Extended single-plate shear connections (Figure 1) offer

Transcription

1 Desig of Ustiffeed Exteded Sigle-Plate Shear Coectios LAY S. MUI ad CHISTOPHE M. HEWITT Exteded sigle-plate shear coectios (Figure 1) offer may advatages that simplify the costructio process. Because the coectio to the supported member is moved clear of the support, copig of the supported member is ot required ad the oly fabricatio process required for the supported member is drillig or puchig. Also, because bolted coectios are oly used i the coectio to the supported member, there is o safety cocer over the use of shared bolts through the web of the support. Additioally, i some istaces, exteded sigle-plate coectios are the oly practical solutio to a framig problem, such as the case of a member framig ito the weak axis of a colum with cotiuity plates. The rigidity of sigle-plate coectios at the support has always bee a gray area. Desigers have ofte bee cocered about a cosiderable, uaticipated momet that could be developed i the coectio, which could the Fig. 1. Exteded sigle-plate shear coectio. Larry S. Muir is presidet, Cives Egieerig Corporatio, ad chief egieer, Cives Steel Compay, oswell, GA. Christopher M. Hewitt is seior egieer, America Istitute of Steel Costructio, Ic., Chicago, IL. result i either a momet delivered to the colum that the colum has ot bee desiged to resist or a sudde rupture of either the weld or the bolts. Sectio B3.6a of the AISC Specifi catio for Structural Steel Buildigs, hereafter referred to as the AISC Specifi catio, requires that simple shear coectios have sufficiet rotatioal capacity to accommodate the required beam ed rotatio. This paper will address each of these cocers ad will preset a geeral desig procedure for exteded sigle-plate shear coectios. This paper outlies the backgroud ad developmet of the desig procedure for exteded sigle-plate shear coectios preseted i the 13th Editio AISC Steel Costructio Maual, hereafter referred to as the AISC Steel Maual. While the method preseted i this paper has bee determied by the AISC Committee o Mauals ad Textbooks to be suitable for all cases, other ratioal methods may be used at the discretio of the desiger. HISTOY OF USE AND ESEACH Exteded sigle-plate shear coectios have a log history of use. Illustratios of the use of exteded sigle-plate shear coectios have bee icluded i the AISC Steel Maual sice 199, ad they have bee used by desigers for several decades. Despite a relatively log history of use, a welldefied, simple ad ratioal desig procedure has ever bee icluded i the AISC Steel Maual, ad the desig procedure was largely left to the discretio of idividual egieers. Fearig that the plate might buckle or that the weld might fracture, may desigers have chose to detail the coectios with top ad bottom stiffeig plates or to exted the plate ad coect it to the top ad bottom flages of a supportig girder (Figure ). Iroically, testig has show that extedig the plate vertically i this maer could actually result i a lower plate bucklig stregth (Sherma ad Ghorbapoor, 00) ad is, i may cases, uecessary. Sherma ad Ghorbapoor (00) coducted testig o exteded sigle-plate shear coectios ad also proposed a desig procedure. The procedure is predicated o the use of top stiffeig plates ad a sigle colum of bolts. The bolts are desiged based o a empirically derived eccetricity related to the umber of bolts, similar to the cotemporary desig procedure for covetioal sigle-plate shear coectios. Strogly tied to the empirical test data, the procedure does ot adequately address the eeds of the practicig egieer for all cases. ENGINEEING JOUNAL / SECOND QUATE / 009 / 67

