l s t r a i n measure-ment switching gear a v a i l a b l e , and the number of s t r a i n gauges required f o r each t e s t , only two of the four beams could have t e s t data recorded from them. In order to economize, a method of s t i f f e n i n g two beams during the t e s t was f i n a l l y adopted so that now two separate tests could be c a r r i e d out on each specimen, and t e s t data gained from a l l four beams on the one specimen. To do t h i s a s t i f f e n i n g beam, as shown i n f i g u r e 11, was connected through two 5/8" 6 rods to the top two beams of the t e s t specimen. The e f f e c t of t h i s was to s t r e s s the lower connections to f a i l u r e , allowing only e l a s t i c s t r a i n s i n the top connections. An analysis of the forces 'produced has been given below. Since only two connections of each type were proposed f o r the t e s t s e r i e s , a f u r t h e r economy was adopted i n the form of two d i f f e r e n t connec-t i o n s on the one specimen, one f o r the top beams and the other f o r the bottom beams. F i n a l l y , a t o t a l of four t e s t specimens was used. To follow p. 15 F i f i . 11 S t i f f e n i n g Beam i n P o s i t i o n 'Shffenmq B e a m . Deflected form of a Top conriizchon. Def lected form of t R 2 rode. F i g - 12 D e f l e c t i o n Analysis at the Top Connection 16 ( i i i ) Load Analysis for Stiffening Beam: In figure 12 l e t : P • load applied by turn-buckle. R » load in the two rods together. 6^  = deflection of stiffening beam at load R. 6 2 = elongation of the two rods under applied R-load. 6^  • deflection of bottom beam at load K. E = Youngs Modulus. I = moment of inertia of beam about axis of bending. A a cross-sectional area of two rods. From geometry then, 6,+ 6 2- 63 - 0 1) From "Strength of Materials", Rb 3 RL 61 " 3EIX 2 " AE 3 6EI2 K j a ' u' - 3EI 2 Substituting these values into the above deflection equation ( l ) , and assuming E to be the same for a l l elements, leaves: R J>? L _b 3 3 I X + A 3 I 2 p ' 61" 3ab2 - b 3 2 2) 17 Finally, substituting the known values into (2) leaves: R - 0.53P 3) Thus the moment in the top connection was reduced to approximately half the applied value in this manner, e.g. actual applied moment » Pa - Rb - Pa - 0.53Pb - 18.7P kip-ins. moment applied without stiffening beam = Pa - 33P kip-ins. For each specimen, the weaker- of the two connections was always tested f i r s t , and in this way, due to the lower failure load for this connection, the smallest moment possible was applied to the top or second connection, which s t i l l had to be tested. When the second or stronger connection for this speci-men was tested, the moment produced at the top connection did not matter since the test on i t had already been carried out. 1. Consider the f i r s t specimen, with connections A-2 and B. A-2 was tested f i r s t . Failure load on A-2 = 11.7 kips. Moment produced at B « 18.7P - 218.8 kip-ins. Values of yield stress were not reached u n t i l an applied moment of approximately 350 kip-ins. was reached in the test on connection B. 2. Consider the second specimen, with connections C and D. C was tested f i r s t . 18 Failure load on C = 12.5 kips. Moment produced at D = 18.7P » 233.8 kip-ins. Values of yield stress were not reached u n t i l an applied moment of approximately 400 kip-ins. was reached in the test on connection D. This indicates then, that the stiffening beam held the stresses in the untested connections to a value below that of yield stress. (iv) Load"Application and Measurement: Test P-loads were applied to the specimen by two hand operated, double-acting turnbuckles, connected between the points A and B shown on figure 10. Since the distance between the beams was LlOn c/c, these turn-buckles had to be made specially for the tests. Load measurement was carried out by means of strain gauges on the turnbuckle rods. To eliminate any stress effects from the threaded section, a clear rod length of approximately 9" was required. Considering these features then, the f i n a l adopted design i s as shown in figure 13(a). On the turnbuckle, the strain gauges were placed diametrically opposite each other, in order that the average strain would be recorded. In this way any stresses due to bending of the rod would not register on the strain indicator, since one gauge would be i n compression and the other in tension. The section on which the gauges were placed was reduced in diameter, such that a higher sensitivity could be attained, i.e. greater strain for same load. The turnbuckles were connected to the beam ends through a linkage system, as shown in figure 13(b). This system allowed a vertical pull to be applied, regardless of beam deflections. To follow p. 18 F i g . 13(a) D e t a i l of Turn-Buckle bottom flanqe width reduced \o I" for c\zorancn. » »» i 6 < b4 \NP at \1-Q 1 ft. 1^ *4z III , I ,11 2 x 44 x ' ^ r" L. V I \ TurnbucLW • V <2) F i g . 13(b) D e t a i l of Load Connection at Beam Ends 19 Knowing the applied load and the distance from the loaded point to the connection, the applied moments could be calculated d i r e c t l y . (v) Angular Measurement: Figure 14 shows the system used to measure the angle change at the connections. The l i g h t aluminum bracket was suspended from the centre of the column web by four pointed b o l t s set i n t o punch marks. Since under load the centre of the column web would have negligable or no movement, t h i s bracket could be considered as f i x e d , r e l a t i v e to the column. Two 1/8" rods with wing nuts, one each on the top and bottom sections, acted as "clamps" to hold these four b o l t s f i r m l y i n p o s i t i o n . F i n a l l y , to stop the whole system from r o t a t i n g about the centre l i n e of the column, two "stays" were connected to the bottom clamp, which i n bearing against the sides of the column flange, held the bracket against r o t a t i o n . To read the angle change, d i a l gauges, connected to the top of magnetic bases, were placed on the beam flanges as shown. The scale of these gauges could be extended by adjusting the brackets at the sections shown. It should be noted that the top d i a l gauge i s outside the bracket and the bottom d i a l gauge inside the bracket. The reason f o r t h i s i s that i n the event of a sudden f a i l u r e , such as a weld f a i l u r e , the d i a l gauge would always be moving away from the bracket, and thus there i s l e s s l i k e l i h o o d of breaking the d i a l gauge. Rotation at the connection occurred due to the elongation of the tension flange and shortening of the compression flange, since angular r o t a t i o n of the cross-section at t h i s point would be negligable. Considering the r o t a t i o n to occur about the centre of the beam, the following equations w i l l be true since ^, and ^_ are very small angles: To follow p. Dial qauqc. Light aluminum b r a c k e t . — D e t a i l s of Beam Rotation Measurement 20 where and are the changes in di a l readings and 6^, ^ anc* r as in the diagram. ^ and a r e measured in radians. The f i n a l angle change was taken as the average of these two "half beam rotation" values, j£ and \£n (vi) Strain Measurement: This was done directly, using e l e c t r i c a l resistance strain gauges, and strain measuring equipment. From these measured strains, the stresses i n -duced could be calculated from the equation or S = eE Assuming a value for E then, stress distributions could be plotted for a l l loads. There are many features which can create distortion in these stress distributions. It can be realized then, that for the same applied moment on connections of the same type, stress distributions would not be the same in every detail. However, experiment showed that i f "check" gauges were placed at pertinent points on the second connection, then very close values could be ob-tained, when both connections were under the same loading conditions. This was the system adopted during testing. The f i r s t connection had gauges at a l l points where a strain measurement was required, and the second connection had gauges which acted only as a check. This method, as well as economizing on the number 21 of gauges used, showed the r e s u l t s of s i m i l a r connections to be very close i n -deed, even though d i s t o r t i o n s i n the f i n a l curves are obvious. One major c o r r e c t i o n to be made to the measured s t r a i n s was a correc-t i o n f o r gauge f a c t o r . In a l l of the t e s t s there were more than 20 gauges to be read, t h e i r factors being d i f f e r e n t . Since only one gauge f a c t o r was set on the s t r a i n measuring bridge, an error was introduced. To correct t h i s error the f o l l o w i n g equation was used: Q corrected reading » _s x i n d i c a t e d reading G where: G • Gauge f a c t o r set on bridge, s G » True gauge f a c t o r of s t r a i n gauge. 22 SECTION D TEST PROCEDURE ( i ) C a l i b r a t i o n of Turnbuckles: As shown previously, the load was applied by turnbuckles at the ends of the t e s t beams, creating moments at the connections. In order to be able to c a l c u l a t e these applied moments, however, the value of the load applied by these turnbuckles had to be measured. This was done with the use of s t r a i n gauges on the turnbuckle rods. Thus, before any actual t e s t i n g could be c a r r i e d out, these s t r a i n gauges had to be c a l i b r a t e d i n terms of a known load, i . e . the s t r a i n i n these s t r a i n gauges corresponding to a known load on the turn-buckle had to be measured. To do this , t h e turnbuckles were connected, one at a time, to the upper and lower heads of a Tin i u s Olsen tension t e s t e r . The t e n s i l e loads applied to the turnbuckle were measured d i r e c t l y from the load i n d i c a t o r on the t e s t i n g machine, and the corresponding s t r a i n s induced i n the turnbuckle, were measured with a s t r a i n i n d i c a t o r connected to the s t r a i n gauges on the turnbuckle rod. Both turnbuckles were c a l i b r a t e d i n t h i s manner and the r e s u l t s of these c a l i b r a t i o n s have been plotted on graphs number 1 and 2. With these graphs, the loads, and hence moments applied to the connections under t e s t , 23 could be calculated. I t w i l l be noticed that two curves are given on each graph, one f o r "load" and the other f o r "unload". These two graphs correspond to s t r a i n and load readings taken during the c a l i b r a t i o n s , when the turnbuckle was f i r s t loaded, and then unloaded. To ca l c u l a t e the applied moments i n t e s t , the "load" curves were used. ( i i ) Procedure f o r Testing: I n i t i a l l y , with no moment applied to the connections, i . e . i n f i g -ure 15, P = 0, the load Q on the column would be increased to 30 kips (6.5 k/i n . ). Loads P would then be applied, creating moments at the connec-t i o n s . In the case of connections A and C, since a small f a i l u r e moment was predicted, the P-loads were given small increments between each set of recordings. In the case of connections B and D, however, a larger f a i l u r e moment was predicted, and correspondingly l a r g e r increments were used. Besides creating a moment at the connections under t e s t , the P-loads also caused a compression i n the section of the column between the beams, as shown i n fi g u r e 15. This meant that the l o n g i t u d i n a l s t r e s s i n th i s s e c t i o n of the column was increasing with every load increment, i . e . load at any time during the t e s t would be (Q + 2P). For the purposes of the t e s t , however, t h i s load of (Q + 2P) was required to remain constant, so the compressive load Q on the column was reduced with every increase i n P. In the case of connections B and D the f a i l u r e load was so high that t h i s decrease i n Q was stopped at a load of Q = 5 kips, such that the specimen could s t i l l be kept steady. This loading system continued u n t i l the onset of f a i l u r e , at which point, the specimen was l e f t to creep f o r about 12 hours before the f i n a l set of readings was taken. To follow p. 23 V e r t i c a l f o r c e s = P- Applied by VurnbucUe. Connections under test. (<a + 2p) P- Applied by tumbuclde. base of Vest inq / /machine./ / / Q - Applied by testing machine f o column of hzsV specimen. F i g . 15 E q u i l i b r i u m of V e r t i c a l Forces on Test Specimen 24 SECTION E TEST RESULTS ( i ) General: The t e s t r e s u l t s are presented here i n four sections, each section being devoted to a s i n g l e connection. The presentation w i t h i n each section i s s i m i l a r and has been written under the following sub-headings. A. Description of Connection. B. F a i l u r e Mechanism C. Moment-rotation C h a r a c t e r i s t i c s . D. Stress D i s t r i b u t i o n a) Gauge Layout b) Discussion of Curves c) F a i l u r e Load and Moment. E. C a l c u l a t i o n s . were adopted throughout, since the values obtained from test specimens varied widely. Values f o r E 35 k i p / i n . 