This document summarizes research on the design of single plate shear connections. Experimental testing was conducted on 5 beam-to-column connection assemblies to evaluate their strength and behavior under a standardized shear-rotation loading path. Key findings include:
- Shear connections must have sufficient strength to transfer beam shear loads and enough rotation capacity to accommodate beam end rotations.
- A standardized tri-linear shear-rotation loading path ("abed" curve) was developed based on analysis of simple beam behavior and used to load the test specimens.
- Testing identified limit states and validated a new design procedure developed for single plate shear connections.
This document summarizes research on the design of single plate shear connections. Experimental testing was conducted on 5 beam-to-column connection assemblies to evaluate their strength and behavior under a standardized shear-rotation loading path. Key findings include:
- Shear connections must have sufficient strength to transfer beam shear loads and enough rotation capacity to accommodate beam end rotations.
- A standardized tri-linear shear-rotation loading path ("abed" curve) was developed based on analysis of simple beam behavior and used to load the test specimens.
- Testing identified limit states and validated a new design procedure developed for single plate shear connections.
This document summarizes research on the design of single plate shear connections. Experimental testing was conducted on 5 beam-to-column connection assemblies to evaluate their strength and behavior under a standardized shear-rotation loading path. Key findings include:
- Shear connections must have sufficient strength to transfer beam shear loads and enough rotation capacity to accommodate beam end rotations.
- A standardized tri-linear shear-rotation loading path ("abed" curve) was developed based on analysis of simple beam behavior and used to load the test specimens.
- Testing identified limit states and validated a new design procedure developed for single plate shear connections.
This document summarizes research on the design of single plate shear connections. Experimental testing was conducted on 5 beam-to-column connection assemblies to evaluate their strength and behavior under a standardized shear-rotation loading path. Key findings include:
- Shear connections must have sufficient strength to transfer beam shear loads and enough rotation capacity to accommodate beam end rotations.
- A standardized tri-linear shear-rotation loading path ("abed" curve) was developed based on analysis of simple beam behavior and used to load the test specimens.
- Testing identified limit states and validated a new design procedure developed for single plate shear connections.
ABOLHASSAN ASTANEH, STEVEN M. CALL AND KURT M. McMULLIN
INTRODUCTION Single plate shear connections, often referred to as shear tabs, have gained considerable popularity in recent years due to their efficiency and ease of fabrication. Shear tab connections are primarily used to transfer beam end reac- tions to the supporting elements. The connection consists of a plate welded to a support at one edge and bolted to a beam web. Figure 1 shows typical applications of single plate shear connections. This paper presents the summary of a research project on the behavior and design of single plate shear connections. Based on experimental and ana- lytical studies, a new design procedure is developed and presented. The AISC-ASD^^ as well as AISC-LRFD^^ specifica- tions have the following provisions with regard to shear connections: "Except as otherwise indicated by the de- signer, connections of beams, girders, or trusses shall be designed as flexible, and may ordinarily be proportioned for the reaction shears only. "Flexible beam connections shall accommo- date end rotations of unrestrained (simple) beams. To accompHsh this, inelastic action in the connection is permitted." Steel shear connections not only should have sufficient strength to transfer the end shear reaction of the beam but according to above provisions, the connections should also have enough rotation capacity (ductility) to accommodate the end rotation demand of a simply supported beam. In addition, the connection should be sufficiently flexible so that beam end moments become negligible. Thus, like any shear connection, single plate shear connections should be designed to satisfy the dual criteria of shear strength and rotational flexibility and ductihty. Shear-Rotation Relationship in a Shear Connection To investigate the behavior and strength of a shear con- nection, it is necessary that realistic shear forces and their corresponding rotations be applied to the connection. In Abolhassan Astaneh is assistant professor, University of Califor- nia, Berkeley. Steven M. Call is graduate researcfi assistant. University of California, Berkeley Kurt M. McMullin was graduate researcfi assistant, University of California, Berkeley an earlier research project,^ the shear-rotation relation- ship for the end supports of simply supported beams was studied. A computer program was developed^ and used to simulate increased monotonic uniform loading of the beams supported by simple connections until the beams collapsed. ^'^ The studies indicated that the relationship between the end shear and end rotation is relatively stable and depends primarily on the shape