2 ESTABLISHING A MODEL FO THE CONNECTION DESIGN A beam coected to a support by a sigle-plate shear coectio is a idetermiate system. The momet applied to the coectio will deped o may factors, icludig the distace that the coectio exteds from the support ad the relative stiffesses of the supported beam, the coectio ad the support. Though it might be assumed that the momets at the support are bouded by those predicted by the pied-ed beam model at the low ed, ad those predicted by the fixed-ed beam model at the high ed, eve this is isufficiet. There is a possibility that the support, or coectio, at oe ed of the beam could be quite flexible, while the other ed is extremely rigid. I such a case the stiffer ed would be subjected to a momet greater tha the fixed-ed beam momet. The upper boud the becomes the momet developed at the fixed ed of a propped catilever. Eve if the stiffesses of the supports ad the beam could be reliably predicted, determiig the stiffess of the coectio is problematic. Not oly must the stiffess of the plate be determied, but factors such as bolt slip ad bearig deformatio must also be accouted for i order to accurately predict the distributio of the momets i the system. Without a accurate predictio of the momet distributio, establishig a desig procedure for the coectio might seem itractable. Fortuately, istead of tryig to predict the behavior of the coectio i service, a assumed model ca be established ad the steps ca be take to cotrol the behavior to support the assumptios. This approach is supported by the lower boud (static) theorem, which states: If a equilibrium state ca be foud which does ot violate the yield coditio, the however ulikely that state may seem to be, the structure is safe. (Baker ad Heyma, 1969) Thus, the applied exteral forces i equilibrium with the iteral force field are less tha or, at most, equal to the applied exteral force that would cause failure, provided that all the limit states are satisfied ad sufficiet ductility exists to allow redistributio of the forces. The most logical model to use is the pied-ed beam model (Figure 3) sice it replicates the typical assumptios made durig the mai member desig. The pied-ed model assumes that the coectio delivers oly the shear reactio from the supported beam to the support. Based o this assumptio, the bolt group will be subjected to a momet equal to the shear reactio multiplied by the distace from the support to the ceter of the bolt group. ANTICIPATED BEHAVIO As stated earlier, the lower boud theorem is predicated o sufficiet ductility beig preset to redistribute the loads. To accomplish this, the plate, as the most ductile elemet i the coectio, is used as a fuse to shed uwated momets prior to rupture of either the bolts or the weld. To describe this behavior the system ca be modeled as a fixed-ed beam of varyig cross sectio. As the beam is loaded momets will be produced at supports, resultig i a momet diagram similar to Figure 4. As the load icreases, the possibility exists that the coectio will be subjected to a momet greater tha its yield Fig. 3. Simply supported beam model. Fig.. Sigle-plate shear coectio legtheed to coect to top ad bottom fl ages of support. Fig. 4. Momets o a fi xed-ed beam. 68 / ENGINEEING JOUNAL / SECOND QUATE / 009

3 stregth. If this occurs, the plate will begi to yield ad it will shed the excess momet to the beam, thereby relievig momet from both the coectio ad the support. The momet distributes to the beam because the yieldig of the plate effectively lowers the plate s stiffess. This ca be see by examiig the stress-strai curve for steel (Figure 5). Whe the plate is first loaded its modulus of elasticity, E, is 9,000 ksi. However, as it is loaded beyod the yield stress, the stress-strai curve is o loger liear, ad the behavior is better predicted by the taget modulus of elasticity, E T, which will be sigificatly lower tha E. SIZING THE PLATE FO STENGTH AND DUCTILITY I order for the plate to act as a fuse, as described earlier, it must yield without rupturig the bolts or the welds ad must possess sufficiet stregth to support the required loads, thereby settig both a lower ad a upper limit o the plate thickess. Determiig the miimum required thickess is straightforward. The limit states of gross shear yieldig, et shear rupture, gross flexural yieldig, ad et flexural rupture all must be satisfied. The plastic sectio modulus is used i checkig both flexural yieldig ad rupture. This is supported by recet test results (Mohr, 005). Though ot preseted as a limit state i the AISC Specifi catio, it is recommeded Stress Modulus of Elasticity Strai (a) Strai (b) Fig. 5. (a) Stress-strai ad (b) modulus of elasticity-strai curves for steel (based o taget modulus). that shear ad bedig iteractio be checked. This is doe by applyig the vo Mises yield criterio: f v fa ϕ v06. Fy + ϕ afy 10. This ca be rewritte i terms of the omial reactio,, as: 4a dt p dt p 10. v06. Fy a F y Fdt y a d where φ = 0.90 Ω = 1.67 It should be oted that the curret AISC procedure recommeds calculatig a reduced bedig stregth related to the applied shear. The AISC approach, also based o the vo Mises yield criterio, is theoretically equivalet to the precedig procedure. However, sice the AISC equatio, Fcr Fy 3 fv, icludes both resistace ad load terms o the right side of the equatio, it may be cumbersome to apply. Block shear ad et shear must also be checked i accordace with Sectios J4.3 ad J4.b of the AISC Specificatio. Additioally, sice the edge of the plate i compressio may buckle, a stability check must be performed usig the relatioship (Muir ad Thorto, 004): ϕf cr = 0.90F y Q where Q = 1 for λ 0.7 Q = ( λ) for 0.7 < λ 1.41 Q = (1.30/λ ) for λ > 1.41 d Fy d 10t p a If λ is less tha or equal to 0.7, the limit state of plate bucklig will ot cotrol. It is advisable to size the plate to prevet this limit state. However, if plate buckig must be cosidered as a cotrollig limit state, it is recommeded that the elastic sectio modulus be used as a coservative method of calculatig of the applied bedig/bucklig capacity of the plate. p ENGINEEING JOUNAL / SECOND QUATE / 009 / 69