2 25 In p l o t t i n g the stress d i s t r i b u t i o n s i n the various sections of the connections f o r both beam and column webs, the average stress from the two sides has been pl o t t e d as a s i n g l e curve. However, i n the case of beam flanges, moment plates and boxing plates, two curves f o r the same applied moment have been p l o t -ted f o r each, one f o r the "outer" surface, and one f o r the "inner" surface. As a d e f i n i t i o n , the inner surfaces of the beam flanges face each other and have the beam web connecting i n t o them. In order to save space and time,selected stress curves for i n c r e a s i n g applied moment have been plotted on the same sheet. Also, i n the case of the beam flanges, moment plates and boxing p l a t e s , these curves f o r inner and outer surfaces have been pl o t t e d on the same sheet. The applied moment, corresponding to these p l o t t e d curves, has been indicated i n the accompanying written m a t e r i a l . Although two connections of each type were tested, only one set of stress curves has been plotted f o r each type. In determining the gauge layout f o r each t e s t specimen, consideration was given to both the type of f a i l u r e expected and a layout which would y i e l d the required s t r e s s d i s t r i b u t i o n s economically. Also, f o r s i m p l i c i t y , the l a y -out to be used was to be adaptable to a l l specimens, with minor modifications where required. For example, the case of a connection with/or without boxing plates. The layout adopted f i n a l l y f o r each connection has been shown diagram-m a t i c a l l y under "Gauge Layout." As mentioned e a r l i e r , to economize on the number of gauges used, one connection of the two i n each t e s t had s t r a i n gauges at a l l points where stre s s was required, and the second connection had check gauges at the most important points only. This system allowed a check on the measured s t r a i n v a l -ues. Since, i n the s t r a i n gauge layout diagrams, many s e c t i o n a l views are r e -quired to describe the layout completely, i n order to reduce t h i s number of 26 views on the beam and column webs, diagonal lines have been inscribed on those gauges which have a second gauge on the opposite side of the web. This diagonal line then, indicates that there is a gauge on both sides of the web at this position. As a final check on the resulting curves, the resisting moments developed under elastic conditions were calculated using a planimeter to measure the area beneath each curve set. These measured values were checked in two ways 1. applied moment » resisting moment 2. Z horizontal forces * 0 where in (2) the horizontal forces arise as tension and compression forces due to the application of moment to the connection. For a l l connections tested, these two checks were carried out on both beam and column sections for the plot-ted stress curves, and the results of these checks have been given in the "Calculations" at the end of each connection write-up. This check has been given regardless of whether stresses above yield stress ( 6y) exist in the individual sections of the connections, assuming a maximum stress of 6y is developed. This check can be carried out with very l i t t l e induced error due to neglecting the strain hardening stresses, as the increase in stress above the yield point is very small. From the given curves of stress distribution in the beam flanges, moment plates and column web, three factors have been calculated for elastic conditions: 1. "a" » stress magnification factor for stress peaks on outer surfaces of both beam flanges. 2. "D" - width of outer surface of beam flange across which this peak stress, over and above the theoretical linear stress, acts. 27 3. "P" » stress magnification f a c t o r f o r tension and compression stress peaks i n column web. Consider the values shown i n f i g u r e 16(a): n n „ Actual peak st r e s s at outer surface 6? /. >, T h e o r e t i c a l stress at outer surface * S<, These values of a are c a l c u l a t e d only f o r the outer surfaces of both beam flanges, since i t i s t h i s outer surface stress which i s used i n the design of s t e e l members. Also, " D " i s the width of beam flange across which the a c t u a l s t r e s s i s greater than the t h e o r e t i c a l value 60 at the outer surface. Since the more highly stressed s e c t i o n occurs over the centre as indicated i n f i g u r e ]6(a), then t h i s width D has been c a l c u l a t e d as w + Xk c c (2) where X - a dimensionless constant w = thickness of column web c k - flange thickness plus f i l l e t width of column, (shown i n f i g u r e 16(a)). The distance D has been calculated i n t h i s form ; as, without boxing p l a t e s , the web thickness of the column plus the width of the column flange containing the f i l l e t s e i t h e r side of the web, i s the strongest s e c t i o n against which the beam flanges have to bear. Consequently, t h i s stronger c e n t r a l section w i l l induce a peak stress value i n both tension and compression beam flanges, since the column flanges outside t h i s c e n t r a l region are r e l a t i v e l y f l e x i b l e and w i l l d e f l e c t under applied load. To follow p. 27 c £ 0 o 6 earn . T h e o r e t i c a l s t ress a c r o s s b e a m - s e c t i o n . Actual st ress pat tern ac ross outer eor^acz o f beam f l anaes . D = width of beam flange across which stress is greater than theoretical. T h e o r e t i c a l s t r e s s b e a m f l a n q e s . at o u t e r s u r f a c e A c t u a l pealc s t r e s s a t ou te r swr{aca, o f b e a m f l a n g e s . Fig. 16(a) : Actual and Theoretical Beam Flange Stress Distributions To follow p. 27 ^ / C o l u m n f lange Bear Flange. Theoretica 6 t ress Weut ral STRESS Pi,TTEeMS WlTWOUT MOMEUT P L ^T E S Column flange. Moment Tension moment y7' plate. t ; Plate. Theoretica "Stress kleuf ra l STE-ESS P^TTBEMS WITH MoMEkiT PLATES. 6 = Actual peak s t ress value. G, = Theoretical pealc stress value-. ?>k Y connecting F i g . I6b(l) Y Descr ip t ion . Depth of- beam. Thickness o f beam f lange, k -d i s tance o f column. Width o f column web. Width o f boxincj plate. Thickness o f boxing plate. tension moment plate. c o m p r n db ¥ t T 4- t c > boxing plate. « 2 F i g . I6b(ii) Symbol Notation Used 28 From f i g u r e 16(b): n f i t ) m Actual peak atresa i n column web m S T h e o r e t i c a l peak stress i n column web * G( where now the stresses shown are the average stresses i n the column web at the section considered. Here, i n order to s i m p l i f y c a l c u l a t i o n s , the t h e o r e t i c a l s t r e s s diagram has been assumed to have the t r i a n g u l a r shape shown, and also i s assumed symmetrical about the neutral axis shown. For the connections without moment plates t h i s n e u t r a l axis would be at the <^ of the beam, and the column web stress pattern would t r u l y be symmetrical about t h i s l i n e . For connection C, (with moment plate s , without boxing p l a t e s ) , t h i s assumed neutral axis i s i n the same p o s i t i o n as that i n d i c a t e d by the ac t u a l column web stress patterns given l a t e r . For connection D, (with moment plate s , with boxing p l a t e s ) , t h i s assumed p o s i t i o n of the neutral axis would be approximately 0.2" cl o s e r to the centre l i n e of the compression moment plate than that i n d i c a t e d by the stress diagrams given f o r the column web. Assuming that the peak stresses f o r the t h e o r e t i c a l stress d i s t r i b u -t i o n occur at the positions i n d i c a t e d i n f i g u r e l 6 b(i), the values of G, can be cal c u l a t e d d i r e c t l y by equating the a c t u a l applied connection moment to the value of the r e s i s t i n g moment given i n terms of S, as below. Connection A: Without moment plates and without boxing plates: ^ r d / • 9k •(<!„ • 2k c) Connection B: Without moment plates but with boxing plates: + 9 k c ( d b • 2k c) * 6 ^ * 3 ^ - t b ) M M - — 7 — 29 where for simplicity i t has been assumed that there i s a uniform stress of acting across the thickness tg of the boxing plates. Connection C: With moment plates and without boxing plates: £ JW w 1 c M = — — 2 Y 2 + 9k (Y + k ) c c where Y - J C ^ + t T • t Q ) Connection D: With moment plates, with boxing plates: 6 ,-w M - A 2 2 Y 2 • 9k (Y + k ) c c * 2 V B V Y - % where Y has the same value as given for connection C, and where again for simplicity, i t has been assumed that there is a uniform tensile stress of 6, acting across the thickness tg of the boxing plates. In a l l these forms given, M i s the value of the applied moment, and 6, the theoretical value of the peak stress in both tension and compression regions of the column web since the diagrams are assumed to be symmetrical, and also, since the thickness of the tension and compression boxing plates are the B a m e . The symbols used are as defined i n figure l 6 b ( i i ) . From these equations, 6,^  c a n ^ e calculated directly and the magnification factor {3 computed as £ is calculated from the strains measured during test. Values of a, P and X have been calculated for the stress peaks i n a l l connections. For comparison, the moment-rotation curves for each connection of the same type have been drawn on one sheet, assuming rotations to occur about 30 the centroid. Since the beams were connected in two ways, i.e. ( i ) beams welded directly to column flanges ( i i ) beams welded to column flanges using moment plates, then the position of the centroid would be different for both cases. In the f i r s t case above, the centroid was considered to be at the centre of the beam web, but i n the second case, as the moment plates had different thicknesses, the position of the centroid was calculated, and the results of this calculation have been shown in figure 23. From the fact that d i a l gauges were placed on both the tension and compression beam flanges or moment plates, and hence elongation of both these sections measured independently, then values of rota-tion were calculated for both tension and compression sections of the beam. These "half-beam rotation" values were compared to one another for the same applied moment, as a check, and the f i n a l beam rotation taken as the average of these two values. This half-beam rotation check showed almost identical results for the connections without moment plates but indicated a difference for those with moment plates. The average value of the two, however, was s t i l l regarded as the f i n a l value of the beam rotation in a l l cases. Finally, the resulting error for the planimeter check on the stress distributions drawn for reference was calculated in terms of: 1. Applied Moment - Resisting Moment m a Applied Moment 2. Horizontal Forces = - kips For ( l ) the "applied moment" is that actually applied by the turn-buckles, and the "resisting moment" is that measured by the planimeter moment check. For (2) the " ^ H o r i z o n t a l forces" is the algebraic sum of the compres-sive and tensile forces set up in the beam or column section as a direct result 31 of the applied moment. Considering t e n s i l e forces as p o s i t i v e and compressive forces as negative, according to the law of s t a t i c s t h i s sum should be zero, as there are no other h o r i z o n t a l forces acting on these sections. These errors can be a t t r i b u t e d to many f a c t o r s , some of which are: 1. assumed value of E, 2. allowable error i n gauge f a c t o r , 3. assumption of a l i n e a r s t r e s s v a r i a t i o n between inner and outer surface s t r e s s d i s t r i b u t i o n s , L. reproduction of str e s s d i s t r i b u t i o n s from given point values. From t h i s planimeter check also, values of r e s i s t i n g moment c a r r i e d by the beam flanges, moment plates and boxing plates i n the various connections, as a percentage of the t o t a l applied moment, have been given f o r reference i n the "Calculations" at the end of each section. In t h i s s e c t i o n also, under the sub-heading of "Web Crippling,"'' f o r connections without boxing p l a t e s , the percentage of the h o r i z o n t a l beam flange or moment plate force d i s t r i b u t e d i n t o a length of column web of (N + 2k ) has been c a l c u l a t e d , c where N «» thickness of beam flange or moment plates k = k-distance f o r column, c This percentage has been ca l c u l a t e d d i r e c t l y as: Horizo n t a l force l n beam flange (or moment plate) m & Horizontal force i n length (N+2k ) of column web " " c where the " h o r i z o n t a l force i n the length (N +2k ) of column web" i s ca l c u l a t e d c using the planimeter. S t e e l Construction Manual of the American I n s t i t u t e of  S t e e l Construction, 1957, p.298, sec.26(h). CoKlWECTlOKl A-l To follow p. 31 around t h a bnam w<zld , continuous th* sect ion. S E C T I O W A - A Column. &" & t 1 7 0 ^ &" at I&-5* b 6 * d 6" t 0 • 'bob" w L o-&2b t 32 CONNECTION A-l A. Description of Connection The beams were welded directly to the column flanges, using 1/4" f i l l e t welds, which were to have been continuous1 around the periphery of the beam sections. This, however, was not so. Gaps were left in the welding at the fi l l e t s between beam web and beam flange, as shown in figure 17. 2 / J / y / / / / / / / , Fig. 17 Gaps Left in Welding on Beam Web These weld discontinuities had an effect on the measured stress in the beam web, near the f i l l e t s , which is discussed later under "Discussion" of stress curves. 