factor Z^/S^ of the cross section, L/d of the beam and the grade of steel used. Figure 2 shows a series of curves representing shear forces and cor- responding rotations that will exist at the ends of simply supported beams. The curves correspond to beams of A36 steel having cross sections from W16 to W33 and L/d ra- tios of 4 to 38. Also shown in Fig. 2 is a tri-linear curve "abed" suggested to be a realistic representative of the shear-rotation curves. The tri-hnear curve "abed" is pro- posed to be used as a standard load path in studies of shear connections. Curve "abed" is used instead of the more conservative curve "aef" because it is felt that curve "abed" represents a more realistic maximum span-to- depth ratio for most steel structures. For special cases of very large span-to-depth ratio or high strength steels, the rotational demand may be greater than that of curve "abed". For such cases special care must be taken to as- sure the rotational ductility demand of the beam is sup- plied by the connection. CONCRETE SUPPORT BEAM rL SHEARH TAB W. JL BEAM- ^ SHEAR-^ TAB I J i 1 la SHEAR- ^ TAB 1 JC ( a) (b) ( c) COLUMN BEAM ^ \ 3^ ^ 1 ,J TT (d) (e) Fig. 1. Typical Single Plate Shear Connections FIRST QUARTER/1 989 21 The shear-rotation curves plotted in Fig. 2 are estab- Ushed based on the assumption of elastic-perfectly-plastic bending moment capacity for the beam. To include the ef- fect of strain hardening, the segment "cd" in curve "abed" is included. The behavior of shear connections has been studied in the past by several investigators.^'^^"^^ However, in most cases, the shear connections have been subjected to mo- ment and rotation or only direct shear without rotation in- stead of a realistic combination of shear and rotation. Fig- ure 3 shows the shear rotation relationships that existed in several studies including this research project. EXPERIMENTAL RESEARCH In order to identify limit states of strength and to verify the validity of the design procedures that were developed and proposed, five full scale beam-to-column connection assembhes were tested. A summary of the experimental studies follows. More detailed information on the research project can be found in References 3 and 6. Test Set-up The test set-up shown in Fig. 4 was used to apply shear- rotation relationship of curve "abed" in Fig. 2 to the speci- mens. The main components of the test set-up were a com- puter based data acquisition and processing system, two actuators R and S and support blocks. Actuator S, which was close to the connection, was force controlled and pro- vided the bulk of the shear force in the connection. Actua- tor R, which was displacement controlled, provided and controlled the beam end rotation. Test Load Path The proposed standard shear-rotation relationship shown as curve "abed" in Fig. 2 was apphed to the connec- tions in all of the test specimens. To establish the curve, coupon tests of the plate material were conducted prior to connection tests and the yield point and ultimate strength of the plate material were obtained. The shear yield capacity of the single plate in each test specimen was calculated by multiplying the von Miess criterion of shear yield stress, l/VSFy, by the shear area of the plate. The shear yield capacity of the plate, denoted as Ry, was taken as equal to the shear at point "c" of curve "abed" in Fig. 2. Thus the shear yield capacity of the shear tab was as- sumed to occur when the moment at midspan was equal to Mp. As a. result, a corresponding Mp can be calculated for each connection to be equal to RyL/4. The end rota- tion of the beam when midspan moment reached Mp was set equal to 0.03 radians. To establish point "b" in curve "abed", the shear at this point was set equal to AMylL and the rotation was set equal to 0.02 radian. This imphes that when beam midspan moment reaches My, the end rotation will be equal to 0.02 radian. The value of My, the end rotation will be equal to 0.02 radian. The value of My for each spec- imen was calculated by dividing Mp by the shape factor. A shape factor of 1.12 was used in all specimens. Segment "cd" in Fig. 2 corresponds to strain hardening of the beam and the increased moment at beam midspan which results in increased shear at the beam ends. To es- tabhsh "cd", it was assumed that when the midspan mo- ment reaches a value of {FJFy)Mp, the beam end rotation will be equal to 0.1 radian. In summary, load path "abed" in Fig. 2 reflects the be- havior of the beam and its effect on connection shear and rotation. Segment "ab" corresponds to the elastic behav- ior of beam. At point "b", midspan moment of the beam reaches My and the beam softens. Segment "be" corre- sponds to inelastic behavior of the beam. At point "c", the midspan moment reaches Mp. Segment "cd" represents extra beam capacity that can develop due to beam strain hardening. > > < LU X en Q END ROTATION, rad. Fig. 2. Shear-Rotation Relationship for Ends of Simple Beams o LU o o 2 o < . ACTUAL SHEAR ROT AT10N_ PROPOSED 0 02 0 04 0 06 ROTATION OF BEAM END, rad. Fig. 3. Shear-Rotation Relationship used in Several Studies 22 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION TEST GROUP ONE TWO TEST NO. 1 2 3 4 5 NO. OF BOLTS 7 5 3 5 3 DIA. OF BOLTS in. % % 3/4 3/4 % Table 1 . Properties of Test Specimens TYPE OF BOLTS* A325-N A325-N A325-N A490-N A490-N PLATE DIMENSIONS in. X in. x in. 21 X 3/8 X 4-V4 1 5 X 