4 Aother possible cocer is the torsioal restrait provided by the exteded coectio. Most beam desigs assume that the beam has full torsioal ed restrait. I terms of torsioal restrait, the exteded sigle-plate shear coectio is very similar to a beam coped at the top ad the bottom flages. As with the case of a coped beam, if a slab is preset, there should be little cocer over the torsioal restrait of the coectio. However, where torsioal restrait is a cocer, it ca be checked usig the procedure preseted by the Australia Istitute of Steel Costructio (Hoga ad Thomas, 1988). The flexural rupture stregth of coectio elemets was ivestigated by Murray ad Mohr (Mohr, 005). It may be oted that durig this testig, a restraiig bolt was istalled i the plates to prevet bucklig prior to developig the full plastic stregth of the member. A review of their data idicates that the values for λ varied from a low of to a high of The precedig theory would ot have predicted the bucklig i ay of the plates. However, there is a importat distictio that ca be made betwee the Murray ad Mohr tests ad exteded sigle-plate shear coectios. The Murray ad Mohr tests were desiged to cause a uiform bedig momet o the plates i order to test the momet capacity i the absece of ay other factors. It has bee show that for a plate subjected to uiform bedig, the critical legth at which bucklig will occur quickly decreases as the sectio progressively yields. For ouiform bedig, the decrease is much less proouced ad is egligible for catilevers. (Baker, Hore, ad Heyma, 1956). A exteded sigle-plate shear coectio will ot be subjected to uiform bedig throughout its legth ad, like a beam desiged usig the plastic sectio modulus, will rarely, if ever, experiece appreciable yieldig i service. Bucklig was ot a sigificat problem i either the Murray ad Metzger (Metzger, 006) tests or the Sherma ad Ghorbapoor (00) tests. Bucklig was give as a failure mode for oly three of the tests i the Sherma ad Ghorbapoor regime, i two cases where the tab plate was exteded to allow weldig to the bottom flage of the support beam ad a third where it is listed as a secodary effect of twist (Sherma, 00). As stated previously, the plate acts as a fuse to protect both the bolts ad the welds from rupture, thereby allowig the momets to redistribute i a acceptable maer. I order to safeguard the weld, the plate must yield prior to the weld fracturig. Prior to the 13th Editio AISC Steel Maual, AISC required that the welds to the support be sized as at least w of the plate thickess. This requiremet was developed to esure that the plate would yield before the weld yielded (Astaeh, 1989). I the latest procedure, this recommedatio has bee modified, ad the ew procedure recommeds that the plate be sized to yield before the weld ruptures. This is a more logical approach, as weld yield is ot a well-defied limit state, ad joit separatio will ot occur util the weld ruptures. The modified requiremet calls for the weld be equal to or greater tha s of the plate thickess. The s t p requiremet is derived here ad was verified by testig (Metzger, 006), as is discussed later i this paper. I the derivatio, the rupture stregth of the weld is assumed to be F EXX. This is more coservative tha the stregth of a trasversely loaded fillet weld reflected i the AISC Steel Maual of 1.5(0.6)F EXX, but results i a closed-form solutio to the problem. It also matches well with the 006 America Weldig Society (AWS) requiremet.4.1.3, which is iteded to prevet the uzippig of welds at tubular coectios. AWS states that the ultimate breakig stregth of fillet welds with 60 ksi or 70 ksi tesile stregth shall be take as.67 times the basic allowable stress. This results i a stress of.67(0.3)(70) = 56.1 ksi compared to (70) = 57.1 ksi with the more coveiet value assumed i this paper to obtai a closed-form solutio. William A. Thorto (upublished) origially proposed this approach prior to the AISC Steel Maual adoptig a icreased stregth for trasversely loaded fillets. The required weld ca also be derived usig the stregth specified i the AISC Steel Maual, but a closed-form solutio caot be obtaied (though the solutios boud a somewhat smaller required weld, as would be expected.) As stated previously, the rupture stregth of the weld is assumed to be F EXX. From this, the shear stregth o the weld ca be calculated as: 1 1 F F F F shear u EXX EXX The iteractio equatio for the weld is: 1 wlw wlwf 3 EXX 3 Solvig for yields: F EXX e 1 wl F w 3 3 wl F w e w L w 1 4 EXX EXX e 3 16 L w 10. F 3 EXX 70 / ENGINEEING JOUNAL / SECOND QUATE / 009

