Uplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611;

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1 Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid, Ginesville, FL 32611; emil: 2 Lecturer, Deprtment of Civil nd Costl Engineering, University of Florid, Ginesville, FL 32611; nd Structurl Engineer, Sputo Engineering, 10 SW 1 st Avenue, Ginesville, FL 32601; emil: Abstrct The uplift resistnce of K-series open web steel joist sets ws determined by physicl testing of twenty-eight specimens to filure. The experimentl dt obtined from the physicl testing ws evluted long with the mechnicl properties of the steel mteril used in fbricting the joist set test specimens. A simple nlyticl model ws developed bsed on the experimentl results using yield-line theory, which dequtely predicts the ultimte uplift cpcity of the joist set. This ultimte strength model ws modified to crete simple AISC-ASD nd AISC-LRFD design equtions to be used in the nlysis of K-series joist sets for uplift. Both the AISC- ASD nd the AISC-LRFD design equtions consider the following vribles: Joist set yield strength (nominlly 50 ksi), nchorge weld length, set length, nd set ngle thickness. Introduction Net uplift due to wind loding is one key design considertion for open web steel joists used in roof systems. The uplift resistnce of the joist set itself, long with the cpcity of the welds which connect the set to the supporting structure, re vitl links in the lod pth when considering wind uplift in roof system. For most joist mnufcturers, the typicl set is 4 inches long, however 6-inch nd 8- inch extended set lengths re occsionlly provided. The Steel Joist Institute (SJI) stndrd (Stndrd, 1994), in Prgrph 5.6 (End Anchorge) requires minimum of two 1/8 inch fillet welds 1 inch long to the supporting structure, be it msonry, concrete, or steel. The prgrph goes on to stte, Where uplift forces re design considertion, roof joists shll be nchored to resist such forces. Current structurl engineering prctice hs the structurl engineer-of-record responsible for the design of the end bering plte nd the nchorge weld of the joist set to the steel plte or bem, not the joist mnufcturer. Wind loding my be criticl design considertion depending where structure utilizing K-series joists is locted. The minimum required nchorge weld or set length my not be sufficient to resist the net uplift forces tht my be pplied to the structure during its design life. 1

2 Objectives nd Scope The objectives of this reserch were first to determine (or verify) tht the nominl uplift resistnce of lightweight nd stndrd K-series joist sets, bsed on the current minimum design requirements s specified in the SJI Mnul (Stndrd, 1994) could chieve or exceed two (2) kips nd four (4) kips, respectively. Once this bseline ws estblished, series of stright pull tests ws conducted on vrious configurtions of joist set ngle size, ngle thickness, ngle length, nd fillet weld length to determine the experimentl uplift cpcities. A typicl experimentl loddeformtion response curve of one of the test specimens is shown in Figure 1 nd its resulting filure mechnism shown in Figure 2. The test dt ws evluted long with the filure ptterns of the test specimens to develop rtionl model to be used s simple design method for properly designing the joist bering set nd nchorge weld to resist specified net uplift lod due to wind forces cting on steel roof joist Lod (kips) Avg P1 & P2 Avg P4 & P Displcement (in.) Figure1. Lod-Deformtion Response of Test Specimen S3-4-1/8-3 Figure 2. End View of Test Specimen S3-4-1/8-3 Showing Filure Mechnism 2

3 Development of Anlyticl Model Visul observtions of the filed joist sets indicted tht yield line mechnism formed in the horizontl set leg s seen in Figures 3 nd 4. Therefore, the use of yield line nlysis in the development of n nlyticl predictive model ws felt to be pproprite. Yield line nlysis is recognized method of clculting the strength of plte-type structurl elements such s those used to fbricte the joist bering sets. The virtul work method of nlysis is employed in the derivtion given below leding to n ultimte strength prediction of the uplift cpcity of the set ngles. In pplying the virtul work method, the difference between the internl work, W I, (plte bending) nd the externl work, W E, (the pplied lod moving through distnce) is set equl to zero. Yielded Portion of Angle Figure 3. Longitudinl View of Set Angle After Test, Test Specimen S1-6-1/8-1 Figure 4. End View of Test Specimen S1-6-1/8-1 fter Test 3