3/8 X 4-y4 9 X 3/8 X 4-y4 I 4- V4 X 3/8 X 3 - % 8-V4 X 3/8 X 3-y8 EDGE DISTANCE in. i-y2 A-V2 1-V2 l - Va l - Vs ACTUAL WELD SIZE in. VA VA VA % 2 % 2 BEAM MATERIAL A36 A36 A36 Gr. 50 Gr. 50 PLATE MATERIAL A36 A36 A36 A36 A36 *AII bolts were tightened to 70% of proof load. In all specimens diameter of bolt hole was Vw inch larger than nominal diameter of bolt. "N" indicates that in all specimens threads were included in shear plane. tSize of all welds was specified as VA inch. Test Specimens Each test specimen consisted of a wide flange beam bolted to a single plate shear connection which was welded to a column flange as shown in Fig. lb. The properties of the test specimens were selected in consultation with a professional advisory panel. These properties are given in Table 1. The bolt holes in all specimens were standard round punched holes. All bolts were tightened to 70% of proof load using turn-of-the-nut method.^^'^"^ All shear tabs were cut from a single piece of steel. The yield stress and ultimate strength for material of shear tabs were 35.5 ksi and 61 ksi respectively. The condition of faying sur- faces was clean mill scale. The electrodes were equivalent of E7018. The bolt spacing in all specimens was 3 in. The edge dis- tance in the horizontal as well as vertical direction for specimens 1,2 and 3 was l-Vz in. (two times diameter of bolt) and for specimens 4 and 5 was l-Vs in. (1.5 times di- ameter of bolts). 0 0 o ACTUATOR v.! CONTROLLER 0 0 o 1 ANALOG PLOTTER Dala Acquisition TO INSTRUMENTAION 3F -m 4)\ I a - ACTUATOR -R" - LOAD CELL I ACTUATOR "S" v\ BEAM ' SINGLE PLATE SHEAR CONNECTION COLUMN REACTION BLOCK Fig. 4. Test Set-up Used in Experiments Behavior of Test Specimens The experiments were conducted in two groups as indi- cated in Table 1. The main differences of specimens in these two groups were the type of bolt (A325 or A490), material of beam (A36 or grade 50) and edge distance (2^^ or l.Sdij). The behavior of specimens in the two groups is summarized in the following sections. Behavior of Specimens 1,2 and 3 (Group One) Specimens 1,2 and 3 showed very similar behavior throughout the loading. The most important observation was the significant inelastic shear deformations that took place in all three specimens as shown in Fig. 5. All test specimens failed due to sudden shear fracture of the bolts connecting the single plate to the beam web as shown in Fig. 6a. The examination of bolts after failure indicated that the A325 bolts in these specimens had de- veloped significant permanent deformations prior to frac- ture as indicated in Fig. 6b. In these three specimens the welds did not show any sign of yielding other than in speci- men 3 which showed minor yielding at the top and bottom of welds prior to fracture of bolts. A study of the bolt holes after the completion of tests 1,2 and 3 indicated that permanent bearing deformations had taken place in the plate as well as in the beam web. The magnitude of the deformations in the plate and beam FIRST QUARTER/1989 23 bolt holes were almost equal but in opposite directions. The deformations of the plate bolt holes, drawn to scale are shown in Fig. 7. The arrows indicate the direction of the movement of the bolts which is expected to be approx- imately the direction of the applied force due to shear and moment. It is interesting to note that nearly vertical orien- tations of arrows indicate the presence of a large vertical shear accompanied by a relatively small moment in the connections. Behavior of Specimens 4 and 5 (Group Two) The behavior of specimens 4 and 5 was similar to the previous three tests. However, shear yielding of the plate was more apparent. Specimen 4 failed due to shear frac- ture of bolts in a manner similar to previous tests shown in Fig. 6a. In addition, minor yielding was observed on the weld lines of this specimen. Specimen 5 failed by almost simultaneous fracture of weld lines and bolts as shown in Fig. 8. It appears that at the time of failure, weld lines started to fracture first while bolts were on the verge of fracture. When sudden fracture of welds occured the re- sulting shock caused fracture of the bolts which appeared to be almost simultaneous with weld fracture. Bolts in specimens 4 and 5 were A490 bolts. An examination of the bolts after fracture showed less permanent deformations in these bolts than the A325 bolts used in previous three tests (see Fig. 6b). Study of bolt holes in the shear tabs of specimens 4 and 5 indicated that significantly larger bolt hole deformations had occured in these two specimens compared to speci- mens 1,2 and 3. However, the bolt holes in the beam web in specimens 4 and 5 had only minor permanent deforma- tions. In summary, based on observations made during the tests, it appears that shear tabs go through three distinc- tive phases of behavior. At the very early stages, a shear tab acts as a short cantilever beam with moment being dominant. As load increases, the shear tab acts as a deep shear beam with the shear yielding effect dominant (as in specimens 1 through 4). If bolts and welds do not fail dur- ing the shear phase, because of large deformations, the shear tab acts similarly to the diagonal member of a truss and carries the appUed shear by a combination of shear and diagonal tension effects (as in specimen 5). Experimental Data The results of experiments at the time of failure are summarized in Table 2. DISCUSSION OF EXPERIMENTAL RESULTS Shear Yielding of Single Plate The yielding of the single plate was primarily due to shear stresses and was quite ductile. It was evident that considerable shear yielding occurred in the plate between the bolt line and weld line. The shear yielding was almost uniformly distributed throughout the depth of the plate as measured by strain gages that were attached to the plates.