5 Similarly for the plate, the iteractio equatio is: V u Mu Vp 10. Mp e tl F y tlf p w p w y 3 4 Solvig for yields: tlf p w y e 3 16 L w Sice the plate must yield before the weld fractures, the followig must be true: tlf p w y e 3 16 L w wl F w EXX Solvig for the weld size, w, yields: w tf p y F 9 e 4 1 L w EXX Assumig F y = 50 ksi ad F EXX = 70 ksi yields: 3 5 w tp t 8 I a similar fashio, the plate safeguards the bolt group by yieldig prior to bolt shear. To esure that this takes place, a maximum plate thickess is determied based o the stregth of the bolt group. To determie the momet stregth of the bolt group, the istataeous ceter of rotatio method is used. To obtai the maximum momet capacity of the bolt group, a momet-oly coditio is assumed. The istataeous ceter of rotatio coicides with the ceter of gravity of the bolt group ad the stregth ca be calculated as: where C' Li 1 e Mmax 15. Fv AbC' Li max 10 Lmax 055. p It should be oted that the bolt shear stregth give i Table J3. of the AISC Specifi catio icludes a 0% reductio to accout for the ueve force distributio that occurs i ed loaded bolt groups (Kulak, 1987). Sice this bolt group is ot ed loaded, the 0% stregth reductio ca be eglected. This is the origi of the 1.5 factor precedig the equatio. It should also be oted that this is a check to esure ductility ad ot stregth; therefore, safety factors have ot bee applied to capacities of either the bolts or the plate. This is similar to the approach used for the weld ductility check show previously. Oce the momet stregth of the bolt group is determied, it ca be compared to the flexural yield stregth of the plate to obtai a maximum plate thickess: t max M 6 Fd y The elastic sectio modulus is used i this check because the plate will begi to redistribute stress after first yieldig. SIZING THE BOLT GOUP Assumig a pied-ed beam model that delivers oly shear to the face of the support, the momet that exists o the bolt group ca be calculated as: M bolt e The stregth of bolt group ca be calculated i the typical fashio, usig the istataeous ceter of rotatio method. Though the bolt group is ot ed loaded, the 0% bolt shear stregth reductio iheret i the AISC Specifi catio caot be eglected whe desigig for stregth i practice. Accoutig for the 0% reductio is a requiremet of the AISC Specifi catio as curretly writte, although from a theoretical stadpoit the reductio is ot ecessary i this case. max SUPPOT OTATION esistace of the support agaist rotatio is ofte questioed whe exteded sigle-plate shear coectios are used. I the curret desig procedure, because all of the coectig elemets are desiged to resist or otherwise accommodate the etire rage of aticipated momets, support rotatio ad coectio deformatio from the plate ad bolts are serviceability ad ot stregth cosideratios. Whe a rigid support coditio exists, all sigificat rotatio of the beam ed is accommodated by deformatio of the plate ad the bolt group, ad serviceability eed ot be cosidered. A rigid support is oe i which the support ad the coected beam ted to stay i place or rotate i the same directio. A rigid support may geerally be assumed i ay of the followig cases: ENGINEEING JOUNAL / SECOND QUATE / 009 / 71

6 Table 1. Vertical Deflectios Due to Short Slotted Holes Δ The sigle-plate coectio is attached to a colum flage. Sigle-plate coectios are framed to both sides of a girder or colum web. A structural slab is preset, attachig to both the girder ad the beam flages. The torsioal resistace of the girder provides sufficiet rotatioal restrait. If the support is cosidered flexible, cosideratio must be give to the serviceable rotatio limit for the coectio. Serviceability merits greater cocer whe short slots are used at a flexible support. It should be oted, however, that the rotatio allowed eve by short slots is limited by the geometry of the coectio. For a coectio with a sigle colum of bolts, the agle of rotatio ca be approximated as: L ta 1 s db 1 s holes, which will result i a theoretical deflectio of about c i. With two or more colums of bolts, the additioal geometrical restrait reduces the rotatio by a factor of 4, effectively elimiatig the problem (Figure 6). I typical cases, the slab, whe cured, ca provide the ecessary resistace to rotatio. Prior to curig, the rotatio caused by the dead load must be resisted by the bolted coectio aloe actig as a slip-critical coectio. For this reaso, if excessive support rotatio durig erectio is a cocer, the bolts should be pretesioed ad a miimum of a Class A fayig surface should be preset whe short slots are used. It should be oted that the worst case for ay serviceability problems is a coectio utilizig a sigle colum of bolts with two rows. As either the umber of rows or colums of bolts are icreased, the rotatio allowed by the movemet i the holes drops off quickly, so that there would be essetially o problems for ay coectios with a double colum of bolts, ad the rotatio of coectios with sigle colums of bolts is oly a cocer whe less tha about five rows are employed. The upper boud of the momet to be resisted by the bolts is defied by the desig resistace of the coectio, which is desiged for bearig ad factored dow to iclude oly the dead load. The required relatioship ca be writte as: C sc ' e 1 C v L/D The ratio of the slip resistace with a Class A fayig surface to the shear stregth of a ASTM A35X bolt is approximately: sc v Dh TN F A u sc b s v b ksi ( 075. )( 60ksi) d b d b 1 The vertical deflectio caused by the rotatio will be approximately equal to: ta e e Ls db 1 s The resultig vertical deflectios, give a 10-i. eccetricity ad 1-i.-diameter bolts i short-slotted holes spaced at 3 i., are as listed i Table 1. Assumig a 4 i. of deflectio ca be tolerated, rotatio problems do ot exist as log as at least five rows of bolts are provided. The limit of 4 i. is derived from the suitable performace history of stadard shear tabs with short-slotted (a) Fig. 6. otatioal restrait provided by (a) sigle colum of bolts ad (b) double colum of bolts. (b) 7 / ENGINEEING JOUNAL / SECOND QUATE / 009