4 Prior to employing the virtul work method, it ws necessry to numericlly describe the length of the yield lines tht were formed. Typicl yield line ptterns observed during the tests re schemticlly illustrted in Figures 5 nd 6. Angle sets with both short nd long nchorge welds displyed ellipticl shped yield lines tht were creted s the horizontl legs were deformed into the inelstic rnge during the tests. It ws decided tht this shpe yield line would be imprcticl to use in the nlyticl model so simpler yield line pttern ws developed tht ws still similr to the pttern observed in the tests. Anchorge Weld (typ.) Anchorge Weld (typ.) Yield Line Formtion (typ.) Figure 5. Pln View Schemtic of Test Specimen Showing Typicl Yield Line Pttern for Short Anchorge Welds Yield Line Formtion (typ.) Figure 6. Pln View Schemtic of Test Specimen Showing Typicl Yield Line Pttern for Long Anchorge Welds The finl simplified shpe of the yield line pttern tht ws chosen is shown in Figure 7. The figure shows single set ngle being loded by one-hlf of the totl uplift lod. Referring to this figure, the externl work, W E, cn be written s follows: WE = ( Pu 2) (1) where: P u = Predicted ultimte uplift lod = Distnce which the lod moves through Likewise, the internl work, W I, cn be written s: W I p ( L ) = M θ (2) YL 4

5 where: M p = Plstic moment cpcity of plte, per unit length of plte = F y Z θ = Angle through which the yield line rottes L YL = Length of the yield line where L YL is the lesser of (L w + π) nd L s L w = Length of nchorge weld L s = Length of set ngle F y = Averge 0.2% offset yield stress of the steel ngle Z = Plstic section modulus of unit length of plte which is t 2 / 4 t = Thickness of set ngle leg Setting the difference between the externl work nd the internl work equl to zero gives: P 2 M θ L (3) ( ) ( ) 0 u p YL = From smll ngle theory, tn θ θ, therefore: θ = (4) where: = The distnce from the toe of the ngle to the yield line Yield Line P u / 2 L s L w P u / 2 Plstic Hinge θ Figure 7. Yield Line Anlysis Model for Prediction of Uplift Cpcity 5

6 Substituting Eqution (4) into Eqution (3), nd solving for P u, gives: 2M p LYL Pu = (5) Eqution 5 predicts the ultimte uplift lod, P u, which will yield the horizontl legs of the two set ngles tht form the joist set. The test dt ws nlyzed to obtin yield line length tht most closely fit the experimentl dt, while still being resonbly simple to pply for design purposes. The best fit ws obtined when the distnce,, ws ssumed to be equl to 2.3t. Tble 1 shows tht the ssumption of = 2.3t provides resonbly good prediction of the ultimte uplift strength of the joist bering set. Exmple 1 For 4-inch long set, constructed of ngles L 1-1/2 x 1-1/2 x 1/8, with 2-1/2 long nchorge welds, wht is the predicted ultimte uplift resistnce? Assume F y = 50 ksi. Z = / 4 = in. 3 /in. = 2.3 (0.125) = in. L s = 4 in. L w = 2.50 in. L YL = π(0.2875) = in. < L s M p = 50 ( ) = in-k = 2 (0.1953) (3.403) / = 4.62 kips P u AISC-ASD Design Procedure The ultimte strength prediction given in Eqution 5 cn be esily modified for use with n Allowble Stress Design (ASD). The following procedure cretes n eqution set up in ASD terms, which is fmilir to most design engineers. The following chnges re necessry: Let: M = Allowble elstic cpcity of plte, per unit length of plte = F b S F b = 0.75 F y (per 9 th Edition AISC-ASD Spec., Eqution F 2-1) S = Elstic section modulus of unit length of plte = t 2 / 6 = ASD llowble uplift cpcity P Therefore, the llowble uplift cpcity of the joist bering set becomes: 2M LYL P = (6) 6