^'^ Therefore, in the proposed design procedure dis- cussed later, the shear capacity of plate is calculated by multiplying gross area of plate by uniformly distributed shear stresses. In specimen 3, at later stages of loading and after signifi- cant shear yielding, the bottom portion of the shear tab showed signs of minor local buckling as shown in Fig. 6a. This local buckling was attributed primarily to loss of stiff- ness of plate material due to shear yielding. Until this phe- \ 1 TEST ONE
i i I t^ t cp 1 i TEST TWO TEST THREE A325 Bolts (15 Bolts Tested) Approx 1/32- Fig. 5. Plate Shear Deformations in Specimens 1,2,3 A490 Bolts (8 Bolts Tested) (a) (b) Fig. 6. Typical Bolt Failure of Test Specimens 24 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 2. Results of shear strength Tests Specimen Test Group (1) One Two Test No. (2) 1 2 3 4 5 No. of Bolts (3) 7 5 3 5 3 Observed Failure Mode (4) Bolts Fractured Bolts Fractured Bolts Fractured Bolts Fractured Welds and Bolts Fractured Connection Response Shear Displacement in. (5) 0.27 0.34 0.46 0.35 0.52 Shear Force kjps (6) 160 137 94 130 79 Beam End Rotation rad. (7) 0.026 0.054 0.056 0.053 0.061 * l\/loment at Bolt Line kip in. (8) 306 314 20 273 - 47 t l\/loment at Weld Line kip in. (9) 745 691 279 631 170 Maximum Moment at Weld Line (10) 1028 734 350 686 237 *ln some cases like these, moment decreased as shear and rotation increased. tPositive moments cause top of connection to be in tension. nomenon is studied thoroughly, it is suggested that local buckling be avoided. To prevent local buckling, it is rec- ommended that the distance between the bolt line and the weld line be less than Vz of the plate length. Fracture of Net Area of Plate In the single plate specimens that were tested, the net area of the plate did not fracture. Only specimen 5 showed signs of approaching fracture of net section. Nevertheless, this failure mode has been observed in similar cases in sev- eral experiments on tee framing connections."^'^ The stem in a tee framing connection behaves similarly to a shear tab. The formula currently used in calculating net area in shear fracture is:^^ ^ns = A^g-n{dh-\-Vi6)tp (1) The studies of tee connections indicated that the shear fracture occurred consistently by fracture of net section along the edge of the bolt hole and not along the centerline of bolts. It was suggested that"^'^ the net area ef- fective in shear be equal to the average of net area along the bolt centerline and the gross area. Using the suggested method to calculate net area in shear, the effective net area in shear can be written as: Anse = A^g-{n/2){df, + Vl6)tp (2) Shear-Rotation Behavior Figure 9 shows the actual shear-rotation relationship that was recorded during each test. It is observed that the rotational ductility of the connections increased as the l ^ k r k h K 1 <H 1 1 7| f % % % J Fig. 7. Plate Bolt Hole Deformations after Tests Fig. 8. Failure of Welds and Bolts in Specimen 5 FIRST QUARTER/1989 25 number of bolts decreased. The rotational ductility of the connection in specimen 1 with 7 bolts was 0.026 radians which was about half the rotational ductility of the connec- tions in specimens 2, 3, 4 and 5 with three or five bolts, all of which were able to reach rotations in excess of 0.05 radians. Movement of Point of Inflection Figure 10 shows movement of point of inflection of the beam toward the support as the shear force was increased. Even under relatively small load, in all specimens, the point of inflection moved toward the support and re- mained almost stationary for the remainder of each test. Using experimental data, the following empirical equa- tion was developed to define the location of the point of inflection for test specimens. e = (n-l )(1. 0), in. (3) where n is the number of bolts used in the connection, and e is the distance of point of inflection from the support (i.e. from the weld line). It is important to realize that in the experiments re- ported here, the columns were fixed to supports and rigid body rotation of the connections was prevented. If due to frame action or other causes, the support to which a shear tab is connected rotates, due to rigid body rotation, the location of point of inflection may be affected. However, the concurrent values of shear and moment acting on the shear tab at any given time cannot exceed the values ob- tained from plasticity conditions (interaction curves) of plate for shear and moment. Behavior and Design of Bolts In all specimens, an examination of bolts and bolt holes after failure indicated that bolt shanks had experienced considerable shear deformations before failure. Studies on the behavior of single bolts in shear^^ have indicated that for A325 bolts and A36 plate, if the thick- ness of the plate is not greater than ^2 times the diameter of the bolt, considerable but tolerable bolt hole deforma- tions will take place. The Hmited bolt hole deformations are desirable since they increase rotational