33 B. F a i l u r e Mechanism The two separate te s t s c a r r i e d out on t h i s connection both revealed the same f a i l u r e mechanism. At f a i l u r e both specimens showed excessive deforma-t i o n caused by a buckling of the column web i n the compression zone. A l l welds remained i n t a c t with no v i s i b l e sign of deformation. With the onset of t h i s column web buckling, h o r i z o n t a l r o t a t i o n of the beams about a v e r t i c a l axis be-came very evident. Because resistance to r o t a t i o n i n t h i s d i r e c t i o n i s small, and as there are no boxing plates i n the column section, a large h o r i z o n t a l beam r o t a t i o n was f i n a l l y r e a l i z e d i n both t e s t s . This h o r i z o n t a l beam r o t a t i o n was produced by the method of loading. C. Moment Rotation C h a r a c t e r i s t i c s ; Graph No. 3 In each of the two t e s t s c a r r i e d out measurements of r o t a t i o n on two separate beams were taken, and the r e s u l t s of these have been p l o t t e d separately i n graphs No. 3(a) and 3(b) f o r each t e s t . Each i n d i v i d u a l curve shown, therefore, represents the average r o t a t i o n at the connection of a s i n g l e beam. Since two separate t e s t s were c a r r i e d out, four curves have been plotted, two from each t e s t . D. D i s t r i b u t i o n of Stress a) - Gauge Layout: In order to obtain a complete st r e s s d i s t r i b u t i o n across a l l sections of t h i s connection, gauges were placed on the second specimen i n the positions shown i n f i g u r e 18. The f i r s t specimen tested had only a l i m i t e d number of gauges which were i n s u f f i c i e n t to give a complete set of the required stress d i s t r i b u t i o n s . To follow p. 33 To follow p. 33 To follow p. 33 _4_ 'ft in E 3 -EsJ-'i' rrrrt l' l" £ S 3 — 1 '8 ill 4 1» 4 fe C\\<LCV. beam C 3 k 5k> 3 k £ 3lc 5\L Eg! -Eg} -EM -EEJ-Tension flange. " 3 1 _ 4 I 1 1 1 fe Test Warn. i II 15 _4 -E3-^ E - C T I O S I D -D . F i g , 18 Gauge Layout f o r Connection A - l 34 The possible f a i l u r e s considered f o r t h i s connection i n r e l a t i o n to the s t r a i n gauge positions were: 1. Column web f a i l u r e i n compression zone. 2 . Weld f a i l u r e at beam tension flange (as f i l l e t welds were used). ' From the f i r s t t e s t on t h i s connection, since the moment-rotation curves were close up u n t i l the buckling f a i l u r e of the column web, i t was assumed that the st r e s s d i s t r i b u t i o n s across the two beam flanges were almost the same. From t h i s reasoning then, and the p o s s i b i l i t y of the weld f a i l u r e , the tension flange of the " t e s t beam" had f i v e gauges symmetrically placed on the outer sur-face and four at the inner surface, whereas the compression flange had only one gauge at the centre of the outer surface and two gauges on the inner surface close to the beam web. As a check,the "second beam" also had f i v e gauges on the outer surface of the tension flange and one on the outer surface of the compression flange. This was done i n case of a weld f a i l u r e i n the second beam. E a r l i e r , a c r i t e r i o n f o r column web f a i l u r e was given having a st r e s s d i s t r i b u t i o n at f a i l u r e extending over a length of column web of (d^ + 6 k c ) . In order that a stress d i s t r i b u t i o n could be measured over t h i s length as a check on t h i s value, gauges were placed on the column web as follows; one on e i t h e r side of the column web opposite the beam flanges, ( t h i s i s i n d i c a t e d by the diagonal l i n e s on these gauges), and at a spacing of 3 kc. e i t h e r side of these, on one side of the column web only. For the beam web, four gauges were placed on one side symmetrically about the c e n t r e - l i n e , and two gauges on the other side as i n d i c a t e d by the diagonal l i n e s on two of the gauges shown. The t o t a l number of gauges used i n t h i s t e s t was: 35 Beam section • 24 Column section = 12 T o t a l - 36 From t h i s gauge layout, stress d i s t r i b u t i o n s corresponding to load numbers 2, 4, 10 and 15, as shown i n the t a b l e of applied moments, have been plo t t e d , b) - Discussion: l 1. Tension Beam Flange - Graph No. 4 Both the inner and outer surfaces of the tension beam flange shows f a i r l y symmetrical curves of stress d i s t r i b u t i o n . Also, both surfaces i n d i c a t e a very d e f i n i t e c e n t r a l peak, even f o r small applied moments, i n d i c a t i n g the s t r e s s r e l i e f caused by the bending of the column flanges. To i n d i c a t e the e f f e c t of the h o r i z o n t a l beam r o t a t i o n , s t r e s s curves No. 4 have been drawn. Here,both the inner and outer surfaces of the flange show a one-sided d i s t o r t i o n caused by t h i s h o r i z o n t a l r o t a t i o n of the beam. I n i t i a l l y , t h e stresses at both surfaces are close,but with in c r e a s i n g applied moment the d i f f e r e n c e between them increases r a p i d l y at the centre where the stresses are high, and at the edges only a small change i s noticeable. 2. Beam Web - Graph No. 5 I n i t i a l l y , the curves are f a i r l y l i n e a r but f i n a l l y become very d i s -t o r t e d near the f i l l e t s . At the compression end of the web the s t r e s s values r i s e , t h e n begin to decrease with increasing moment, and at the tension end,the stresses remain very small. These low stress values are caused by the gaps i n the welding shown i n f i g u r e 17. Since the ends of the web are not welded at these points, t h e o r e t i c a l l y , where there i s no weld there w i l l be no f l e x u r a l stress induced by the applied moments. However, a s t r a i n would be i n d i c a t e d 36 due to l o c a l deformations set up by shear, and i t i s these values which have been recorded by the s t r a i n gauges i n these p o s i t i o n s . In drawing the curves i n the beam web then, the stresses i n these unwelded regions have been neglected and the curves approximated, assuming a s i m i l a r shape to those drawn f o r connec-t i o n A-2. 3. Column Web - Graph Nos. 6 ^ 7 These two graphs represent the induced s t r a i n s and corresponding stresses r e s p e c t i v e l y , i n the column web. Here, the build-up of s t r a i n i n the web opposite the beam flanges was so ra p i d that a s t r a i n diagram, as well as a stress diagram, has been drawn. Comparison of curve No. 5 with the c r i t e r i o n set forward by Beedle^ shows that p l a s t i c s t r e s s values e x i s t over a region a l i t t l e wider than (d^ + 6 k c ) , and i n p a r t i c u l a r , at (d^ + I2k c), the stress values are s t i l l approximately 50$ of y i e l d s t r e s s . Outside t h i s region however, they go to zero r a p i d l y as indic a t e d by the planimeter moment check. This comparison shows then that Beedle's assumption i s on the'safe sid e . c) - F a i l u r e Moment: Values of f a i l u r e moment were recorded f o r the two t e s t s c a r r i e d out and the values obtained are tabulated below: Specimen No. F a i l u r e Load (kips) F a i l u r e Moment (kip - i n s . ) 1 10.1 333 2 11.4 • 376 Beedle, " P l a s t i c Design of S t e e l Frames", p.177-178 Connection A - l  Table of Applied Moments 1 Load No. Applied Moment (k i p / i n s ) Remarks 0 0 1 0 Q-load 30 on column 2 50 P l o t t e d curve No. 1 3 69 4 116 ti it n 2 5 167 6 178 7 194 8 206 9 220 1 10 233 II II II g 11 246 12 260 13 276 14 282 15 290 n n II 4 16 303 17 317 18 326 19 376* Maximum moment Stress d i s t r i b u t i o n f o r maximum moment, load No.19, has been pl o t t e d f o r column web, as curve No. 5-To follow p. 37 Yield e lnze^ 5b / i n . 2>6 To follow p. 37 A - l ^Te&6S Dl6TElBL)TIC»Kl IKJ fe&AKA W&fe. Yield S t r e s s 56 W i 12. 24 : Compla' <Z\r<i<b<b in l ^ ' p / m ' z - Kl. fe. ?\o\Ydd points oots'ide the welded length" have been d isregarded. The numbers given to the<=>e points cor respond to the curve" numbers. Th<z. tension values be<gin to d e c r e a s e , as indicated by 4 being higher than 4-COKJKIECTIOM To.follow p. 37 6 E M > M K ! ° 7 -Yield S t r e s s 2>9 w:/n'Z Yield S t ress $ E > % 2 "Fa i lu re moment stress d is t r ibu t ion has been s h a d e d in o r d e r that a compar ison with ocedle's c r i t e r i on may be made visuaWu. 38 E. C a l c u l a t i o n s a) - Check on S t a t i c s : The r e s u l t s of the s t a t i c s check on both beam and column sections are tabulated below. Moment Check on Beam Section Curve No. Flange Moment Web Moment T o t a l Moment Applied Moment Er r o r % % Resisted by Flanges Tension Comp'n. 1 20.6 6.7 49.5 85 2 48.6 15.4 115.5 — 84 3 96.9 - 31.4 - 232.7 - 86 4 116.8 - 48.5 - 290.4 - 83 (Moments i n k i p - i n s . ) H o r i z o n t a l Force Check on Beam Section Curve No. Flange Force Web Force E Horiz. Forces. Tension Comp'n Tension Comp'n 1 + 4.6 _ + 1.9 - 1.2 _ 2 +10.2 - + 4.0 - 3.1 -3 +25.2 - + 7.8 - 6.7 -4 +30.3 - +12.0 -10.4 -(Forces i n kips.) Since there were not enough s t r a i n gauges on the compression beam flange to draw str e s s d i s t r i b u t i o n s f o r the inner and outer surfaces, the s t a t i c s check above has been l e f t incomplete. These values given above, however, i n d i -cate from both moment and hori z o n t a l force checks, that the average area beneath 39 the compression flange curve i s close, i f not equal,to that f o r the tension flange. In order to c a l c u l a t e the percentage of the applied moment r e s i s t e d by the beam flanges, the web moment was subtracted from the applied moment and t h i s value, as a percentage of the applied moment, was considered to be that r e s i s t e d by the flanges. Moment Check on Column Section Curve No. Calculated Moment Applied Moment % E r r o r 1 49.0 49.5 1.0 2 116.5 115.5 0.9 3 229.3 232.7 1.5 4 285.5 290.4 1.7 5 377.4 376.2 0 (Moments i n kip - i n s . ) Horizontal Force Check on Column Section Curve No. Web Tension Force Compression Z Horiz. Forces 1 • 6.4 - 6.4 0 2 +15.4 -15.3 0.1 3 +29.7 -30.0 ' 0.3 4 +31.8 -31.4 0.4 5 +50.7 -50.3 0.4 (Force i n kips.) I 40 Here the momenta and h o r i z o n t a l forces c o n t r i b u t i n g to s t a t i c a l equilibrium i n the column web have been tabulated f o r the p l o t t e d curves. The above values show only small errors for both checks, i n d i c a t i n g that the curves drawn approximate the true s t r e s s d i s t r i b u t i o n s very c l o s e l y . b) - M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses: Under conditions of e l a s t i c stress i n the beam or column sections, values of a and p, the magnification f a c t o r s , have been ca l c u l a t e d . "a" = Stress Mag&n Factor at Centre-Line of Beam Flanges Load No. 2 3 4 5 6 7 8 9 Tension Flange 2.0 2.0 2.0 2.0 2.0 2.1 2.1 2.1 a Comp'n Flange 0.8 0.9 1.2 1.4 1.4 1.5 1.5 1.5 "g" » Stress Mag'n Factor f o r Column Web Peak Stresses Load No. 2 3 4 0 Tension 0.9 1-3 1.4 Comp'n 0.9 0.9 0.9 From the previous s t a t i c a l check on the beam i t was deduced that f o r the same applied moment, the average area beneath the compression flange stress curves was greater than that beneath the tension flange curves. This point, to-gether with the above values of a, lead to the conclusion that the peak stresses are more c e n t r a l l y l o c a l i z e d i n the tension beam flange than i n the compression beam flange. S i m i l a r l y , f o r the column web the peak stresses i n the tension 41 region are more l o c a l i z e d than those i n the compression region f o r the same applied moment. This e f f e c t i s very noticeable i n the given stress curves f o r the column web. For the tension beam flange, the width "D" has been c a l c u l a t e d f o r a l l stress curves from which the values of a have been taken. X-values From "D" = (w + Xk ) Load No. 2 3 4 5 6 7 8 9 Tension Flange 4.2 4.4 4.6 5.1 5.4 5.8 5.9 6.0 X Comp'n Flange - - - - - - - -Here, since there was only one gauge on the compression flange, values of X could not be ca l c u l a t e d f o r t h i s flange. c) - F a i l u r e Moment i n Column Web: 7 Considering Beedle's c r i t e r i o n f o r column web f a i l u r e , as given e a r l i e r , and using the assumed value of y i e l d s t r e s s of 35 k / i n . , the t h e o r e t i c a l f a i l u r e moment i s Mp - 273 k i p - i n s . F a i l u r e moment i n the tests were: Test No. 1 = 333 k i p - i n s . Test No. 2 = 376 k i p - i n s . I t would seem,then,that Beedle's assumption i s on the safe s i d e . 7 Ibid.p.177-178 42 This f a c t i s emphasized when i t i s remembered that the measured f a i l u r e moments i n t e s t were considered to be influenced by r o t a t i o n of the beam about a v e r t i c a l a x i s. For t h i s reason, these test moments are regarded as being lower than the actua l value f o r a beam re s t r a i n e d from t h i s sideways motion, which i s more the p r a c t i c a l case when a beam frames into a column at both ends of i t s span. d) - Web C r i p p l i n g : According to the American I n s t i t u t e of S t e e l Construction s p e c i f i -cations, the compressive stress at the web toe of the f i l l e t s i n the column, r e s u l t i n g from i n t e r i o r loads not supported by bearing s t i f f n e s s s h a l l be: wdn i> 2/-° k/in-2 c ' where R • concentrated i n t e r i o r load i n kips, t » web thickness i n inches, N = bearing length i n inches, k = k-distance f o r column section, c This formula allows the load to be d i s t r i b u t e d into a length of the column web of (N + 2k ), where N i n t h i s case i s the thickness of the beam c flange. C a l c u l a t i o n s show that while e l a s t i c conditions e x i s t i n the column web, only approximately 50% of R i s d i s t r i b u t e d into t h i s length of web. The values obtained by measurement are % of Applied Load D i s t r i b u t e d Into (N+2k ) Load No. 2 3 4 % 50% 55% 56% U3 With higher applied moments p l a s t i c stresses are induced, and the above percentage reduces when these s t r a i n hardening stresses are neglected. A -2 . To follow p. 43 single butt welds across all be<am f langes. 4 f i l let welds, both sides of beam web. SECTION A - A . beam Column. ^Secfion &" YvJr at 170^ fe' W1- a t 15 b ^ b G" d t o-Soft" w 0.24" o.l4l L o-Q>V? 11 0 hQ>% 44 CONNECTION A-2 A. Description of Connection The beams were welded d i r e c t l y to the column flanges with 1/4" sing l e butt welds across a l l beam flanges. For shear re s i s t a n c e , two 6" runs of 1/4" f i l l e t weld, one on e i t h e r side of the beam web were used to connect the beam web to the column flange. B. F a i l u r e Mechanism One t e s t only was c a r r i e d out on t h i s connection g i v i n g the same type of column web f a i l u r e as was the case f o r connection A - l . At f a i l u r e , the buckled column web allowed excessive v e r t i c a l beam r o t a t i o n and once again, due to lack of r i g i d i t y against r o t a t i o n about a v e r t i c a l axis, h o r i z o n t a l r o t a t i o n of the beam accompanied t h i s . C. Moment-Rotation C h a r a c t e r i s t i c s : Graph No.8 Values of r o t a t i o n were taken from the two beams i n the s i n g l e t e s t c a r r i e d out, and. from these r e s u l t s , two curves have been pl o t t e d . Each curve shown therefore represents the r o t a t i o n of a si n g l e beam. D. D i s t r i b u t i o n of Stress a) - Gauge Layout: 'The p o s i t i o n i n g of the gauges on t h i s connection has been indi c a t e d i n f i g u r e 19. Since connection A - l f a i l e d by a buckling of the column web, and also, since the welds holding the beam flanges to the column section i n A-2 were more s u b s t a n t i a l than those f o r A - l , the only f a i l u r e mode considered po s s i b l e To follow p. 44 To follow p. 4 4 f 4 i 1 - E g g — 4 6 Chec-lc beam. 3 It 5k> 5k4 3 k 41c Sic j§|g-^ E r C T I O K ) b-b. -isl--Hi -EM--m - ® § --m 1*3 Teneion flange. I  >4 i I  •5 '8 J J 4 i I Test beam. i II Comp" flange. D 6E-CTIC»M C-C. 6 " 2| 2& G&OTIOKJ D-D. F i g . 