7 It should be oted that i this ratio, the bolt pretesio is take to be 70% of the omial tesile stregth of the bolt istead of the values give i the AISC Specifi catio. This is doe to provide a closed-form solutio to the problem. The ratio for ASTM A490 bolts is similar. It ca also be show that the ratio of C' to C is approximately 10 for eccetricities of 9 to 10 i. From this, a maximum eccetricity, e, ca be calculated as: e = (1 + L/D)0.471(10) = 4.71(1 + L/D) I the formulatio of the origial LFD Specifi catio, a live-to-dead load ratio of 3 was assumed. Usig the same assumptio here results i a maximum eccetricity of 17.8 i. Sice this is greater tha the typical eccetricity used i practice, the coectio will experiece o serviceability problems before the cocrete is cured, so log as pretesioed bolts are used with a Class A fayig surface. Eve with a live-to-dead load ratio as low as 1.5, serviceability will ot be a problem for eccetricities up to 10 i. Of course, oce the cocrete has cured, the coectio may be subjected to the full live ad dead loadig. Serviceability must be cosidered for this case as well, though a differet model ca be used. A couple cosistig of a tesio force at the bolt group ad a compressio force i the slab will resist the rotatio caused by the eccetric gravity loads. Agai cosiderig a upper boud defied by the desig resistace of the coectio i bearig, the required relatioship for a bolt spacig of 3 i. is: sc 3 i. Ce v Agai recogizig the ratio of the slip resistace with a Class A fayig surface to the shear capacity of a ASTM A35 bolt is: We fid that: sc v Cee 14. C Table. Allowable Eccetricity with Cured Cocrete Slab e o slab C e with slab (i.) Lookig at the worst case, a two-row coectio, the resultig eccetricities are show i Table. Table demostrates that the eccetricity that ca be resisted assumig model (c) i Figure 7 is greater tha or equal to the eccetricity that the bolt group would be desiged to resist as a bearig coectio. Therefore, excessive support rotatio ad vertical deflectios are ulikely to occur i practice whe the assumed coditios are met. The precedig discussio emphasized the effects of support rotatio as it applies to a urestraied support. I such cases, the support is assumed to have o stiffess, ad o momet is resisted by the support. The problem is strictly oe of serviceability. However, the report issued by Sherma ad Ghorbapoor (00) addressed a web mechaism limit state. The web mechaism was created whe the momet resistace of the colum was mobilized through deformatio of the colum web. Sice the desig procedure i the AISC Steel Maual sizes the compoets to resist the full (a) (b) (c) Fig. 7. Support rotatio at short slotted holes. (a) Support restraied by bolts slippig ito bearig. (b) Support restraied by slip resistace to momet. (c) Support restraied by slip resistace to tesio ad compressio i slab. ENGINEEING JOUNAL / SECOND QUATE / 009 / 73

8 eccetricity at the bolted coectio, the rotatioal resistace of the support is ot required to resist the desig loads. The rotatio is therefore limited to the simple beam ed rotatio (usually assumed to be o the order of 0.03 radia) ad the rotatio allowed by the bolt slip i the holes ad bearig deformatios i the plates ad the bolts. Sice this deformatio is self-limitig, it is oly a serviceability cocer. The limited rotatio that results from the AISC procedure ca be see by examiig a plot of shear versus rotatio from the Sherma ad Ghorbapoor test 1-U (Figure 8). I this test, the girder rotated more tha 9 degrees. This obviously exceeds the rotatio predicted by simple beam ed rotatio ad coectio slip. However, whe the predicted capacity from the AISC Steel Maual is show (represeted by the heavy horizotal lie), it ca be see that the resultig support rotatio is limited to less tha 3 degrees. The combied rotatio that could be expected from the simple beam ed rotatio, ad the coectio slip would be about 4 degrees. Limitig the applied load to the desig capacity istead of the omial capacity would result i a further decrease i the support rotatio. COMPAISON TO TEST ESULTS There is data available from 13 tests performed o ustiffeed, exteded sigle-plate coectios. Sherma ad Ghorbapoor (00) preseted the results of eight tests. Murray ad Metzger (Metzger, 006) performed five additioal tests sposored by Cives Steel Compay. The plates i seve of the tests coformed to the parameters of the desig procedure preseted i this paper. However, all of the Sherma tests used a weld equal to w of the plate thickess, ad all of the Murray tests used a weld equal to the plate thickess. The objective of the Sherma ad Ghorbapoor project Fig. 8. Plot of shear versus rotatio for the Sherma ad Ghorbapoor test 1-U. was to develop a desig procedure for exteded sigle-plate coectios. The objective of the Murray ad Metzger testig program was to verify the procedures cotaied i the AISC Steel Maual for both covetioal ad exteded sigle-plate coectios. A special emphasis of the Murray ad Metzger testig was to validate the reductio i required weld size from w of the plate thickess to s of the plate thickess. Thus, the available test data represet a wide spectrum of coditios. The sigle-plate coectios i the Sherma testig were all attached to the webs of either colums or girders ad are represetative of coectios with flexible supports, where the bolts would ted to be the more critical tha the welds. The Murray sigle-plate coectios were all attached to the flage of a W14 90 ad are represetative of coectios with rigid supports, where the welds would ted to be the more critical tha the bolts. As ca be see i Table 3, the desig procedure cotaied i the AISC Steel Maual provides a good margi of safety. Though ot typically cosidered i the desig of shear coectios, oe failure mode emphasized i the work of Sherma ad Ghorbapoor, which is ot explicitly cosidered i the curret desig procedure, is that of plate twist. Two tests, -U ad 4-U, are reported as havig failed primarily by twistig of the plate. Work by Beetts, Thomas, ad Grudy (1981) ivestigated shear coectios with the specific goal of developig a uderstadig of the torsioal behavior of shear coectios due to the eccetricity of load betwee the coectig plates ad the adjacet beam web. This ivestigatio icluded testig to determie the torsioal stiffess of may types of shear coectios, icludig exteded sigle-plate coectios. I that work, the researchers showed that sigle -plate coectios maitai the majority of their torsioal rigidity util the plate yields, at which time, as oe might expect, the torsioal rigidity of the coectio decreases ad the twist of the coectio becomes apparet. To desig for this effect, the limit state of twist i the ew desig procedure is implicitly checked cosiderig the vo Mises iteractio of forces o the plate, which esures that the plate does ot yield i the presece of shear forces. Effects of twistig ca be further mitigated by the lateral bracig of the beam whe a slab is preset. As ca be see i the test results from Sherma ad Ghorbapoor, the measured capacity was 8.9 kips for test -U ad 98.7 kips for test 4-U. The limit predicted by the vo Mises iteractio for both coditios is 85.6 kips, which is accurate to withi approximately 3% of the measured capacity of the coectio ad supports the assumptio that twist effects are appropriately addressed by the limit state of yieldig of the coectio. Twist is listed as a secodary failure mode for tests 6-U ad 6-UB, which resisted 138 kips ad 136 kips, respectively. The vo Mises limit state predicts a capacity of oly 116 kips. Further work to refie procedures for cosiderig torsioal limit states i all types of shear coectios may be appropriate. 74 / ENGINEEING JOUNAL / SECOND QUATE / 009

9 Test Colums of Bolts Table 3. Summary ad Compariso of Ustiffeed Exteded Sigle-Plate Coectio Test Data ows of Bolts Depth of Plate (i.) a (i.) Maximum Allowed Plate Thickess (i.) Plate Thickess Provided (i.) Meets Criteria for Exteded Shear Tab? Meets Criteria for Stadard Shear Tab? Tested Capacity Tested Predicted Tested Desig (Factor of Safety) Tested Adj. Desig* (Factor of Safety) Sherma ad Ghorbapoor 1-U a YES NO U a YES NO U a YES NO UM a YES NO U NO NO U NO NO UB NO NO U NO NO Murray ad Metzger a NO YES a NO YES a NO YES a NO YES YES NO YES NO a YES NO A** NO NO * Where bolt shear cotrols the desig value, the 0% reductio for ed-loaded coectios has bee removed. ** Coectio failure did ot occur. Plate bucklig was ot listed as a failure mode for ay of the ustiffeed, exteded sigle-plate coectio tests. Iterestigly whe the plate was exteded to the bottom flage of the supportig girder, as illustrated i Figure, the plate was more likely to buckle. SUMMAY OF ECOMMENDED DESIGN POCEDUE The followig procedure has bee adopted ito the AISC Steel Maual as a uiversally applicable method of desigig sigle plate shear coectios. A geeral exteded sigle-plate shear coectio is show i Figure 9. The procedure, referred to as the exteded procedure, is useful whe the dimesioal ad other limitatios of the covetioal sigle-plate shear coectio desig method caot be satisfied. This procedure ca be used to determie the stregth of sigle-plate shear coectios with multiple vertical rows of bolts. Fig. 9. Geeral exteded sigle-plate coectio cofi guratio. ENGINEEING JOUNAL / SECOND QUATE / 009 / 75

10 Limitatios 1. The use of holes must satisfy AISC Specifi catio Sectio J3. requiremets. The shear load ca be cosidered to be applied trasverse to the slots. The eccetricity does ot require that the bolts be desiged as slip-critical.. The horizotal ad vertical edge distaces, L eh ad L ev, must satisfy AISC Specifi catio Table J3.4 requiremets. Desig Checks 1. Determie the bolt group required for bolt shear ad bolt bearig with eccetricity, e, measured as the distace from the support to the ceter of the bolt group. Alterative cosideratios of the desig eccetricity are acceptable whe justified by ratioal aalysis. For example, see Sherma ad Ghorbapoor (00).. Determie the maximum plate thickess permitted such that the plate momet stregth does ot exceed the momet stregth of the bolt group i shear, as follows: t max M 6 Fd y max where M max = 1.5F v A b C' 1.5F v = shear stregth of a idividual bolt from AISC Specifi catio Table J3., ksi, multiplied by a factor of 1.5 to remove the 0 percet reductio for ueve force distributio i ed-loaded bolt groups (Kulak, 00). The joit i questio is ot ed loaded. A b = area of a idividual bolt, i. C' = coefficiet from Part 7 of the AISC Steel Maual for the momet-oly case (istataeous ceter of rotatio at the cetroid of the bolt group), i. F y = plate specified yield stress, ksi d = plate depth, i. The foregoig check is made at the omial stregth level, sice the check is to esure ductility, ot stregth. Exceptios: a. For a sigle vertical row of bolts oly, the foregoig criterio eed ot be satisfied if either the beam web or the plate satisfies t d b / + z ad both satisfy L eh d b. b. For a double vertical row of bolts oly, the foregoig criterio eed ot be satisfied if both the beam web ad the plate satisfy t d b / + z ad L eh d b. 3. Check the plate for shear yieldig, shear rupture ad block shear rupture. 4. Check the plate for flexure with the vo Mises shear reductio. That is, check the available flexural yieldig stregth of the plate, ϕm or M /Ω, based upo a critical stress F cr : F F 3f cr y v M =FcrZ ϕ = 0.90 Ω = 1.67 These equatios ca be rearraged to be directly solvable i terms of the coectio available stregth as ϕ or /Ω such that Fdt y a d ϕ = 0.90 Ω = Check the plate for bucklig. 6. Size weld as w = st p 7. Esure that the supported beam is braced at poits of support. 8. Check serviceability criteria. The desig procedure for exteded sigle-plate shear coectios permits the colum to be desiged for a axial force without eccetricity. I some cases, ecoomy may be gaied by cosiderig alterative desig procedures that allow the trasfer of some momet ito the support, for example, 5% of the beam fixed-ed momet, provided that this momet is also cosidered i the desig of the supportig member. To provide for stability durig erectio ad lateral support of the beam, it is recommeded that the miimum plate legth be oe-half the T-dimesio of the beam to be supported. The maximum legth of the plate must be compatible with the T-dimesio of a ucoped beam ad the remaiig web depth, exclusive of fillets, of a coped beam. Note that the plate may ecroach upo the fillet(s) as show i Figure 10-3 of the AISC Steel Maual. p 76 / ENGINEEING JOUNAL / SECOND QUATE / 009

11 DESIGN EXAMPLE Cosider a W16 6 with a 100 kip (LFD) ed reactio (see figure). Fid a exteded sigle-plate shear coectio to support the ed reactio. Assume 1-i. diameter ASTM A490-N bolts (φ v = 35.3 kips/bolt), a = 9.5 i., ad all edge distaces equal to 1.5 i. Determie the equivalet bolt stregth of the bolt group. C = 3.44 Maximum stregth of bolt group due to bearig. 4Ft u wdb ksi 0 5 i. 1.0 i kips/bolt Determie required C-value C req ' d u 100 kips o.k. 9 3 kips / bolt. The check, however, will be performed to demostrate the calculatios ivolved. Fid maximum plate thickess such that plate will yield before bolts rupture by accoutig for the 0% reductio i bolt stregth geerally applied to accout for the case of ed-loaded coectios. v kips (. ) kips/bolt Fid the pure momet stregth of the bolt group (May coditios are tabulated i the AISC Steel Maual Part 7, i Tables 7-7 through 7-14) C' C' 50.7 i e e e e The momet stregth of the bolt group is therefore, M C' 50.7 i kips, 980 kip-i. Determie the maximum plate thickess. Note that the elastic sectio modulus is used because the plate will begi to redistribute stress after first yieldig. t max 6M 6, 980 kip-i. Fd y 50 ksi 1 i. 48. i. Try a 1-i.-thick plate with F y = 50 ksi. Check shear ad bedig iteractio o gross plate sectio (vo Mises criteria) Fdt y p a d 0.90(50 ksi)(1 i.)(1 i.) 154 kips i i. Check et shear rupture o the plate = 0.6F u A v = 0.75(0.6)(65 ksi)(7.5 i. ) = 19 kips > 100 kips o.k. Check block shear rupture o the plate ϕ = ϕf u A t U bs + mi (ϕ0.6f y A gv, ϕ0.6f u A v ) ENGINEEING JOUNAL / SECOND QUATE / 009 / 77