flexibility and ductility of the connections. In studies of tee connec- tions'^'^ in three specimens, Vi in. thick tee stems were used with Ys in. diameter bolts. The behavior of these tee specimens indicated that even when thickness of stem was equal to di, + Vie in., desirable bearing deformations took place in the bolt holes. Therefore, based on these studies, and to obtain flexible and ductile single plate connections, the thickness of the plate is recommended to be less than or equal to ^2 of the bolt diameter plus Vie in. An examination of the deformations of bolts and bolt holes at the completion of the tests indicated that the bolts were primarily subjected to direct shear accompanied by a small moment (see arrows in Fig. 6a). As Fig. 10 indicates, the point of inflection for test spec- imens was almost stationary, fluctuating between an ec- centricity of n and n 1 in. At the time of failure of the bolts in all specimens, the location of the point of inflec- tion was close Xo n 1 in. Therefore, it is recommended that bolts be designed for combined effects of direct shear and a moment equal to the shear multipHed by the eccen- tricity of the bolt line from point of inflection given by: e^ = {n-l)(1.0)-a (4) where, a = distance between the bolt line and weld line, e^ = distance from the point of inflection to the bolt line. Behavior and Design of Welds Table 2 gives values of shear and moment at failure for each test. The fillet welds mainly experienced a direct 200 0.02 0.04 0.06 ROTATION AT BOLT LINE, rad. 9- DC < LU X C/) 150 H 100 Test 1 (7-A325 Bolts) Test 2 (5-A325 Bolts) Test 3 (3-A325 Bolts) ^ Test 4 (5-A490 Bolts) 0 1I I I I I 11 11 I I I I I I I 11 11 0 10 20 30 40 50 DISTANCE OF PT. OF INFL. FROM WELD, in. Fig. 9. Shear-Rotation Curves for Test Specimens Fig. 10. Movement of Point of Inflection 26 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION shear accompanied by a relatively small moment. The strain measurements adjacent to the welds also supported this conclusion.^'^ Therefore, fillet welds are recom- mended to be designed for the combined effects of shear and a small bending moment. The main goal of the proposed design procedure is to ensure yielding of shear tab prior to failure of welds. In order to achieve this goal the welds should be designed to be stronger than the plate. Thus, the design shear force acting on the welds is recommended to be equal to the shear capacity of the plate and not the applied shear force. Therefore, the maximum shear force acting on the weld is equal to l/VS FyLptp. In Allowable Stress Design, the design shear force for welds is equal to 0.40i^L^r^. The moment acting on the weld is equal to shear force multi- pUed by the eccentricity of the point of inflection from the weld line. To be conservative, it is recommended that the eccentricity of the point of inflection from the weld line be equal to n inches. e^ = (n)(1.0) (5) Since the design of welds in the proposed method is a capacity design, it is not necessary to use welds that can resist forces much greater than the plate capacity. As part of phase two of this investigation, a study was conducted to establish minimum and maximum weld requirements to develop the strength of single plate. The study indicated that for A36 plate and E70 electrodes the weld size need not be more than 0.75^^ and should not be greater than tp. The upper limit of tp on the weld size was imposed to prevent excessive welding of the plate which will be costly and might cause heat damage to the plate without achiev- ing extra strength in the connection. Moment-Rotation Curves Moment-rotation curves for the test specimens are shown in Fig. 11. Moments and rotations were measured 1200' Specimens with A325 Bolts Specimens with A490 Bolts ^ Test 2 * Test 4 (5-Bolt) Test s (3-Bolt) 0.02 0.04 0.06 ROTATION OF BEAM END, rad. Fig. 11. Moment-Rotation Curves for Test Specimens along the bolt line. As the plots indicate, connections with fewer bolts developed smaller moments and exhibited larger rotational ductility. During the elastic range of be- havior, moment increased with shear. As the load in- creased, due to connection deformations, rotational stiff- ness and bending moment decreased and then gradually increased at a much smaller rate. The decrease is attrib- uted to slips and inelastic deformations in the connections and the increase is attributed to strain hardening. PROPOSED DESIGN PROCEDURE The following design procedure is based on the analyses of the experimental results and the information available on the actual behavior of shear connections.^'^'^ General Requirements The single plate framing connections covered by these procedures consist of a plate bolted to a beam web and welded to a support on one edge of plate. In design of a single plate framing connection, the fol- lowing requirements should be satisfied: 1. The connection has only one vertical row of bolts and the number of bolts is not less than 2 or more than 7. 2. Bolt spacing is equal to 3 in. 3. Edge distances are equal to or greater than l.Sdfy. The vertical edge distance for the lowest bolt is pre- ferred not to be less than 1.5 in. 4. The distance from bolt line to weld line is equal to 3 in. 5. Material of the shear plate is A36 steel to facilitate yielding. 6. Welds are fillet welds with E70xx or E60xx elec- trodes. 