19 Gauge Layout f o r Connection A-2 45 f o r A-2, was that of column web c r i p p l i n g i n the compression region. Gauges were placed on the column web section then, i n exactly the same pattern as was the case f o r connection A - l . Two gauges were placed opposite each beam flange, one on e i t h e r side of the column web, and the r e s t on one side of the web only at a spacing of 3 k c centre to centre, from those opposite the beam flanges. For the beam section, f i v e gauges were speaced symmetrically across the outer surface and four across the inner surface of the tension flange,as shown i n the f i g u r e . For the compression flange, one gauge only was placed i n a c e n t r a l p o s i t i o n on the outer surface and two only on the inner surface as shown. F i n a l l y , f o r the beam web, four gauges were placed on one side, and two more on the second side, as indicated by the diagonal l i n e s drawn on two of the gauges i n the layout diagram. The second beam i n the connection did not have gauges attached to i t , a s r e s u l t s produced by these check gauges on the second beam of connection A - l indi c a t e d values very close to those recorded from gauges i on the t e s t beam f o r the same connection. The t o t a l number of gauges used f o r the t e s t was: Beam s e c t i o n = 18 Column section » 12 T o t a l - 30 From t h i s gauge layout stress d i s t r i b u t i o n s corresponding to load numbers 2, 4, 6 and 10, as shown i n the table of applied moments, have been plotted. b) - Discussion: 1. Tension Beam Flange - Graph No. 9 The shape of these curves i s very s i m i l a r to those shown f o r connection 46 A - l , but here the d i s t o r t i o n i s not as great. Horizontal r o t a t i o n of the beam during t h i s t e s t was reduced considerably as compared to the t e s t s on A - l , and t h i s seems to have reduced t h i s d i s t o r t i o n . I t should be noticed that the cen-t r a l peak str e s s i s s t i l l a predominant feature of these curves. 2. Beam Web - Graph No. 10 Since the t o t a l height of the beam web was not welded to the column, the imposed f l e x u r a l stresses due to the applied moments, would be developed with-i n t h i s welded length only. The shape of the curves f o r t h i s connection are more symmetrical than those i n d i c a t e d f o r connection A - l . Here, the areas be-neath tension and compression loop are very nearly equal, a f a c t which points toward equally stressed beam flanges. 3. Column Web - Graph No. 11 As was the case f o r connection A - l , so here too, peak stress values e x i s t i n the column web opposite the beam flanges. These st r e s s peaks r e a l i z e p l a s t i c values very r a p i d l y . Here again, as f o r A - l , the width of column web highly stressed opposite the tension beam flange, i s much less than that opposite the compression beam flange. As a r e s u l t of t h i s , f o r the same applied moment, the peak stress values opposite the tension beam flange are higher than those opposite the compression beam flange. c) - F a i l u r e Moment: The values of f a i l u r e load, and f a i l u r e moment recorded f o r t h i s t e s t are tabulated below. F a i l u r e Load (kips.) F a i l u r e Moment (kip - i n s . ) 11.7 386.0 Table of Applied Moments Load No. Applied Moment Remarks 0 0 1 0 Q-load 30 oh column 2 24 P l o t t e d curve No. 1 3 69 4 103 it ti " 2 5 139 6 175 II n « 3 7 206 8 244 9 271 10 311 .. II .1 ^ 11 342 12 369 13 386 Maximum moment To follow p. hi CoMKi&CTlOKl A-2. To follow p. hi ' o T e E ' S . ' S . D \ e T e i b u T ) o k \ m &EA.KA WEB. ?ea\t 6>Ws><=> \Ja\o£<b are more. \occ\\c3&& in tension reg ion than in comp" rayon. 48 E. C a l c u l a t i o n s a) - Check on S t a t i c s : The r e s u l t s of the s t a t i c s check on both beam and column sections are tabulated below. Moment Check on Beam Section Curve No. Flange Moment Web Moment T o t a l Moment Applied Moment E r r o r % % Resisted by Flanges Tension Comp'n. 1 11.1 _ 2.5 24-0 _ 90 2 48.1 _ 9.2 — 103.0 - 92 3 78.3 - 15.7 - 175.0 - 91 4 133.8 - 24.9 - 311.0 - 92 (Moments i n k i p - i n s . ) h o r i z o n t a l Force Check on Beam Section Curve No. Flange Force Web Force £ Horiz. Forces. Tension Comp'n. Tension Comp'n 1 + 2.9 +0.6 -0.8 2 +12.5 - +2.3 -2.8 -3 +20.4 - +4.7 -3.9 -4 +34.7 - +7.6 -6.2 -(Forces i n kips.) As f o r connection A - l , there were i n s u f f i c i e n t gauges on the com-pression beam flange to draw stress d i s t r i b u t i o n s f o r the inner and outer sur-faces, hence the statics check above i s once again incomplete. Using the above 49 r e s u l t s , however, both checks i n d i c a t e that the average area beneath compression flange curves i s close, i f not equal, to that f o r the tension flange curves. Once again,in c a l c u l a t i n g the percentage of the applied moment r e s i s t e d by the beam flanges, the beam web moment was subtracted from the applied moment, and t h i s value, as a percentage of the applied moment, considered to be that r e s i s t e d by the beam flanges. Moment Check on Column Section Curve No. Calculated Moment Applied Moment % E r r o r 1 24.4 24.0 2 2 103.0 103.0 0 3 174.5 175.0 0.3 4 306.5 311.0 1.5 (Moments i n ki p - i n s . ) Horizontal Force Check on Column Section Curve No. Web Force E Horiz, Forces Tension Comp'n. 1 + 3.1 - 3.3 0.2 2 +13-3 -13.5 0.2 3 +22.2 -23.1 0.9 4 +39.6 -39.9 0.3 (Force i n kips.) 50 The errors indicated f o r t h i s connection, i n the above s t a t i c a l check, are s l i g h t l y higher than those given i n the same check f o r connection A - l . However, they are s t i l l s m a l l , i n d i c a t i n g that the curves drawn approximate c l o s e l y the true stress d i s t r i b u t i o n s . b) - M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses: For those stress curves which l i e wholly within the e l a s t i c range of the beam and column sections, values of a and \3, the magnification f a c t o r s , have been c a l c u l a t e d . "a" - Stress Mag'n Factor at Centre-Line of Beam Flanges Load No. 2 3 4 5 6 Tension Flange 2.1 2.1 2.5 2.6 2.6 a Comp'n. Flange 1.4 1.7 1.9 1.9 2.1 "g" - Stress Mag'n Factor f o r Column Web Peak Stresses Load No. 2 3 4 5 Tension 0.8 1.0 1.1 1.2 Comp'n 0.7 0.8 1,0 1.0 Once again, as f o r connection A - l , i t can be concluded that since the average area beneath the beam flange stress curves i s almost the same, f o r the same applied moment, then the peak stress values i n the beam flanges are more l o c a l i z e d i n the tension flange than i n the compression flange. These peak stress values i n the column web are also more l o c a l i z e d i n the tension region 51 than i n the compression region as indic a t e d by the values of p. For the tension beam flange, the width D has been c a l c u l a t e d f o r a l l s tress curves from which a-values have been obtained. X-values From "D" - (w + Xk ) _ c c l Load No. 2 3 4 5 6 X Tension Flange 2.3 3.4 4.1 4.4 4.9 Comp'n Flange - - - - -Comparison of the above values of a and D, with those c a l c u l a t e d for connection A - l , in d i c a t e s an increase i n a, and a decrease i n X. A point which may have influenced t h i s d i f f e r e n c e i s the amount of welding on the beam , web. In connection A - l , apart from the weld d i s c o n t i n u i t i e s mentioned, the t o t a l height of the web was operative i n r e s i s t i n g the app l i e d moment. Under these conditions approximately 84$ of the applied moment was r e s i s t e d by the beam flanges. In connection A-2 the beam web had only 6" of weld along i t s length, thus reducing the moment c a r r i e d by t h i s s ection (compare values i n moment check f o r A - l and A-2).- This automatically increases the percentage moment r e s i s t e d by the beam flanges, and hence i n A-2 approximately 91$ of the applied moment i s . r e s i s t e d by the beam flanges. This 7% increase i n moment r e s i s t e d by the beam flanges, i t seems, has influenced the values of a and D as indic a t e d pre-v i o u s l y . c) - F a i l u r e Moment i n Column Web: Once again, comparing the f a i l u r e moment developed i n test to that 52 given by Beedle shows: 1. F a i l u r e moment from t e s t = 386 k i p - i n s . 2. Beedle's f a i l u r e moment - 273 k i p - i n s . a comparison which again i n d i c a t e s that Beedle"s assumption i s on the safe s i d e . d) - Web C r i p p l i n g : From the American I n s t i t u t e of S t e e l Construction s p e c i f i c a t i o n on i n t e r i o r loads not supported by bearing s t i f f e n e r s , the following values are those c a l c u l a t e d f o r connection A-2, as the percentage of the applied load d i s -t r i b u t e d into the length of the column web (N + 2k ), where again, N i s the c thickness of the beam flange. % of Load D i s t r i b u t e d Into (N + 2k ) c Load No. 2 3 k % 63 62 60 The values ind i c a t e d here are higher than those i n d i c a t e d f o r connection A - l . Beedle, " P l a s t i c Design of S t e e l Frames", p.177-178 To follow p. 52 CoKlWECTtOW fe. \ single butt- welds across all beam ^ \ar\c^H6. 3 f i l le t welds both sides of beam web. 3 f i l let weld sides on a 6 both boxing S E C T I O M A - A beam. Co\v<V\r\. Section &" at V\Fr at \bh * b d G" t 0 • w L O • b<bo" lc w 53 CONNECTION B A. D e s c r i p t i o n of Connection The beams were welded d i r e c t l y to the column flanges using 1/4" s i n g l e butt welds across a l l beam flanges. On each beam web there were two 6" runs of 1/4" f i l l e t weld, one on e i t h e r side of the web and symmetrically placed with respect to the ce n t r e - l i n e of the web. In the column s e c t i o n , opposite the beam flanges, there were 3/8" t h i c k boxing plates welded into p o s i t i o n with 1/4" f i l l e t welds. This welding was continuous around the edges of the boxing plates, and i n p a r t i c u l a r , these welds were placed on both sides of each boxing pl a t e . One defect which had a d e f i n i t e e f f e c t on the measured stresses was the p o s i t i o n i n g of these boxing pl a t e s . Tension hoxmq plates. G Tension beam f lange . F i g . 20 Displacement of Tension Boxing Plates  With Respect to Tension Beam Flange For the " t e s t beam", the cent r e - l i n e s of the compression beam flange and compression boxing plates were i n l i n e , but the cent r e - l i n e s of the tension boxing plates and tension beam flange were as shown i n f i g u r e 20. The gap G 5k shown i n t h i s f i g u r e was 3/16" for one side and 1/A" f o r the other, (these values have been indi c a t e d with respect to the str e s s curves on the s t r e s s d i s t r i b u t i o n s f o r the tension beam flange and tension boxing p l a t e s ) . The e f -fec t of t h i s gap G would be to induce somewhat higher stresses at the inner surface of the tension beam flange and the outer surfaces of the tension boxing plates. B. F a i l u r e Mechanism One t e s t only was c a r r i e d out on t h i s connection type, with stress and r o t a t i o n measurements being measured from the two beams on the specimen. The f a i l u r e was i n the beam at the tension flange with one beam f a i l i n g before the other. However, p r i o r to f a i l u r e , both beams showed excessive creep under l o a d , i n d i c a t i n g that f a i l u r e conditions were near f o r both. At the onset of f a i l u r e the tension flange of the second beam began to tear away from the butt weld holding i t to the column flange, i . e . t h i s was not a weld f a i l u r e but a te a r i n g of the parent metal of the beam flange at the weld. This separation was i n i t i a t e d i n the centre of the tension beam flange where the str e s s peak e x i s t s . Although the beam could s t i l l withstand applied moment, t h i s point was considered as f a i l u r e since the most highly stressed section of the butt weld was now inoperative. S l i g h t h o r i z o n t a l r o t a t i o n of the beams was noticeable at f a i l u r e but not to the extent of that i n connections A - l and A-2. Evidence of t h i s r o t a t i o n was indic a t e d by a buckled form on one side only of the compression flange of the beam. 55 C. Moment-Rotation C h a r a c t e r i s t i c s : Graph No. 12 For both the beams tested, values of beam r o t a t i o n were measured and curves of applied moment against connection r o t a t i o n have been plotted. Comparison of these curves with those f o r A - l and A-2 ind i c a t e s a d e f i n i t e increase i n r i g i d i t y due to the addi t i o n of the boxing plates to the column section. Indeed, the f a i l u r e moment has been increased by a f a c t o r of 2„5 approximately. D. D i s t r i b u t i o n of Stress a) - Gauge Layout: Figure 21 ind i c a t e s the p o s i t i o n i n g of a l l s t r a i n gauges f o r stress measurement i n connection B. The two f a i l u r e s considered i n r e l a t i o n to gauge placement were: 1. Beam F a i l u r e 2. Weld F a i l u r e ( i ) at beam tension flanges, ( i i ) at boxing plate / column flange f i l l e t welds. Since from connections A - l and A-2 i t was concluded that the stress d i s t r i b u t i o n s across tension and compression flanges of the same beam were not i d e n t i c a l , both flanges of the t e s t beam had f i v e gauges placed on the outer surface and four gauges at the inner surface as shown. Also, the t e s t beam web had four gauges on one side symmetrically placed and two gauges on the other side, as indicated by the diagonal l i n e s on two of the gauges on t h i s section. For the column web, gauges were placed as close as possible to both sides of both boxing plates as none could be placed d i r e c t l y opposite the beam flanges To follow p. 55 °>oo 2o 4o £>o Anqle chcinqe in R . a d i a n 6 x Io .' To follow p. 55 if 4 ^6 2 S %/4 -pa-4 i II 4 & C T I O M '8 i l 4 A-A. Check, beam 5k V -1 16 V 3L ?4 V4 V 4 ! 24 -g|3 ,ill V 74 -fgt Tension f lange. i 1 i " fe 'V' 1 Tesr beam. 1 ii >4 C Comp™ flange.. F l g . 