12 Tesio rupture compoet ϕf u A t U bs = 0.75(65 ksi)(6.69 i.)(1 i.)(0.5) = 163 kips Shear yieldig compoet ϕ0.6f y A gv = 0.75(0.6)(50 ksi)(10.5 i.)(1 i.) = 36 kips Shear rupture compoet ϕ0.6f u A v = 0.75(0.6)(65 ksi)(6.56 i.)(1 i.) = 19 kips = (163 kips + 19 kips) = 355 kips 100 kips o.k. Check plate bucklig d Fy d t p 47, , 000 e' , , Bucklig does ot cotrol. Size the weld to esure that the plate will yield before the weld ruptures: w i. t p SYMBOLS a = the distace from the face of the support to the first vertical lie of bolts c = umber of colum (vertical rows) of bolts d = plate depth d b = bolt diameter e = the distace from the face of the support to the ceter of the bolt group f a = the applied bedig stress (et or gross) f v = the applied shear stress (et or gross) = the umber of rows s = the spacig betwee rows of bolts t p = plate thickess, i. w = weld leg size, i. A b = area of bolt, i. C = coefficiet for eccetrically loaded bolt groups, from AISC Steel Maual Part 7. C' = coefficiet used i determiig the equivalet pure-momet bolt group stregth D = live load E = modulus of elasticity, ksi E T = taget modulus of elasticity, ksi L = live load F EXX = electrode classificatio umber, ksi F v = the shear stregth of a idividual bolt from AISC Specifi catio Table J3., ksi F y = the miimum specified yield stress, ksi F u = the miimum specified tesile stress, ksi L i = the distace of the ith bolt from the ceter of gravity of the bolt group L max = the distace of the bolt furthest from the ceter of gravity of the bolt group to the ceter L s = the legth of the slot L w = legth of weld, i. = the simple beam ed reactio ϕ sc = the slip resistace provided by a sigle bolt as a serviceability limit state ϕ brg = the shear capacity of a sigle bolt Δ = vertical deflectio caused by the rotatio of bolts i short slotted holes Δ max = the maximum deformatio o the bolt furthest from the ceter of gravity, 0.34 i. λ = slederess parameter, dimesioless (Youg s modulus is icorporated i formula) θ = rotatio allowed by movemet i short slotted holes EFEENCES AISC (005), Specifi catio for Structural Steel Buildigs, ANSI/AISC , America Istitute of Steel Costructio, Chicago, Illiois. AISC (005), Steel Costructio Maual, 13th Editio, America Istitute of Steel Costructio, Chicago, Illiois AWS (006), Structural Weldig Code Steel, AWS D1.1/ D1.1M:06, America Weldig Society, Miami, Florida. Astaeh, A., Call, S.M. ad McMulli, K.M. (1989), Desig of Sigle-Plate Shear Coectios, AISC, Egieerig Joural, 1st Quarter, pp Baker, J.F., Hore, M.. ad Heyma, J. (1956), The Steel Skeleto: Volume II Plastic Behavior ad Desig, The Sydics of the Cambridge Uiversity Press, Cambridge. 78 / ENGINEEING JOUNAL / SECOND QUATE / 009

13 Baker, J.F. ad Heyma J. (1969), Plastic Desig of Frames, The Sydics of the Cambridge Uiversity Press, Cambridge. Beetts, I.D., Thomas, I.. ad Grudy, P. (1981), Torsioal Stiffess of Shear Coectios, Proceedigs of the Metal Structures Cogress, Natioal Committee o Metal Structures of the Istitutio of Egieers, Australia, Newcastle, N.S.W., May 11 14, pp Hoga, T.J. ad Thomas, I.. (1988), Desig of Structural Coectios, 3rd Editio, Australia Istitute of Steel Costructio. Kulak, G.L., Fisher, J.W. ad Struik, J.A.H. (1987), Guide to Desig Criteria for Bolted ad iveted Joits, d Editio, Joh Wiley, New York. Metzger, K.A.B. ad Murray, T.M. (006). Experimetal Verificatio of a New Sigle Plate Shear Coectio Desig Model, Masters Thesis, Virgiia Tech, Blacksburg, VA. Mohr, B. ad Murray, T.M. (005). Ivestigatio of Ultimate Bedig Stregth of Steel Bracket Plates. Masters Thesis, Virgiia Tech, Blacksburg, VA. Muir, L.S. ad Thorto, W.A. (004), A Direct Method for Obtaiig the Plate Bucklig Coefficiet for Double- Coped Beams, Egieerig Joural, AISC, 3rd Quarter, pp Neal, B.G. (1977), Plastic Methods of Structural Aalysis, 3rd editio, Taylor ad Fracis, Lodo. Sherma, D.. ad Ghorbapoor, A. (00), Desig of Exteded Shear Tabs, America Istitute of Steel Costructio Fial eport, Uiversity of Wiscosi-Milwaukee. ENGINEEING JOUNAL / SECOND QUATE / 009 / 79

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