7. Thickness of the single plate should be less than or equal to db/2 + Vie. 8. The ratio of Lp/a of the plate should be greater than or equal to 2 to prevent local buckling of plate. 9. ASTM A325 and A490 bolts may be used. Fully tightened as well as snug tight bolts are permitted. The procedure is not appHcable to oversized or long slotted bolt holes. Standard or short-slotted punched or drilled holes are permitted. Consideration of Limit States in Design The following limit states are associated with the single plate framing connections. 1. Shear failure of bolts. 2. Yielding of gross area of plate. 3. Fracture of net area of plate. 4. Fracture of welds 5. Bearing failure of beam web or plate. FIRST QUARTER/1 989 27 Shear Failure of Bolts Bolts are designed for the combined effects of direct shear and a moment due to the eccentricity e^ of the reac- tion from the bolt line. The eccentricity e^, for single plate connections covered by these procedures can be assumed to be equal to 3 in., which is the distance from bolt line to weld line. The value is conservative when the single plate is welded to a rigid support. The value is more reahs- tic when the supporting member is a relatively flexible ele- ment. More realistic values for e^ can be calculated from the following equations: if single plate is welded to a rotationally rigid element, e^ is obtained from: et, = ( n- l ) ( 1. 0) - a (6) if single plate is welded to a rotationally flexible element, e^ is larger value obtained from: e^ = Max (n-l)(1. 0) -a (7a) a (7b) where, n = number of bolts a = distance from bolt line to weld Hne, in. e^ = eccentricity, in. By using methods outlined in Reference 7 including using Tables X of the AISC-ASD Manual^^ the bolts are designed for the combined effects of shear R, and moment equal to Re^. If the beam is coped, the block shear failure of the beam web also should be considered as discussed in the AISC- ASD Specification.^^ Weld Failure The welds connecting the plate to the support are de- signed for the combined effects of direct shear and a mo- ment due to the eccentricity of the reaction from the weld line, e^^. The eccentricity e^ is equal to the larger value obtained from: e^ = Max (n)(1.0) (16a) (16b) where, n = number of bolts e^ = eccentricity, in. a = distance from bolt line to weld line, in. By using met hods outlined in Reference 7 including using Tables XI X of the AISC-ASD Manual,^^ the fillet welds are designed for the combined effects of shear equal t o R and moment equal t o Re^. Bearing Failure of Plate or Beam Web To avoid reaching this hmit state, it is recommended that the established rule of horizontal and vertical edge distances equaling at least 1.5 the bolt diameter be fol- lowed. The bolt spacings should satisfy requirements of the AISC-ASD Specification.^^ The bearing strength of connection can be calculated using the provisions of the AISC-ASD Specification. 1^ Yielding of Gross Area of Plate The equation defining this limit state in allowable stress design (ASD) format is: where, f < F J vy '^ vy F,y = 0.40 Fy Ayg = Lp tp (8) (9) (10) (11) Fracture of Net Area of Plate The equation defining this limit state in allowable stress design (ASD) format is: where. J VU -* VM jvu ~ R I -^ns F, = 0.30 F As = [Lp - n{dh + Vi6)\tp (12) (13) (14) (15) Summary of Design Procedure The following steps are recommended to be taken in de- sign of single plate framing connections: 1. Calculate number of bolts required to resist combined effects of shear R, and moment Re^ using Table X of the AISC-ASD Manual. ^^ If the single plate is welded to a rotationally rigid sup- port ei, is the value obtained from Eq. 6. If the single plate is welded to a rotationally flexible ele- ment , eij is the value obtained from Eq. 7: 2. Calculate required gross area of plate: A,g>RI 0.40F^ (17) Use A36 steel and select a plate satisfying the following requirements: a. Ih and /^ > l.Sdi,. b. Lp > la C. tp < 4 / 2 + 1/16 d. tp > A^g /Lp e. Bolt spacing =3 in. (18) (19) (20) (21) 28 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION 3. Check effective net section: Calculate allowable shear strength of the effective net area: R,,==[Lp-n(d,+Vi6)](t,)(03F,) (22) and satisfy that R^s ^ R- 4. Calculate actual allowable shear yield strength of the selected plate: R, = LJ, (OAOFy) (23) Design fillet welds for the combined effects of shear Ro and moment Ro^^ using Table XIX of the AISC Manual. ^^ Cy^ is given in Eq. 16 as: ()(1.0) (16a) e^ = Max (16b) The weld is designed for a capacity of Ro, and not for the applied R, to ensure that the plate yields before the welds. However, for A36 steel and E70 electrodes the weld size need not be larger than VA of the plate thickness. 5. Check bearing capacity of bolt group: {n)(t)(d,){1.2F,) > R (24) If the bolts are expected to resist a moment (as they nor- mally would), this calculation should reflect the reduced strength as determined by Table X of the AISC Manual^^ as demonstrated in the following examples. 