21 4>ecn<2U C - C Gauge Layout f o r Connection B in 4 <SE-<:TIO>LI D-D. ill 4 gsa—1 f—• 1 1*' t ..L/i l" m I1 - H — '8 i« 4 56 as i n A - l and A-2. E x t e r n a l l y to the boxing plates, a gauge was placed at a d i s -tance of 3 k c from the centre l i n e of both beam flanges, the object of these being to compare st r e s s values at these points with those i n d i c a t e d i n the same po s i t i o n from connections A - l and A-2. Inside the boxing p l a t e s , gauges were spaced 2" from those d i r e c t l y opposite the boxing plates. Diagonal l i n e s have been drawn on gauges which have a check gauge on the opposite side of the column web. For the boxing plates, as higher stresses were expected on the outer sur-face of the tension boxing plates, four gauges were placed on the outer surfaces and two on the inner surfaces of both tension and compression sets as shown. On the second beam, three gauges were placed on the outer surface of both tension and compression flanges as a check on the values indicated by the gauges on the t e s t beam. The t o t a l number of gauges used i n t h i s t e s t were: Beam sections • 30 Column sections = 12 Boxing plates - 12 T o t a l = 54 From t h i s gauge layout, stress d i s t r i b u t i o n s corresponding to load numbers 2, 4, 6 and 10,as indicated i n the table of applied moments, have been drawn. b) - Discussion: 1. Beam Flanges: Graphs No. 13 § 14 The compression flange shows very good symmetry, while the tension flange, due to t h e welded p o s i t i o n of the boxing plates at t h i s point, indicates a higher stress on one side. This feature was mentioned e a r l i e r . I n i t i a l l y , 57 i the s t r e s s d i s t r i b u t i o n s are f a i r l y l i n e a r , agreeing with the e l a s t i c theory, but very r a p i d l y stress concentrations begin to appear at the centre and both edges of both flanges. For the same applied moment the measured stress values are higher i n the compression flange than i n the tension flange, and i t i s thought that the welded p o s i t i o n of the boxing plates has a f f e c t e d the tension flange stresses, producing these lower values. The values i n d i c a t e d by the compression flange are considered here to be more correct, 2. Beam Web: Graph No. 15 Stresses i n the beam web are i n i t i a l l y l i n e a r , as i n the case of connections A. The tension side has a la r g e r enclosed area than the compression side, and t h i s i s once again a t t r i b u t e d to the welded p o s i t i o n of the boxing plates opposite the tension flange. As f o r connections A, the stress d i s t r i b u -t ions i n the beam web have been drawn only f o r the welded length of beam web. 3. Column Web; Graph No. 16 Again, as i n connections A, the column web indicates high stress concentrations opposite both beam flanges. Due to the presence of the boxing plates however, these peak stresses are smaller i n connection B. There i s a rap i d decrease i n stress outside the region of the boxing plates and, i n par-t i c u l a r , at a distance of 3 k c outside the boxing plates, the stress i s v i r t u a l l y zero. Without these boxing plates, as indicated i n connections A, stresses at t h i s point would have reached y i e l d value. k. Boxing Plates: Graphs No. 17 e 18 Stress d i s t r i b u t i o n across both boxing plates i s s i m i l a r to that i n the beam flanges. Both inner and outer surface curves show d i s t o r t e d forms i n d i c a t i n g high edge stresses on opposite edges. This a r i s e s from the tendency See "Conclusions" 58 of the beams to rotate about a v e r t i c a l axis when the moments are applied. This h o r i z o n t a l beam r o t a t i o n i s r e s i s t e d d i r e c t l y by the boxing plates, and due to t h i s , very d i s t o r t e d stress patterns could be expected f o r both surfaces of the boxing pla t e s . c) - F a i l u r e Moment: The values of f a i l u r e load and f a i l u r e moment recorded f o r t h i s t e s t are: F a i l u r e Load (kips) F a i l u r e Moment (ki p - i n s . ) 27.8 917.4 Table of Applied Moments Load No. Applied Moment Remarks 0 0 1 0 Q-load 3 0 on column 2 33 P l o t t e d Curve No. 1 3 66 4 99 it II ti 2 5 1 3 2 6 165 » II II ^ 7 198 8 2 6 4 9 296 10 3 3 0 it ti .. u 11 396 12 465 13 548 14 640 15 683 1 6 726 17 766 18 812 19 917 Maximum moment CoMM&CTIOkl b. T° f 0 l l ° W P* 5 9 Cel. f lange.-^ T<Z-n<=>i<pn boxing plahz-. Col, w<zb-ocam web. T < t n 6 i o n beam' flangt. GEAPH NJ° IS. O — Ouhzr *>vrfac<z,. fa — Inner -surface. To follow p. 59 COMKI&CTIOKJ b. ^>TZZ<Z><b D ) 6 T E.I& U T I O r 4 IKi COM PENSION FlAUGfc. Ge.APu. M° 14. C O U M E C T I O M h. T o f o l l o w P* 5 9 Overall stress di-sh-'ibuHon reduced as compared Vo a n d A -7. To follow p. 59 To follow p. 59 b, T&Ki6\OKl fetfXlUG PLATE'S. ( D o l i n g plaV<z<=, opposite h t r v & i o n flange.) 6 ^ A P U w ° \y. CoKikJECTIOM &>. To follow p. 59 ( &ox\ncj . p la tee o p p o s e cotnp" b e a m f l a n g e ) Yield tree's! 3& GIZAPW M" 16. Higher stress values tin*, side {' are I probably due to beam r o t a t i o n . ^ Pealc valuer fo r both ii •surface-'*. taken f rom graph no. So a-60 E. Calculations a) - Check on S t a t i c s : The r e s u l t s of the s t a t i c s check on both beam and column sections are tabulated below. Moment Check on Beam Section Curve No. Flange Moment Web Moment T o t a l Moment Applied Moment Error % % Resisted by Flanges Tension Comp'n 1 14.7 14.9 2.9 32.5 33 1.-5 91 2 43.7 45.6 9.3 98.6 99 0.4 90 3 71.3 74.9 16.5 162.7 165 1.3 91 4 139.4 147.7 38.5 325.6 330.0 1.3 89 (Moments i n kip - i n s . ) Horizontal Force Check on Beam Section Curve No. Flange Force Web Force Z Horiz. Forces Tension Comp'n Tension Gomp1n 1 + 3.8 - 3.8 + 0.5 -0.6 0.1 2 +11.3 -11.8 + 2.0 -1,4 0.1 3 +18.3 -19.2 + 3.8 -2.6 0-3 4 +36.2 -38.3 +10.8 -7.2 1.5 (Forces i n kips.) The above two checks on the beam section i n d i c a t e that the tension and compression beam flanges have s i m i l a r average areas beneath the s t r e s s curves f o r inner and outer surfaces. Also here, as i n the case of connection A-2, only 6" of the beam web was welded to the column flange, and, i n both cases, the beam 61 flanges r e s i s t approximately 91$ of the applied moment. Moment Check on Column Section Curve Boxing Plate Moment Web T o t a l Applied E r r o r % Resisted No. Tension Comp'n Moment Moment Moment % by 3. PI. 1 13.4 9.5 9.8 32.7 33.0 1.0 70 2 40.8 35.4 25.6 101.8 99.0 3.0 74 3 49.6 60.8 56.0 166.4 165.0 0.8 70 4 108.0 120.7 109.0 337.7 330.0 2.3 69 (Moments i n ki p - i n s . ) Horizontal Force Check on Column Section Curve No. Boxing Plate Force Web Force £ Horiz. Forces Tension Comp'n Tension Comp'n 1 + 3.6 - 2.5 + 0.6 - 1.9 -0.2 2 +10.9 - 9.5 + 2.7 - 3.7 +0.4 3 +13.2 -16.3 + 8.4 - 4.9 +C.2 4 +28.9 -32.2 +15.0 -11.3 +0.4 (Forces i n kips.) From the moment check on the column s e c t i o n i t can be seen that, since the boxing plates r e s i s t approximately 2/3 of the applied moment, then the stress peaks i n the column web would be gr e a t l y reduced i n magnitude, as i s shown on the stress d i s t r i b u t i o n s f o r the column web. 62 b) - Modificat ion of T h e o r e t i c a l E l a s t i c Stresses: Using the stress d i s t r i b u t i o n s from moments that produce wholly e l a s t i c stresses i n the beam or column s e c t i o n , the following magnification factors were calc u l a t e d . a.. = Stress Mag'n Factor at Centre-Line of Beam Flanges Load No. 2 3 4 5 6 7 8 a l Tension 1.2 1.2 1.3 1.3 1.3 1.3 1.3 Comp'n 1.1 1.2 1.5 1.5 1.3 1.3 1.3 a0 • Stress Mag'n Factor at Edges of Flanges Load No. 2 3 4 5 6 7 8 Q2 Tension 0.7 0.9 0.9 0.9 0.9 0.9 0.9 Comp'n 1.1 1.2 1.2 1.3 1.3 1.4 1.4 Values of a here have been tabulated f o r the str e s s peaks i n both beam flanges at the centre l i n e ( a ^ ) , and also at the edges of the flanges C 0 ^ * The values i n d i c a t e d above f o r are average values takem from the two edges of the tension or compression flange. These values of ca l c u l a t e d above show that with the higher a p p l i e d moments the str e s s at the edges becomes greater than that at the centre of the compression flange, but i t i s f e l t that d i s t o r t i o n s due to hori z o n t a l beam r o t a t i o n has caused t h i s . Values of and a^, c a l c u l a -ted f o r the check beam, agree very w e l l with those tabulated above. 63 g - Stress Mag'n Factor For Column Web: Stress Peaks Load No. 2 3 4 5 6 7 8 9 10 P Tension 0.7 1.3 1.3 1.5 1.6 1.4 1.3 1.3 1.3 Comp'n 1.5 1.4 1.3 1.3 1.3 1.2 1.2 1.3 1.2 These tabulated values of \3 are only approximate since the curves of stress opposite the beam flanges could be drawn i n only with the use of the planimeter moment check. Due to the presence of the boxing plates no gauges could be placed opposite the beam flanges i n order that an accurate s t r e s s measurement be made. Values f o r the width D have been c a l c u l a t e d f o r both tension and compression flanges of the t e s t beam and the values of X corresponding to these are tabulated below. X-values From D « (w +Xk ) c c Load No. 2 3 4 5 6 7 8 X Tension 2.4 2.4 2.6 2.3 2.2 2.1 2.1 Comp'n To1 t a i out< sr surfa 1 ice stre ssed at M sove T: 1 Z i Here, the str e s s at the outer surface of the tension flange shows a peak, which alone, i s greater than the act u a l design s t r e s s , whereas with the compression flange the stress across the t o t a l outer surface i s greater than the a c t u a l design s t r e s s . The stress value at the two minimum points on e i t h e r side mf the c e n t r a l peak stress f o r the compression flange, however, are equal 64 i n magnitude to the act u a l design s t r e s s . ' Once again, these factors i n d i c a t e a more l o c a l i z e d stress i n the ce n t r a l region of the tension flange, although the welded p o s i t i o n of the boxing plates may have a f f e c t e d the values. CoKIKJE-CTlOkl C To follow p. 64 4 WUt weld connecting plate to beam web. •2 x il w ^onnecrmg plate. Beam. Column. Secfion g>" * t 1 7 0 ^ G>11 at \bb^ b G" d 6" J t O • IG?" w O • 24 O • 2 4 : • It II 0 • Q>lb O • b'b'b 7-7 65 CONNECTION C A. Description of Connection The beams were welded to the column flanges through the moment plates of the shape shown i n the i n i t i a l diagram. Clearance of g" was l e f t between the beam and column sections. The tension moment plates were welded to the column flanges with 5/16" s i n g l e butt welds, and to the beam tension flanges with 12|" of 1/4" f i l l e t weld. The compression moment plates were connected to the column flanges with 1/4" f i l l e t welds on both sides of the moment pla t e , and to the beam compression flanges with two 5^ " lengths of 1/4" f i l l e t weld, one at each edge of the moment plate. The web connecting plates were welded to the column flanges with 3/16" f i l l e t welds on both sides of t h i s plate, and to the beam web with 1/4" f i l l e t weld around the edge as shown. I t should be noted here that there was only one web connecting plate to each beam. B. F a i l u r e Mechanism One t e s t only was c a r r i e d out on t h i s connection, and i n t h i s s i n g l e t e s t only one beam had s t r a i n gauges on i t i n order to measure the induced s t r e s -ses. This was so as t h i s t e s t was not o r i g i n a l l y planned, and only a l i m i t e d number of s t r a i n gauges were a v a i l a b l e f o r the t e s t . F a i l u r e moment induced the same type of column web buckling i n the compression zone as exhibited by connections A. The value of the f a i l u r e moment however, was higher than those given f o r connections A. C. Moment Rotation C h a r a c t e r i s t i c s : Graph No. 19 Rotation values were recorded from beams i n the sing l e t e s t c a r r i e d 66 out, but due to the d i f f e r e n t thicknesses of the moment plates, i n order to c a l c u l a t e the a c t u a l beam r o t a t i o n , r o t a t i o n was assumed to take place about the centre of g r a v i t y of the cross s e c t i o n . Figure 23 shows the position of t h i s centre of g r a v i t y with respect to both moment plates. The beam rotations as calculated from the values indicated on the d i a l gauges on the tension and compression moment plates, d i d not agree as w e l l as i n the previous connections. This i n d i c a t e s that the centre of r o t a t i o n was not a c t u a l l y at the centre of g r a v i t y c a l c u l a t e d . However, f o r each applied moment, the average value of these two was used to p l o t the r e s u l t i n g curves. D. D i s t r i b u t i o n of Stress a) - Gauge Layout: Figure 22 represents the gauge layout used f o r measurement of stress i n t h i s t e s t . The only f a i l u r e considered possible, i n the l i g h t of previous t e s t s , was that of column web buckling i n the compression region. The outer surfaces of both moment plates had f i v e gauges symmetrically placed across them, but since the inner surfaces of both moment plates were concealed by the beam flanges, no gauges were placed on these surfaces. Also, as there were no boxing plates i n the column sect i o n , i t was considered that at the welds connecting both moment plates to column flange, the outer surface of each moment plate would be more h i g h l y stressed than the inner surface, a point which was shown to be true by the s t a t i c a l check. In order to measure stresses i n the connecting plate, tjwo gauges were placed on the plate, and two more on one side only of the beam web, and i n t h i s way i t was hoped to be able to approximate the stresses i n the connecting plate. For the column web, the same gauge layout was used as f o r connections A. Two gauges were placed on each side of the column web opposite To follow p. 66 To follow p. 66 4 Check." beam. r L _ 3k 4k 3 k 3k 3L c 31c 3k 'S'E-CTIOM C - C . -H3 — Tension Moment plate. 1. _ w e b conne-cHng placet-. Hrl . I If -2 „ 1 2* 5 4r Test beam. C o m p " Moment plate. •m-<3E-CTIOW D-D. F i g . 