7 Exmple 2 For the sme set configurtion used in Exmple 1, clculte the ASD llowble uplift cpcity. S L s L YL F b M P P = / 6 = in. 3 /in. = in. = 4 in. = in. < L s = 0.75 (50) = 37.5 ksi (without 1 / 3 stress increse) = 0.75 (50) (1.33) = 50.0 ksi (with 1 / 3 stress increse) = 37.5 ( ) = in-k (w/o stress increse) = 50.0 ( ) = in-k (w/ stress increse) = 2 (0.0975)(3.403) / = 2.31 kips (w/o 1 / 3 stress increse) = 2 (0.1300)(3.403) / = 3.08 kips (w/ 1 / 3 stress increse) AISC-LRFD Design Procedure The ultimte strength prediction given by Eqution 5 is formulted to clculte the predicted ultimte strength, P u. Eqution 5 my be rewritten in LRFD formt s: 2M p LYL Pn = (7) where: P n = Nominl predicted ultimte uplift lod φ = 0.90 (AISC-LRFD resistnce fctor for bending) The AISC-LRFD fctored lod combintions would be used for the lod effect. Exmple 3 For the sme set configurtion used in Exmple 1, clculte the fctored nominl resistnce of the joist set to uplift. P n φp n = 2 (0.1953) (3.403) / = 4.62 kips = 0.90 (4.62) = 4.16 kips The fctored nominl resistnce, φp n, would be compred to the mximum lod effect from the pplicble LRFD lod combintions. 7

8 Tble 1. Experimentl Test Lod vs. Predicted Ultimte Resistnce Tble 1 Experimentl Test Lod, P test vs. Predicted Ultimte Resistnce, P u Specimen t vg L w vg L s vg P test F y predicted predicted L YL P u (Eq. 4.5) P test No. (in.) (in.) (in.) (kips) (ksi) (in.) t vg (in.) (kips) P u (Eq. 4.5) S1-4-1/ S1-4-1/ N/A S1-6-1/ S1-6-1/ S2-4-1/ S2-4-1/ N/A S2-6-1/ S2-61/ S3-4-1/8-1A S3-4-1/ N/A S3-6-1/8-1A S3-6-1/ S3-6-1/ N/A S3-8-1/ S3-8-1/ S3-8-1/ S4-4-1/8-1A S4-4-1/ N/A S4-6-1/8-1A S4-6-1/ S4-6-1/ N/A S4-8-1/ S4-8-1/ S4-8-1/ predicted / t vg P test / P u (Eq. 4.5) Men Men Stndrd Error Stndrd Error Medin Medin Stndrd Devition Stndrd Devition Confidence Level(95.0%) Confidence Level(95.0%) Summry nd Conclusions An eqution for predicting the ultimte uplift strength of K-series open web steel joist set ws developed from bsic engineering mechnics principles nd bsed on experimentl observtions. This ultimte strength prediction eqution ws modified to crete the following Allowble Stress Design (ASD) nd Lod nd Resistnce Fctor Design (LRFD) equtions: ASD: LRFD: 2M LYL P = (6) 2M p LYL Pn = (7) 8

9 Considering the prmeters of the experimentl test progrm, the following limittions exist in pplying these design equtions: (1) The joist set must be welded to the steel nchorge plte or supporting steel bem or joist girder with pproximtely equl length fillet welds on ech side. The fillet weld must hve minimum equivlent throt equl to tht of 5 / 32 inch equl leg fillet weld. While this exceeds the SJI minimum 1 / 8 inch leg weld, in prctice most field pplied nchorge welds exceed this minimum. Ech weld provided must be minimum of one (1 ) inch long. (2) The mximum thickness of the horizontl (bering) leg of the set ngle must not exceed 1 / 4 inch. It is unknown whether the 5 / 32 inch nominl fillet weld is dequte to develop the yield line mechnism for thicker sets bsed on the scope of this reserch. (3) The joist set length must be minimum four (4 ) inches long, nd must not exceed eight (8 ) inches in length. (4) For set configurtions where the set ngles overlp the top chord ngles, the set ngles must be welded to the top chord from both the inside nd outside. The result of not providing the outside weld is clerly illustrted in Figure 8. This outside weld is necessry to prevent rigid body rottion of the set ngles tht will prevent development of the yield line mechnism. Figure 8. Rigid Body Rottion of Joist Set with No Outside Weld Provided Acknowledgment This reserch ws funded by the Vulcrft Division of the Nucor Corportion. 9

10 References AISC (1989), Mnul of Steel Construction, Allowble Stress Design, Ninth Edition, Americn Institute of Steel Construction, Chicgo. AISC (1994), Mnul of Steel Construction, Lod & Resistnce Fctor Design, Second Edition, Americn Institute of Steel Construction, Chicgo. SJI (1994), Stndrd Specifictions for Open Web Steel Joists, K-Series, Steel Joist Institute, Myrtle Bech, SC. 10

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