6. If the beam is coped, the possibility of block shear fail- ure should be investigated. Application to Design Problems The following examples show how the design procedure can be implemented into the design of steel structures. Design Example 1 Given: Beam: W27 x 114, t^ = 0.570 in. Beam Material: A36 steel Support: Column flange (Assumed rigid) Reaction: 102 kips (Service Load) Bolts: Vs in. dia. A490-N (snug tight) Bolt Spacing: 3 in. Welds: E70XX fillet welds Design a single plate framing connection to transfer the beam reaction to supporting column. Solution: 1. Calculate number of bolts: Shear = R = 102 kips Let us assume M = 0, (will be checked later) n = RI r= 102/16.8 = 6.1 Try 7 bohs The distance between the bolt fine and the weld line a is selected equal to 3 in. Check moment: ei, = (AZ-I)I. O - fl = 7 - 1 - 3 = 3.0 in. Moment = 3 x 102 = 306 kip-in. Using Table X of the AISC-ASD Manual^^ with eccentric- ity of 3 in., a value of 6.06 is obtained for effective number of bolts (7 bolts are only as effective as 6.06 bolts). Therefore, Rboit = 6.06 X 16.8 = 101.8 102 kips O.K. Use: Seven ^^ in. dia. A490-N bolts. 2. Calculate required gross area of the plate: A^g = R/ OAOFy A^g = 102/(0.40 X 36) = 7.08 in.^ Use A36 steel and select a plate satisfying the following requirements: a. Ih and /^ > 1.5J^ lh = K = 1.5(y8) = 1.32 in. W=f l H- 4 = 3 + 1.32 = 4.32; use W = 41/2 i n. b. Lp/a > 2.0 Lp = 2 X 1.32 + 6 X 3.0 = 20.6 in.; use Lp = 21 in. Check: Lp/a = 21/3 = 7 > 2 O.K. c. tp < db/2 + Vi6 tp < (y8)/ 2 + 1/16 = 1/2 i n. d. tp = Ayg /Lup tp = 7.08/21 = 0.337 in. Try PL 21 x Vs x 4-1/2 3. Calculate allowable shear strength of the net area: R,, = [Lp~n(d, + Vi6)]{tp){03F,) Rns = [21-7(7/8 + Vi6)](y8)(0.3 X 58) = 94 < 102 kips N.G. Try Vz in. thick plate: R^s = [21-1 {Vs + Vi6)](i/2)(0,3 X 58) = 125 > 102 kips. O.K. Use: PL 21x1/2x4^2, A36 Steel. 4. Calculate the actual allowable yield strength of the se- lected plate: Ro = Lptp {OAOFy) Ro = 21 X 0.5 X 0.40 X 36 = 151 kips Design fillet welds for the combined effects of shear and moment: Shear = R^ = 151 kips ^H; = Max n{1.0) = 7(1.0) = 7 in. a = 3 in. Therefore, e^ = 7.0 in. Moment = R^e^ = 151 x 7 = 1057 kip-in. Using Table XIX AISC Manual^^ FIRST QUARTER/1 989 29 a = 7/21 = 0.333 Ci = 1.0 C = 1.07 Di6 = RolCCiLp = 151/(1.0 X 1.07 x 21) = 6.72 Since weld size need not be greater than 0.75tp, Use: % in. E70 Fillet Welds. 5. Check bearing capacity: For plate: r^ = dbtp (1.2FJ = .875 x .5 x 1.2 x 58 = 30.45 Rt,rg = 6.06(30.45) = 184.5 kips > 102 kips. O.K. Since the beam web is thicker than the plate, the web will not fail. 6. Beam is not coped, therefore, there is no need for con- sideration of block shear failure. Design Example 2 Given: Beam: Beam Material Support: Reaction: Bolts: Bolt Spacing: Welds: W16X31, t^ = 0.275 A572 Gr. 50 steel Condition of support is unknown 33 kips (Service Load) 3/4 in. dia. A325-N or A490 (snug tight) 3 in. E70XX fillet welds Design a single plate shear connection to transfer the beam reaction to the support. Solution: 1. Calculate number of bolts: Shear = 33 kips Let us assume M = 0, (will be checked later) Try A325-N bolts with 9.3 kips/bolt shear capacity: n = Rl r^ = 33/9.3 = 3.5 Try 4 bolts. The distance between bolt line and weld line a is selected equal to 3 in. Check moment: Since condition of support is not known, the sup- port is conservatively assumed to be flexible for bolt design. Therefore e^ is equal to 3 in. Moment = 3 x 33 = 99.0 kip-in. Interpolating from Table X^^ C -= 2.81 Rail = 2.81 X 9.3 = 26.1 kips < 33 N.G. Which indicates 4 A325 bolts are not enough. Let us try 4 A490-N bolts: Rail = 2.81 X 12.4 = 34.8 kips > 33 O.K. Use: Four % in. dia. A490-N bolts, 2. Calculate required gross area of plate: A^g = R/ OAOFy A^g = 33/(0.40 X 36) = 2.29 in.^ Use A36 steel and select a plate satisfying the following requirements: a. 4 ^^^ h l-5(i^. lh = K = 1.5(3/4) = 1.125 in. W=f l + 4 = 3 + 1.125 = 4.125 in. Use: W = 4V2 in. b. Lp/a > 2.0 L^ = 3 + 3 X 3 = 12 in. Check: Lp/a = 12/3 = 4 > 2 O.K. c. tp < 4 / 2 + 1/16 tp < (y4)/2 + 1/16 = yi6 in. d. tp = A^g ILp tp = 2.29/12 = 0.19 in. Use: PL 12xV4x4V2, A36 Steel. 3. Calculate allowable shear strength of the net area: R,, = [Lp-n(d, + Vi6)](g(0.3Fj R^s = [12 - 4(3/4 + i/i6)](y4)(0.3 X 58) = 38.1 kips R^s ^ ^ is satisfied. 4. Calculate actual allowable yield strength of the selected plate: R, = Lptp (0.40F,) Ro= llx 0.25 X 0.40 X 36 = 43.2 kips Design fillet welds for the combined effects of shear and moment: Shear = Ro = 43.2 kips e^ = Max (n)(1.0) 4(1.0) = 4 in. = 3.0 Therefore, e^, 4.0 in. Moment = R^e^ = 43.2 x 4 = 172.8 kip-in. Using Table XIX AISC Manual^^ a = 4/12 = 0.33 Ci = 1.0 C = 1.07 D16 = RJCCiLp = 43.2/(1.0 X 1.07 x 12) = 3.36 Since weld size need not be greater than O.lStp, Use: 3/16 in. E70 Fillet Welds. Check bearing capacity. For plate: ndf^tp (1.2FJ = 2.81 x .75 x .25 x 1.2 x 58 = 36.7 kips > 33 kips, and for beam: ndi,t^{l.2F^) = 2.81 x .75 x .27 x 1.2 x 65 = 44.4 kips > 33 kips. Beam is not coped, therefore, no need for considera- tion of block shear failure. CONCLUSIONS Based on the studies reported here, the following con- clusions were reached: 1. The experimental studies of single plate connections in- 30 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION dicated that considerable shear and bearing yielding occurred in the plate prior to the failure. The yielding caused reduction of the rotational stiffness which in turn caused release of the end moments to midspan of the beam. 2. The limit states associated with single plate connections are: a. Plate yielding. b. Fracture of net section of plate. c. Bolt fracture. d. Weld fracture. e. Bearing failure of bolt holes. 3. A new design procedure for single plate shear connec- tions is developed and recommended. The procedure is based on a concept that emphasizes facilitating shear and bearing yielding of the plate to reduce rotational stiffness of the connection. 