22 Gauge Layout f o r Connection C 67 the centre l i n e of each moment plate, and the rest at a spacing of 3 k from c these on one side of the web only. The t o t a l number of gauges used i n t h i s t e s t was : Beam section => 14 Column section = 12 T o t a l = 26 • From t h i s gauge layout, stress d i s t r i b u t i o n s corresponding to load numbers 2, 4, 6 and 8 as in d i c a t e d i n the table of applied moments, have been drawn. b) - Discussion: 1. Moment Plates: Graphs No. 20 e 21 Both moment plate stress d i s t r i b u t i o n s i n d i c a t e the stress peak at the centre l i n e due to the presence of the column web. These peaks are very prominant even i n the curves f o r small applied moments. The shape of the curves i s very symmetrical about the c e n t r a l peak i n both moment pl a t e s . Due to the d i f f e r e n t thicknesses of the two moment plates, the peak value on the outer sur-face of the tension plate i s l e s s than that f o r the outer surface of the compres-sion plate f o r the same applied moment. Stress values at both edges of each moment plate are considerably smaller. I t i s f e l t that the stress d i s t r i b u t i o n s at the inner surface of each moment plate would have the same general shape as' those at the outer surface, but the stress values would be smaller. This assump-t i o n i s based on the curves obtained f o r the stress d i s t r i b u t i o n s at the inner and outer surfaces of the beam flanges i n connections A - l and A-2. I t i s to be remembered here of course, that the beam web w i l l not d i r e c t l y a f f e c t the stresses at the inner surfaces of the moment pl a t e s . 68 2. Web Connecting Plate: Graph No. 22 The stress curves p l o t t e d f o r t h i s plate have been approximated from the values of stress obtained at each point where gauges were placed, and the assumption of zero stress at the centre of g r a v i t y of the section (see f i g u r e 23). In order to p l o t the average st r e s s at the two points where str e s s values have been given on the curve, stresses at the two surfaces were required. Stres-ses at the one surface were measured d i r e c t l y , and f o r the surface concealed by the beam web, the s t r e s s values were assumed to be those indicated by the gauges on the beam web, since the thicknesses of the web connecting plate and beam web were not too d i f f e r e n t . These stress values i n d i c a t e d then are an average of stresses measured by the two gauges at each section. As would be expected, i t was found that the concealed surface was more h i g h l y stressed. 3. Column Web: Graph No. 23 Here again, the peak stresses are opposite the c e n t r e - l i n e of each moment plate, and i n p a r t i c u l a r , the tension peaks are more l o c a l i z e d than the compression peaks. In comparison with connections A - l and A-2 however, the magnitude of these peaks i s reduced. This feature could probably be caused by two f a c t s : a) width of moment plates greater than width of beam flange, b) increased moment arm between the moment plates. (a) above would spread the applied load over a greater length of column web, and (b) would decrease t h i s applied load due to the moment plates which o v e r a l l , would have the e f f e c t of decreasing the magnitude of the peak stresses at both tension and compression regions of the column web. c) - F a i l u r e Moment: The values of f a i l u r e load and f a i l u r e moment recorded f o r t h i s t e s t 69 are: F a i l u r e Load (kips) F a i l u r e Moment (k i p - i n s . ) 12.5 412.0 Table of Applied Moments Load No. Applied Moment Remarks 0 0 1 0 Q-load 30 on column 2 33 P l o t t e d curve No. 1 3 68 4 103 ti t: " 2 5 140 6 173 ti tt tt ^ 7 211 8 244 .1 tl 11 ^ 9 279 10 314 11 349 12 385 13 412 Maximum moment To follow p. 69 CoklKlECTIOM C 'bo <=>TZE*>e D I S T I Z I & U T I O U i u T E K I 6 \ O K) M O M E N T PLATE.. t • -i") Yie ld s t r e s s ?>b ^/a 2 4 16 6 Curves for the inner /surface have b<s:en approx , using the planimehir ; moment check a<& a guide. O — O u t e r -sur face ( t r u e ) . • — Inner s u r f a c e ( a s s u m e d ) To follow p. 69 CoKJUfcCTl f lM C. ^izzee DieTzibuTioKi m CoKApe&^eig^ M O M E N T PLATE-. Y i e l d S W s s hb % 2 GdAPU M? 1\ O — OoVer su r face ( t rue) . nner s u r f a c e (assom ed). To follow p. 69 1 6 £ A P W W 22 . CoKJM&CTIOkl C To follow p. 69 £ T E , E 6 S DlSTeifeUTIOkl Ikl COLUMW Wtfe. 6KAPU W<? 22>. Tension peak s t r e s s is again more loca l ised than the comp v. 4 peak s t r ^ s . 70 E. C a l c u l a t i o n s a) - Check on S t a t i c s : Although curves of stress d i s t r i b u t i o n have been given f o r both surfaces of both moment plates, the s t r e s s d i s t r i b u t i o n s at both inner surfaces have been assumed, and thus no s t a t i c check i s given f o r the beam section. I t should be noted however, that these given curves are a s t a t i c a l l y possible set. % Moment Resisted by Moment Plates Load No. 2 3 4 d 95 93 92 These values of percentage moment r e s i s t e d by the moment plates can only be regarded as approximate, since a true s t a t i c a l check on the beam section could not be made. The values indicated however, are close to those given f o r the beam flanges of connections A-2 and B. Moment Check on Column Section Curve No. Web Moment Applied Moment E r r o r % 1 32.8 33.0 0.6 2 102.4 103.0 0.6 3 174.0 173.3 0 4 253.6 244.0 3.9 (Moment i n ki p - i n s . ) 71 Horizontal Force Check on Column Section Curve No. Web Force Z Horiz. Tension Comp1 n Forces 1 + 3-9 - 3 . 8 0.1 2 +12.2 -12.3 0 . 1 3 +20.5 - 2 0 . 7 0 .2 +30.1 - 3 2 . 2 2.1 (Force i n kips.) For the column section, the values indicated i n the above s t a t i c a l check show the stress d i s t r i b u t i o n s are very close to the true d i s t r i b u t i o n . b) - M o d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stress: Te nsion Moment Plate. 5? * 2 Web Connect ing Plate. c. cj, o f cross - s<ic\\or\. u/////////////// rm-Comp" Moment" Plate. 4.16" K l e u t r a l 4-7o : i i 7 if / ' tcn^'u 6. 9*>*> in.4 4lfe i n . 4-7o in. F i g . 23 Calculated P o s i t i o n of Centre of Gravity 72 Using the values c a l c u l a t e d i n figu r e 23, the following magnification factors were c a l c u l a t e d f o r stress d i s t r i b u t i o n s wholly within the e l a s t i c region f o r both beam and column sections. . a » Stress Mag'n Factor at Centre-line of Moment Plates Load No. 2 3 8 5 6 7 a Tension 2.0 1.8 1.9 2.3 2.1 2.4 Comp'n 2.9 2.9 3.0 2.9 2.9 2.9 Values of a tabulated here show lower values f o r the tension moment plate than f o r the compression moment pl a t e . I t should be remembered however, that the compression moment plate i s 2/3 the thickness of the tension moment pl a t e . 3 » Stress Mag'n Factor f o r Column Web Stress Peaks Load No. 2 3 4 5 6 P Tension 0.9 1.0 1.1 1.0 1.0 Comp'n 1.0 1.0 1.1 1.0 1.0 The above ta b u l a t i o n shows the values of p f o r the tension and compression regions of the column web to be equal. Inspection of the stress d i s t r i b u t i o n s f o r the column web however, s t i l l tends to show a more l o c a l i z e d tension s t r e s s peak as compared to the compression stress peak. Values f o r the width D have been calculated for the stress curves of both tension and compression moment plates, and the corresponding X-values have been tabulated below: 73 X-values From D = (w + Xk ) c c Load No. 2 3 4 5 6 7 X Tension 3.7 4.4 4.7 4.4 4.5 4.2 Comp'n 3.1 4.1 4.4 4.2 4.2 4.2 These values of X tabulated above i n d i c a t e that the highly stressed sections for both moment plates are approximately the same width, which would be expected i n a connection of t h i s type. Since the beam web does not a f f e c t the stress d i s t r i b u t i o n s i n the moment plates, t h i s highly stressed width of the moments plates i s a f f e c t e d d i r e c t l y by the action of the column web alone. c) - F a i l u r e Moment i n Column Web: Comparing Beedle's f a i l u r e c r i t e r i o n f o r f a i l u r e i n the column web to the a c t u a l f a i l u r e moment y i e l d s : Actual f a i l u r e moment » 412 k i p - i n s . Beedle's c r i t e r i o n = 314 k i p - i n s . This again shows that Beedle's c r i t e r i o n i s on the safe side. d) - Web C r i p p l i n g : As f o r connections A, using the formula set f o r t h i n the s t e e l hand-book, the following values were found to be the percentage of the applied load d i s t r i b u t e d into the length of column web of (N + 2k Q) Load No. 2 4 6 % 46 49 48 These values are s l i g h t l y lower than those c a l c u l a t e d f o r e i t h e r A - l or A-2. C o U W E r C T l O U D . To follow p. 73 weld a c r o s s tension momanl plates. 4 fillet weld connecting plate to beam web. I, fillet welds both sidz<s i 11 5^X4 fillet weld-b| X 4 " fillet weld.-4 f i l ie t welds an both s ides o f compression mom<w\ plate. fillet welds both sides Aon ail boxincj plates. 7 !\ I / St,cr\chi A-A. b x J fillet weld. 2 ^ x 4 fillet weld. b x ^  fillet weld. <S&CTIOM E>-E> T e n s i o n and comp" mo\r)itr\\ p la tes tiave s a m e d i m e n s i o n s as shown f o r C o n n e c t i o n C . beam Column. S e c t i o n &" Wr at 1 7 0 £ <J at \bb * b b W G* d fe" G 7 " t 0 • 3o&'" O 2fc<?' w __o-U" L 0 • £ 2 b " O • bCo'b1' d 74 CONNECTION D A. Description of Co'nnection The beams i n t h i s connection were welded to moment plates which i n turn were welded to the column flanges as was the case f o r connection C. The tension moment plates were welded to the column flanges with 5/16" s i n g l e butt welds, and the compression moment plates were welded to the column flanges with two 1/4" f i l l e t welds each, one on e i t h e r side of the moment plate. The tension moment plate was welded to the tension beam flange with a t o t a l of 12g" of 1/4" f i l l e t weld as shown, and the compression moment plate was welded to the compres-sion beam flange with two 5^ " lengths of 1/4" f i l l e t weld as shown. The web connecting plate was welded to the column flange with 3/16" f i l l e t welds on both sides, and with 1/4" f i l l e t weld connecting i t to the beam web as shown. The 3/8" t h i c k boxing plates were welded into p o s i t i o n with 1/4" f i l l e t welds on both sides of a l l boxing plates. One defect which had an e f f e c t on the measu-red stress was the welded p o s i t i o n of these boxing plates. Figure 24 represents a side view of part of connection D, showing the welded p o s i t i o n of both tension and compression boxing plates with respect to the moment plates. The gaps G^ and G^ shown, had the following measured values f o r the two sides of the connection: 1" 7" G l " 2 a n d 16 15" 1" G 2 = 16 a n d *lT Considering the e f f e c t s shown i n connection B due to the pos i t i o n i n g of the boxing plates, i t would be expected here that the outer surfaces of a l l boxing plates would be highly stressed, and the inner surfaces of the tension To follow p. Ik Com?n M o m e n t P l a t e . C~oimpn &o*ing Plate Tension boxing Plate . / / / / / / / / / / / / / / / / / f f / / f Wdb Connect ing Plate. b<zam. / / / / Tension Moment Plate. Co\vmr\ Range. F i g . 2k Gaps L e f t Between Moment Plates and  Boxing Platcs on Connection 0 75 moment plate would have one side more highly stressed than the other due to the unequal values of G^. B. F a i l u r e Mechanism In the t e s t c a r r i e d out on t h i s connection values of r o t a t i o n and induced stress were recorded from the two beams. At f a i l u r e moment the f i l l e t welds holding both tension boxing plates to the column flange broke i n tension. The f a i l u r e was very sudden, and due to the high value of the moment applied at t h i s point, the t e n s i l e s t r e s s induced i n the column web was so great as to cause the column web to be torn from the column flange. This t e a r i n g e f f e c t allowed a large value of beam r o t a t i o n and i n p a r t i c u l a r , considerable column flange d i s t o r t i o n . P r i o r to t h i s f a i l u r e i t should be noted that higher values of applied moment were reached, but a high creep rate, i n d i c a t i n g large p l a s t i c deformations,allowed only the given f a i l u r e moment value to be r e s i s t e d . This creep i s well indicated by the long h o r i z o n t a l section of the moment-rotation curves f o r t h i s connection. A second form of f a i l u r e was being induced i n the l a t t e r stages of t h i s t e s t , and t h i s was a buckling of the compression moment plate and beam flange. Figure 25 shows two views of the compression moment plate and beam flange with approaching f a i l u r e moment. This buckling of the compression beam flange reduced the resistance of the beam to ho r i z o n t a l r o t a t i o n , with the r e s u l t that the beam rotated about the v e r t i c a l axis X-X shown i n f i g u r e 25. This v e r t i c a l axis X-X, i t was found] cut the tension flange at a point near the edge of the tension mement plate. The e f f e c t of t h i s horizontal beam r o t a t i o n was to reduce the above mentioned buckled form on one side of the compression To follow p. 75 Comp" bcxing plate. / / / / Tension box ing plate. / / / / / / / / / / / / / / / f / / / / C o m p " Moment Plate. X fa Duclcled ehape or eomp n beam flange a n d moment plate. beam.  Web Connecting Plate. Tens ion M o m e n t P la ta . Comp" Axis o f h o r i z o n t a l b e a m r o t a t i o n cu te beam f lange near end of tension m o m e n t p la te. M o m e n t P l a t e . curved cornp" €>ErCTlOM A - A . S e c t i o n snowing c ross - e c c t i o n o f m o m e n t p late and beam f l a n g e . F i g . 25 Mode of Secondary Buckling F a i l u r e  Connection D 76 beam flange and increase i t on the other u n t i l f i n a l l y at f a i l u r e , t h i s buckled form was noticeable on one side only of the compression beam flange. C. Moment Rotation C h a r a c t e r i s t i c s : Graph No. 24 Values of r o t a t i o n were measured f o r both beams i n the t e s t c a r r i e d out and the r e s u l t i n g curves p l o t t e d f o r each beam. As f o r connection C, so here too, the moment plates d i f f e r e d i n thickness, so i n order to ca l c u l a t e the ver-t i c a l beam r o t a t i o n values, r o t a t i o n was assumed to take place about the centre of g r a v i t y of the section (see f i g u r e 2 3 ) . Values of r o t a t i o n c a l c u l a t e d about t h i s point, using the indicated readings from the d i a l gauges on both tension and compression moment plates, showed a much c l o s e r agreement than those f o r connection C. The f i n a l p l o t t e d values of beam r o t a t i o n were taken as the average of these two ca l c u l a t e d values. D. Stress D i s t r i b u t i o n a) - Gauge Layout: Figure 26 represents the gauge layout used on t h i s connection. The two f a i l u r e s considered possible i n t h i s connection with respect to s t r a i n gauge layout were: 1. buckling f a i l u r e i n the beam section, 2 . weld f a i l u r e i n tension region of beam and column. The outer surface of both moment plates of the t e s t beam then, had f i v e gauges symmetrically placed on them, and the outer surfaces of the check beam had three gauges each spaced as shown. The inner surfaces of the moment plates however, were concealed by the beam flanges. In order then to obtain stress d i s t r i b u t i o n s across the inner surface of the tension moment plate, a To follow p. 76 MOMENT ROTATION CU2VE,6 C C W W B C T I O M D To follow p. 76 4 I 1» 4 m 4 .1" G&CTIOM /k-A. 6fcCTIOkl fe-fe 6 r" Checlc beam. L _ 3 L V-' 8 51c -S3* 11 4 *4 1" 11 1 section OT beam flange removed to allow Tendon gauge* to be placed Moment p l a t e . on the inner surface of the tension moment plate. £ 3 -^ W e b ' ConnccVinig plahi. . 0 3 -i'l •2 6 Test beam. 1 11 i " 1 4 ! 4 D 111 L i . StcT iow C-C. •SECTION D - D . 111 F i g . 26 Gauge Layout f o r Connection D 77 section of the tension beam flange 1" wide was removed and f i v e gauges were placed on t h i s inner surface. Due to the position of the welds holding the com-pression moment plate to the compression beam flange, the removal of a section of the compression beam flange could not be done. For t h i s reason there were no gauges on the inner surface of the compression moment plate. For the web connecting plate, two gauges were placed on the connecting plate and two more on one side of the beam web as shown. These gauge positions are exactly the same as those used f o r connection C i n t h i s plate. The f i n a l readings obtained from the two gauges i n the tension or compression region were considered as the surface stresses i n the web connecting plate, the gauges on the beam web being considered to i n d i c a t e a stress not too d i f f e r e n t from that on the concealed side of the web connecting plate. The f i n a l readings then were taken as the average value of the two gauges at each point. Due to the r e l a t i v e positions of the moment plates and boxing plates indicated e a r l i e r , two gauges were placed on inner and outer surface of a l l four boxing plates as indicated. This gauge placement, i t i s hoped, would c l e a r l y i n d i c a t e the e f f e c t of the gaps between the boxing plates and moment plates. F i n a l l y , f o r the column web, two gauges were placed as close as possible to the inner and outer surfaces of the boxing plates on one side of the column web. In order to measure the length of column web stressed, a s i n g l e gauge was placed at a distance of 3 k from the centre-l i n e of the tension and compression moment plates on one side only of the column web, and outside the region of the boxing p l a t e s . Inside the region of the boxing plates gauges were placed at a distance of 2" from those d i r e c t l y below the boxing plates. The four gauges ins i d e the region of the boxing plates have diagonal l i n e s on them i n d i c a t i n g that there i s a second gauge on the opposite side of the column web at t h i s point. 78 The t o t a l number of gauges used i n t h i s t e s t was : Beam sec t i o n = 25 Column se c t i o n = 12 Boxing plates = 16 To t a l = 53 From t h i s gauge layout stress d i s t r i b u t i o n s corresponding to load numbers 2, 4, 6 and 8, as indic a t e d i n the ta b l e of applied moments, have been drawn. b) - Discussion: 1. Moment Plates: Graphs No.25 e 26 Consider the tension moment plate. The curves f o r the outer surface are symmetrical about the centre of the plate showing a peak at the centre and much lower values at the edges. The curves f o r the inner surface generally exhibit l a r g e r values at the edges than at the centre }and i n p a r t i c u l a r , these edge values are higher than those f o r the outer surface. I t i s considered here that the welded p o s i t i o n of the tension boxing plates has a f f e c t e d these edge values and i t seems very l i k e l y that had the boxing plates been welded i n a posi t i o n opposite the tension moment plate then these edge stresses at the outer surface would have been much higher. The compression moment plate exhibits t h i s same type of curve on the outer surface but here the edge stresses are very small indeed. In t h i s case i t i s f e l t that the stresses have d e f i n i t e l y been a f f e c t e d by the p o s i t i o n of the compression boxing plates, since i t i s i n these regions that the d i r e c t compressive thrust due to the applied moment i s t r a n s f e r r e d from the beam corn-See "Conclusions" 7 9 pression flange to the compression moment plate, and hence very high stresses •would be expected here. I t i s with t h i s i n mind,and the f a c t that t h e centre of the plate w i l l have a stress peak due to the a c t i o n of the column web, that the stress curves shown f o r the inner surface have been approximated. A f u r t h e r assumption of equal stress at the edges and centre of the moment plate was used. It should be noted that these inner surface curves, although s t a t i c a l l y possible, are only approximate,and have been drawn only to give some idea of the area re-quired beneath these curves f o r s t a t i c a l equilibrium. 2. Web Connecting Plate: Graph No. 2 7 These curves are f o r the gauges shown on the beam web and connecting plate, and represent at the points plotted, the average value of the two gauges at each section. As can be seen the area beneath the curves i s very small and hence the value of the r e s i s t i n g moment i s a l s o small. Thus the assumption made e a r l i e r of averaging the stress values from the two gauges at each section would not involve any great e r r o r . Assuming zero stress at the centre of g r a v i t y , i n i t i a l l y the d i s t r i b u t i o n i s l i n e a r , but l a t e r loses t h i s property and shows a curve t y p i c a l of a l l the preceding t e s t s i n t h i s region. 3. Column Web: Graph No. 28 These curves show two features. F i r s t , the tension stress peak seems more l o c a l i z e d then the compresion stress peak f o r the same applied moment and second, comparison of these curves with those f o r connection C, f o r the same applied moments, indicates a reduction i n area beneath the s t r e s s curves. The centre l i n e s of both the boxing plates and moment plates have been drawn on these curves^and i n p a r t i c u l a r , stress values have been read from these curves and plotted on the curves shown f o r the boxing plates as indicated. 80 4. Boxing Plates: Graphs No. 29 £30 A major feature of these graphs i s the difference i n area beneath the stress curves on the inner and outer surfaces f o r the same applied moment. The outer surfaces are more highly stressed i n both cases. The c e n t r a l regions of the inner surfaces, close to the column web, of both tension and compression plates indicate a stress peak at the column web, which would be expected a f t e r seeing the stress d i s t r i b u t i o n s f o r the moment plates,and i n p a r t i c u l a r , that for the column web. Indeed, pl o t t e d values were taken from the column web as indica t e d e a r l i e r . This large d i f f e r e n c e i n stresses on the inner and outer surfaces i s one again assumed to be due to the welded p o s i t i o n of the boxing plates. Table of Applied Moments Load No. Applied Moment Remarks 0 0 1 0 Q-load 40 on column. 2 78 P l o t t e d curve No. 1 3 122 A 201 « tt " 2 5 274 6 336 tt tt tt 2 7 434 8 532 tt t. tt ^ 9 615 10 740 11 812 12 917 13 1011 14 1089 Maximum moment C o k J K J E C T I O K i D. To follow p. 80 ^ T e t e e D i e T e i&im ^ M IM TBM61OM MOMENT PUTE. 6KAPU U° 2&. Tension boxing pi ate > _ Tension mom<z.nV_ t p la te . O — O u t e r e u r f a t e . A - \ n n e r surfc CoKlklECTIOM D. To follow p. 80 Dl6T£!g>UTI0Kl |W C 0 M P E . E 6 S I O M KAoMErWT PUTE. Column flange. _v Compn boxing 6 p\aVe~.' 6eM>u Kl° 7(3. Comp n moment. O — OuYer <surf ace (true). inner s u r f a c e (assumed). To follow p. 80 ^Tg - f r S S DlSTRIbOTiOM IN W&fe C^KIMECTIMG PLATE. To follow p. 80 Cc?MMBCT)QM D -4>TILES6 D\eTei&0Tios4 iM COLUMN W&D-Gzwu W° 2 6 . i Tension boxing plafes. To follow p. 80 ^ t * |" opposite tension morr\cr\\ plate.) C O M K I E C T I O K I D. To follow p. 80 4?TIZ.E D)6TEt&UTIC>M Ik] COMPEE^ON PgXlMG PLATE'S. ^ b =• |" — opposite comp" moment plate.) 6eAPW 10° 2>o. 81 E. C a l c u l a t i o n s a) - Check on S t a t i c s : The r e s u l t s of the s t a t i c s check on both beam and column sections are tabulated below: Moment Check on Beam Section Curve Moment Plate Web T o t a l Applied E r r o r % Resisted No. Tension Comp'n Plate Moment Moment % by K-Plates 1 31.7 5.6 77.9 _ 93 2 71.1 15.5 201.4 92 3 126.7 _ 24.5 _ 336.7 93 4 234.0 - 39.0 - 531.5 - 93 (Moment i n kip - i n s . ) Horizontal Force Check on Beam Section Curve No. Moment Plate Web Conn. Plate Z Horiz. Forces Tension Comp'n Tension Comp'n 1 + 7.9 +0.8 - 1.8 2' +18.1 _ +2.6 - 4.7 — 3 +32.2 - +4-0 - 7.5 -4 +59.5 - +6.8 -11.6 -(Force i n kips.) Here again, since a f u l l set of curves f o r the compression moment plate could not be obtained, the above s t a t i c a l check on the beam section i s incomplete. The moment r e s i s t e d by the web connecting plate was used to com-pute the percentage moment r e s i s t e d by the moment plates. 82 Moment Check on Column Section Curve Ko. Boxing Plate Moment Web Moment To t a l Moment Applied Moment Er r o r cf /° % Resisted by B. PI. Tension Comp'n 1 20.5 25.7 32.4 78.6 77.9 0.9 59 2 49.5 62.6 90.6 202.7 201.4 0.6 56 3 82.5 108.0 151.9 342.4 336.7 1.7 57 4 140.3 185.2 202.4 527.9 531.5 0.7 48 (Moment i n ki p - i n s . ) Horizontal Force Check on Column Section Curve No. Boxing Plate Force Web Force Z Horiz. Forces. Tension Comp'n Tension Comp' n 1- + 6.2 - 5.7 + 3.0 - 3.7 0.2 2 +15.0 -13.9 + 8.7 -10.2 0.4 3 +25.0 -24.0 +15.1 -16.6 0.5 4 +42.5 -41.2 +22.8 -25.0 0.9 (Force i n kips) From the above moment check on the column section i t can be seen that only approximately 57$ of the applied moment i s r e s i s t e d by the boxing plates. This f i g u r e would be higher i f the boxing plates had been positioned opposite the moment plat e s . Even though these boxing plates are positioned i n -c o r r e c t l y the above f i g u r e s i n d i c a t e quite a reduction i n the moment r e s i s t e d by the column web. 83 b) - Mo d i f i c a t i o n of T h e o r e t i c a l E l a s t i c Stresses: The following magnification factors were calculated from the stress d i s t r i b u t i o n s producing only e l a s t i c stresses i n the beam or column sections. a = Stress Mag'n Factor at Centre-line of Moment Plates Load No. 2 3 4 5 6 7 a Tension 1.1 1.4 1.4 1.4 1.4 1.5 Comp'n 1.3 1.5 1.5 1.5 1.5 1.5 These tabulated values of a f o r both the tension and compression moment plates are the values c a l c u l a t e d f o r the t e s t beam. Calculated values for the check beam are exactly the same f o r both moment plates. Since the stre s s curves do not r i s e at the edges of the moment plate s , as wes the case f o r the beam flanges of connection B, no magnification f a c t o r s have been tabu-l a t e d f o r these points. I t i s f e l t however, that i f the boxing plates had been positioned c o r r e c t l y a str e s s r i s e at the edges would be noticeable, and i n p a r t i c u l a r , the above values of o would be smaller. 3 ° Stress Mag'n Factor f o r Column Web Stress Peaks Load No. 2 3 4 5 6 7 8 P Tension 1.4 1.5 1.6 1.5 1.6 1.6 1.6 Comp'n 1.4 1.4 1-4 1.4 1.3 1.4 1.3 The values of 3 tabulated above are only approximate,as no gauges could be placed on the column web at these sections i n order that an accurate See "Conclusions" 84 s t r e s s reading be obtained, due to the boxing plates. However, the values as calculated are close. Had the boxing plates been welded i n d i r e c t l y opposite the moment plates i t i s f e l t that the above values would have been reduced. Values of the width D have been ca l c u l a t e d f o r both the tension and compression moment plates of the t e s t beam, and the X-values corresponding to these are tabulated below. X-values From D = (w + Xk ) Load No. 2 3 4 5 6 7 X Tension 1.2 2.0 2.3 2.4 2.4 2.7 Comp'n 1.3 2.0 2.1 2.1 2.1 2.0 The above X-values indicate widths D which are approximately the same, as was the case f o r connection C. This would once again be expected, due to the act i o n of the column web on the moment plates. 8 5 SECTION F CONCLUSIONS ( i ) General This t e s t s e r i e s indicates the type of f a i l u r e very l i k e l y to occur i n these welded connections. For connections A and C, a column web buckling would be considered, and with connections B and D, f a i l u r e of a weld i n the ten-sion region, as w e l l as a buckling i n the compression region, would be considered. The s t r e s s d i s t r i b u t i o n s given f o r the various components of each connection indi c a t e i n p a r t i c u l a r the peak stress values which i n i t i a t e these f a i l u r e s . A point which must be emphasized here i s that the stress d i s t r i b u t i o n s given are f o r "s k i n " or "surface" stresses. However, i n the case of the column ' web and beam web these s k i n stresses at any point are considered to have a con-stant value across the thickness of the section. These peak values of ski n stress can i n i t i a t e l o c a l f a i l u r e s of the type indicated i n connection B, i . e . a l o c a l t e a r i n g of the parent metal at the surface most highly stressed. This i n d i c a t e s that although t h i s peak value i s only at the surface, and most probably the stress decreases at the inner f i b r e s , these surface stresses can induce f a i l u r e . 86 ( i i ) Comparison of Test Values 1. Connections A - l , A-2 ^ B: These three connections had one feature i n common, i . e . no moment plate s . The following t a b l e indicates an average set of calculated values f o r these connections: Connection a X 3 % M. by Flanges Tension Comp'n Tension Comp'n Tension Comp'n A - l 2.0 1.4 5.2 _ 1.3 0.9 8U% A-2 2.5 1.8 4.6 - 1.1 1.0 91% Connection a V 0 % M. by % M. by Flanges Edge A Tens. Comp. Tens. Box.Pl. Tens. Comp'n Tens. Comp. oomp. B 1.3 1.4 0.9 1.3 2.3 whole flange 1.3 1.3 91* Since f o r connections A - l and A-2 the ho r i z o n t a l force check i n d i c a -tes a small d i f f e r e n c e between the areas enclosed beneath the stress curves on the tension and compression sides of the beam web, then the average area beneath the inner and outer curves of the beam flanges should also be very nearly equal f o r Z h o r i z o n t a l forces = 0. Also without boxing plates, the peak str e s s at the centre of the tension flange i s higher than that at the centre of the compression flange, as in d i c a t e d by the cx-values f o r A - l and A-2. From t h i s i t could be as-sumed then that the peak stress i s more l o c a l i z e d i n the tension flange, and hence the value of X f o r the compression flange would be higher than that f o r the tension flange. To fu r t h e r support t h i s , i n v e s t i g a t i o n of the column web stresses shows t h i s l o c a l i z e d e f f e c t i n the tension region as compared to the compression region i n a l l connections which do not have boxing plates. t 87 As an explanation for the small values of a f o r connection A - l , i t i s considered that since the t o t a l height of the beam web i n A - l has been welded, the moment r e s i s t e d by the beam flanges would be smaller than that f o r A-2 as indicated.above. This would e f f e c t i v e l y reduce the average area beneath the stress curves i n the beam flanges, and correspondingly reduce a. With the i n c l u s i o n of boxing plates, connection B, the values of a f o r both tension and compression flanges are equal. Also, these peak stresses defined by a are much reduced as compared to thos indicated f o r connections A - l and A-2. This, of course, i s due to the more uniform stress d i s t r i b u t i o n across both surfaces of the beam flanges, as shown i n the stress curves given e a r l i e r . Values of X f o r the tension flange of B are approximately h a l f those indicated f o r A - l and A-2. For the compression flange of B however, the whole outer sur-face i s stressed above the t h e o r e t i c a l design s t r e s s , the minimum points on eit h e r side of t h i s c e n t r a l peak stress being just s l i g h t l y greater than the t h e o r e t i c a l design s t r e s s . The percentage of the applied moment r e s i s t e d by the beam f l a n -ges i n B i s the same as that f o r connection A-2. (3-values f o r the three connec-tions are almost i d e n t i c a l f o r the compression regions but vary f o r the tension regions. For connection A - l the tension p-values seem very high as compared to those f o r A-2. Stress curves f o r the outer surface of the tension beam flange, corresponding to a moment producing 20 k i p / i n s . t h e o r e t i c a l l i n e a r stress at t h i s surface, have been given f o r comparison i n graph No. 31. These curves have been drawn symmetrical, the plotted values having been approximated from t e s t information, and for t h i s reason they are c a l l e d " i d e a l i z e d curves." This moment value i s : M - 282 k i p - i n s . To follow p. 87 CQMM&CTVOMS A- l , k-l , I b. To follow p. 87 fefcAM p L A U 6 f c . Applied Moment = 262 l6 'p-lns. io 24 16 Yield <b>re<5s *>5 W. GtcAPW Sl . Wo boxing plates Pi lief welds. Boxing, plates. ButtI welds. O 1 , — 'bo 16 88 As a f i n a l comparison of these connections, the moment-rotation curves f o r the " t e s t " beam of these connections have been drawn on one sheet i n graph No. 32. 2. Connections C | D Both these connections had moment plates. The table below indicates an average set of values c a l c u l a t e d from the tes t information: Connection a i 0 % M. by M. Plates Tension Comp'n Tension Comp'n Tension Comp'n C 2.2 2.9 4.3 4.2 1.0 1.0 93% Connec-t i o n a X 3 % M. by Boxing PI. % M. by Moment PI. Tens. Comp. Tens. Comp. Tens. Comp. D 1.5 1.5 2.3 2.1 1.6 1.4 58^ 93% Without boxing plates the values of a are again unequal, but now the st r e s s peak i s higher i n the compression moment plate than i n the tension plate, as shown i n connection C. However, the X-values indicate s i m i l a r widths of the moment plates more hig h l y stressed f o r connection C. These f a c t s could indi c a t e that the t h i c k e r moment plate has a tendency to spread the applied load more uniformly across i t s width than the thinner moment plate. Values of B as compared with those f o r connections A - l and A-2 show i d e n t i c a l values f o r the compression region of the column web, but s l i g h t l y lower values f o r the tension region. This low value of (3 i n the tension region would be expected as the tension moment plate was very much thicker than the beam tension flange, and hence the applied h o r i z o n t a l load from t h i s moment plate would tend to be spread more along the column web. The moment r e s i s t e d by the moment plates i s almost the same as that f o r oonnections A-2 and B. 89 V/ith boxing plates, connection D, the values of a are once again found to be equal as was the case f o r connection B. The X-values ind i c a t e almost s i m i l a r widths of moment plate more highly stressed, and i n p a r t i c u l a r the values are approximately h a l f tho3=shown f o r connection C. The values of (3 are very much higher i n t h i s connection, but t h i s i s a t t r i b u t e d to the welded p o s i t i o n of the boxing plates, and i t i s f e l t that had they been welded i n op-posite the moment plates these values of (3 would have been reduced. In c a l -c u l a t i n g these values of (3 the po s i t i o n i n g of the boxing plates was taken into consideration. The percentage of applied moment r e s i s t e d by the boxing plates i s smaller than that f o r connection B, and the percentage of applied moment r e s i s t e d by the moment plates i s the same as that f o r connection C. As f o r connections A - l , A-2 and B, stress d i s t r i b u t i o n s f o r the outer surfaces of the tension moment plates f o r connections C and D have been drawn i n the form of " i d e a l i z e d " curves, as shown i n graph No. 33. The moment-ro t a t i o n graphs f o r the " t e s t " beam of the two connections have been drawn on one sheet f o r comparison i n graph No. 34. For these two connections the moment which produces a maximum t h e o r e t i c a l l i n e a r stress of 20 k i p / i n s . i s : M * 398 k i p - i n s . It i s f e l t that the indicated values of a, (3 and X given f o r connec-t i o n D have d e f i n i t e l y been aff e c t e d by the po s i t i o n i n g of the boxing plates, - and t h i s e f f e c t w i l l now be discussed. ( i i i ) E f f e c t of P o s i t i o n of Boxing Plates This discussion w i l l deal with beam flanges only, but i t i s to be remembered that the same argument w i l l apply for moment plates as w e l l . The p o s i t i o n of the boxing plates i n r e l a t i o n to the beam flanges To follow p. 89 M O M E N T ROTATION CORVEE GCAPW M° H. To follow p. 89 C o O K I ' S C t D IpsAUSE-P Cuev&e F-coe 4Te&56 AT OL)T&& ^uePAOE: O F T&M6\Okl MoMErMT PlATES-- A p p l i e d m o m e n t = 596 kip-ins. Yield st ress &E>%? 90 of a welded connection can a f f e c t the stress d i s t r i b u t i o n i n these flanges markedly. In order to develop the required r e s i s t i n g moment i n these sections, the s t r e s s i s d i s t r i b u t e d across the connecting welds i n such a manner that the more r i g i d regions are more hig h l y stressed, i . e . opposite the column web i n both tension and compression beam flanges. Because the column flanges are r e l a t i v e l y very f l e x i b l e without boxing plates, the stress at the edges of the beam flanges would be very small compared t o that at the centre,and under ap-p l i e d moment, a bowing of the flanges would r e s u l t . Yv'lth boxing plates how-ever, t h i s bowing e f f e c t i s much reduced since the flange now has a much greater r i g i d i t y . This increased r i g i d i t y increases the streas induced at the edges of the beam flanges f o r the same applied moment and i n p a r t i c u l a r , decreases the peak value of stress at the centre opposite the column web. Reference t o graph No. '31, connections A-2 and B, indicates t h i s point w e l l . Thus, with the boxing plates welded into a p o s i t i o n d i r e c t l y opposite the beam flanges the stress d i s t r i b u t i o n i n thesf flanges does not exhibit such a high peak s t r e s s . Consider now the case where the boxing plates are displaced to one side of the beam flanges, as was the case f o r connection D. Here, the edges of the column flanges have a r i g i d i t y intermediate between that f o r no boxing and that f o r boxing plates positioned opposite the beam flanges. The r e s u l t of t h i s i s that a smaller stress i s induced i n the edges of the beam flanges and consequently, the s t r e s s peak at the centre increases i n order that the necessary r e s i s t i n g moment be developed. Also, a bowing of the column flange i s noticeable at both the beam flange and boxing plate connections, with the r e s u l t that a double curve i n the form of an " S " i s developed as shown i n f i g u r e 27. 91 F i g . 27 Bowing of Column Flange as a Result of Boxing Plate Conditioning. This f i g u r e shows the tension beam flange and tension boxing plate framing i n t o the column,and as a r e s u l t of the forces T^ and T^, the column flange has been bent into the form of an S. As a d i r e c t r e s u l t of t h i s , higher surface stresses than normal would be induced at points A on both beam flange and boxing plate. I f now, as i n connection D, f i l l e t welds were used to connect the boxing plates to the column section, these higher stresses at A would most l i k e l y tend to i n i t i a t e on e a r l i e r f a i l u r e . I t i s f e l t that t h i s was the case f o r connection D, since these high values of surface stress were measured i n the positions given above, and f a i l u r e of the f i l l e t welds represented the f a i l u r e mechanism. 1 To conclude then, i t seems most l i k e l y that correct p o s i t i o n i n g of the boxing plates leads to the following: 92 1. More uniform stress d i s t r i b u t i o n i n beam flanges. 2. Smaller stress peak at the centre of the beam flanges. 3. More uniform stress gradation between inner and outer sur-faces of beam flanges and boxing pl a t e s . A. P o s s i b i l i t y of a stronger connection. ( i v ) Factors of Safety Considering a design stress of 20 k i p / i n s . and a t h e o r e t i c a l l i n e a r stress d i s t r i b u t i o n , the design moment f o r each connection would be (a) with moment plates = 398 k i p - i n s . (b) without " " = 282 k i p - i n s . Using the f a i l u r e moments measured i n t e s t , the f a c t o r s of safety fo r each connection would be: Connection A - l A-2 B C D Factor of Safety 1.12 1.33 3.25 1.03 2.74* From these f i g u r e s i t would seem that about 30$ only of t h i s theo-r e t i c a l design moment could be used f o r connections without boxing plates i n order to gain a f a c t o r of safety greater than 3.0. (v) Concluding Remarks From the four connection types tested, i t seems that the stress peak i n the centre of the beam flange or moment plate w i l l e x i s t regardless of the use of boxing plates. With boxing plates of course, the magnitude of t h i s stress peak i s reduced. This value considered to be low due to explanation given e a r l i e r regarding the boxing pl a t e s . 93 The values c a l c u l a t e d from the t e s t information ind i c a t e to the designer of welded structures some idea of the magnitude of the stress and i t s d i s t r i b u t i o n within the connection. However, the actual values given are correct only f o r t h i s r a t i o of beam s i z e to column s i z e . In order to give a general r u l e , f u r t h e r i n v e s t i g a t i o n with varying beam and column si z e s would be necessary. i BIBLIOGRAPHY A. BOOKS Beedle, L.S. Hetenyi, M.I. Lee, G.H. Perry, C.C. Lissner, H.R. Plastic Design of Steel Frames. New York, Wiley, 1958 Handbook of Experimental Stress Analysis. New York, Wiley, 1950 An Introduction to Experimental Stress Analysis. New York, Wiley, 1950 Strain Gauge Primer. New York, McGraw-Hill, 1955 Timo8henko, S. Elements of Strength of Materials. MacCullough,G.H. New York, Van Nostrand, 1949 B. JOURNALS AND PAMPHLETS Pray, R.F. Jensen, C. Topractsoglov,A, Beedle,L.S. Johnston,B.G. Beedle,L.S. Topractsoglov,A. Johnston,B.G. Brandes, J.L Mains, R.M. Johnston,B.G. Deits, G.R. Schenker, L. Salmon, C.G. Johnston, B.G. Jensen, CD. Graham, J.D. Sherbourne,A.N. Khabbaz,R.N. "Welded Top Plate Beam-Column Connections." Welding  Journal Research Supplement. No.35' pp.3359-3479, 1956 .A."Connections for Welded Continuous Portal Frames." Progress Report No.4, Part 1, Welding Journal Research  Supplement. No.30: pp.3599-3849, 1951 "Connections for Welded Continuous Portal Frames." .A. Prog. rep. No.4, Pt. I I , Welding Journal Research  Supplement. No.30? pp.3979-4059, 1951 "Report of Tests of Welded Top Plate and Seat Building Connections." Welding Journal Research Supplement, No.23: pp.1463-1659, 1944 "Tests of Miscellaneous Welded Building Connections." Welding Journal Research Supplement, No.21: pp.56-276, 1942 "Structural Steel Connections." Armed Forces Special  Weapons Pro.lect. Report No. 352 "Welded Interior Beam-to-Column Connections." American Institute of Steel Construction. 1959 G r i f f i t h s , J.D. "Single Span Rigid Frames in Steel," American Institute of Steel Construction. 1948 Bleich, F. "Design of Rigid Frame Knees." American Institute of Steel Construction. 1943 F a i l u r e of Connection D - notice section removed from beam tension flange, and tearing of column web. Also notice S-shape of column flange as i n d i c a t e d i n F i g . 27. R e l a t i o n between welded positions of boxing plates and moment plates i n Connection D. Buckling of compression flange of Connection B. F a i l u r e of tearing of parent metal of tension flange i n Connection B. V I 

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