4. To avoid bearing fracture, the horizontal and vertical edge distance of the bolt holes are recommended to be at least 1.5 times diameter of the bolt. The study re- ported here indicated that vertical edge distance, par- ticularly below the bottom bolt is the most critical edge distance. 5. Single plate connections that were tested were very ductile and tolerated rotations from 0.026 to 0.061 radi- ans at the point of maximum shear. Rotational flexibil- ity and ductility decreased with increase in number of bolts. ACKNOWLEDGMENTS The project was supported by the Department of Civil Engineering, the University of California, Berkeley and the American Institute of Steel Construction, Inc. The support and constructive comments provided by R. O. Disque, N. Iwankiw and Dr. W. A. Thornton are sin- cerely appreciated. Single plates used in the test speci- mens were fabricated and supplied by the Cives Steel Company. The assistance of R. Stephen, laboratory man- ager, in conducting the experiments was essential and is appreciated. REFERENCES 1. Astaneh, A., "Experimental Investigation of Tee- Framing Connection", Progress Report submitted to American Institute of Steel Construction, April 1987. 2. Astaneh, A., "Demand and Supply of Ductility in Steel Shear Connections", Journal of Steel Construc- tion Research, 1989. 3. Astaneh, A., K. M. McMullin, and S. M. Call, "De- sign of Single Plate Framing Connections," Report No. UCB/SEMM-88/12, Department of Civil Engi- neering, University of California, Berkeley, July, 1988. 4. Astaneh, A., and M. Nader, "Design of Tee Framing Shear Connections," Engineering Journal, American Institute of Steel Construction, First Quarter, 1989. 5. Astaneh, A., and M. Nader, "Behavior and Design of Steel Tee Framing Connections," Report No. UCBI SEMM-88111, Department of Civil Engineering, Uni- versity of California, Berkeley, July, 1988. 6. Call, S. M., and A. Astaneh, "Behavior of Single Plate Shear Connections with A325 and A490 Bolts", Report No. UCB/SEMM-89/04, Department of Civil Engineering, University of California, Berkeley, April 1989. 7. Iwankiw, N. R., "Design for Eccentric and Inclined Loads on Bolts and Weld Groups," Engineering Jour- nal, American Institute of Steel Construction, 4th Quarter, 1987. 8. Lipson, S. L., "Single-Angle Welded-Bolted Connec- tions," Journal of the Structural Division, March, 1977. 9. McMullin, K. M., and A. Astaneh, "Analytical and Experimental Investigations of Double-Angle Con- nections", Report No. UCBISEMM-88114, Depart- ment of Civil Engineering, University of California, Berkeley, August, 1988. 10. Patrick, M., I. R. Thomas, and I. D. Bennetts, "Test- ing of the Web Side Plate Connection," Australian Welding Research, December, 1986. 11. Richard, R. M., P. E. Gillett, J. D. Kriegh, and B. A. Lewis, "The Analysis and Design of Single Plate Framing Connections," Engineering Journal, Ameri- can Institute of Steel Construction, 2nd Quarter, 1980. 12. White, R. N., "Framing Connections for Square and Rectangular Structural Tubing, Engineering Journal, American Institute of Steel Construction, July, 1965. 13. American Institute of Steel Construction, Manual of Steel Construction, 8th Edition, Chicago, 1980. 14. American Institute of Steel Construction, Manual of Steel Construction. LRFD, 1st Edition, Chicago, 1986. 15. American Institute of Steel Construction, Inc., Speci- fication for the Design, Fabrication and Erection of Structural Steel for Buildings, Chicago, November 13, 1978. 16. American Institute of Steel Construction, Inc., Load and Resistance Factor Design Specification for Struc- tural Steel Buildings, Chicago, September 1, 1986. FIRST QUARTER/1 989 31 A Ayg c Ci NOMENCLATURE Net area in shear, in.^ Effective net area of plate in shear, in.^ Gross area of plate in shear, in^. Coefficient in the AISC Manual Tables X and XIX Coefficient in the AISC Manual Table XIX Number of sixteenth of an inch in fillet weld size Specified minimum tensile strength of steel, ksi F^y Allowable shear stress for plate in yielding = 0.40F^, ksi F^u Allowable ultimate shear strength = 0.30F^, ksi Fy Specified yield stress of steel, ksi L Length of span, in. Lp Length of plate, in. Mp Plastic moment capacity of cross section = Z^Fy My R ^bolt Ro R. Yield moment of beam cross section, kip-in. Reaction of the beam due to service load, kips Allowable shear capacity of bolt group Allowable shear fracture capacity of the net section Allowable shear yield strength of plate, kips Reaction corresponding to plastic collapse of beam, kips Sx Section modulus in.^ V Shear force, kips W Width of pl at e, in. Zx Plastic section modulus, in.^ a Coefficient in the AISC Manual Table XIX a Distance between bolt line and weld line, in. d Dept h of beam, in. dh Di amet er of bolt, in. e Eccentricity of point of inflection from the support e^ Eccentricity of beam reaction from bolt line, in. ^w Eccentricity of beam reaction from weld line, in. fyy Comput ed shear stress in plate gross area, ksi f^u Comput ed shear stress in plate effective net area, ksi Ih Horizontal edge distance of bolts, in. l^ Vertical edge distance of bolts, in. n Number of bolts r^ Allowable shear strength of one bolt, kips tp Thickness of plate, in. ty^, Thickness of beam web, in. 32 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION