Comparative Study of Load and Resistance Factor Design vs. Allowable Stress Design

Transcription

1 Missuri University f Science and Technlgy Schlars' Mine Internatinal Specialty Cnference n Cld- Frmed Steel Structures (1984) - 7th Internatinal Specialty Cnference n Cld-Frmed Steel Structures Nv 13th Cmparative Study f Lad and Resistance Factr Design vs. Allwable Stress Design Brian K. Snyder Lan-Cheng Pan Wei-wen Yu Missuri University f Science and Technlgy, wwy4@mst.edu Fllw this and additinal wrks at: Part f the Structural Engineering Cmmns Recmmended Citatin Snyder, Brian K.; Pan, Lan-Cheng; and Yu, Wei-wen, "Cmparative Study f Lad and Resistance Factr Design vs. Allwable Stress Design" (1984). Internatinal Specialty Cnference n Cld-Frmed Steel Structures This Article - Cnference prceedings is brught t yu fr free and pen access by Schlars' Mine. It has been accepted fr inclusin in Internatinal Specialty Cnference n Cld-Frmed Steel Structures by an authrized administratr f Schlars' Mine. This wrk is prtected by U. S. Cpyright Law. Unauthrized use including reprductin fr redistributin requires the permissin f the cpyright hlder. Fr mre infrmatin, please cntact schlarsmine@mst.edu.

2 Seventh Internatinal Specialty Cnference n Cld-Frmed Steel Structures St. Luis, Missuri, U.S.A., Nvember 13-14, 1984 COMPARATIVE STUDY OF LOAD AND RESISTANCE FACTOR DESIGN VERSUS AlLOWABLE STRESS DESIGN by Brian K. Snyder l, Lan-Cheng Pan 2 and Wei-Wen Yu 3 INTRODUCTION The 1980 Editin f the American Irn and Steel Institute (AISI) Specificatin fr the Design f Cld-Frmed Steel Structural Members (Ref. 1) prvides design frmulas fr determining allwable stresses r allwable lads fr structural members and cnnectins. In allwable stress design, the actual stresses are cmputed frm service lads that include dead, live, snw, wind, and/r earthquake lads. The allwable stresses r allwable lads are based n apprpriate factrs f safety recmmended by AISI fr different types f structural members. Recently, the prpsed lad and resistance factr design (LRFD) criteria fr ht-rlled steel members and cnnectins (Ref. 2) have been develped using prbabilistic and statistical techniques t accunt fr the uncertainties in design, fabricatin, material prperties, and applied lads. Fr cld-frmed steel structural members, the lad and resistance factr design methd has been studied under a jint research prject entitled "Lad and Resistance Factr Design f Cld-Frmed Steel" cnducted at the University f Missuri-Rlla and Washingtn University (Refs. 3-10). Subsequently, the tentative recmmendatin n the LRFD criteria were recmmended in Ref. 9. In this methd, lad factrs are applied t the external lad and resistance factrs are applied t the internal resistance capacities f the structure. lstructural Engineer, Burns & McDnnell, Kansas City, Missuri; frmerly Research Assistant, Department f Civil Engineering, University f Missuri-Rlla, Rlla, Missuri. 2 Research Assistant. Department f Civil Engineering, University f Missuri-Rlla, Rlla, Missuri. 3 Curatrs' Prfessr, Department f Civil Engineering, University f Missuri-Rlla, Rlla, Missuri. 543

3 544 SEVENTH SPECIALTY CONFERENCE The primary purpse f this investigatin was t study and cmpare the prpsed tentative recmmendatins n the lad and resistance factr design criteria fr cld-frmed steel (Ref. 9) with the existing allwable stress design (ASD) criteria which are included in the 1980 Editin f the AISI Specificatin fr the Design f Cld-Frmed Steel Structural Members (Ref. 1). LOAD AND RESISTANCE FACTOR DESIGN The prpsed recmmendatins n the lad and resistance factr design criteria fr cld- frmed steel (Ref. 9) are based n the first-rder principles f prbabilistic thery. The general frmat fr the LRFD criteria is as fllws: j cp Ru > L Y k Qkn (1) k;l where. resistance factr R n Yk nminal resistance lad factr Qkn nminal lad effect On the left side f Eq. (1). the resistance factr. CP. is a nndimensinal factr less than r equal t 1.0 that accunts fr the uncertainties in calculating the nminal resistance. The nminal resistance f the structure is the predicted ultimate resistance r lad determined frm design frmulas using specified mechanical prperties f material and sectin prperties. On the right side f the equatin, factr Y is a nndimensinal lad factr used t reflect the pssibility f verlads and uncertainties in cmputing the lad effects. Each lad factr applies t a nminal lad effect Q and the subscript k crrespnds t different types f lads. Only dad and live lad effects were used t develp the LRFD criteria fr cld-frmed steel and t cmpare these tw design methds. COMPARISON The design equatin fr the LRFD crtieria based n dead and live lads is as fllws: where Dn nminal dead lad (2) L n nminal live lad

4 COMPARATIVE STUDY OF DESIGN METHODS 545 Fr the purpse f cmparisn, the unfactred lad cmbinatin (Du + In) r allwable lad can be cmputed frm the nminal resistance BU, the resistance factr, and a given Dn/Lu rati as fllws: Therefre, BU > (1.2 Du/Lu + 1.6)Ln Rn > (1.2 Du/ln + 1.6) [(Dn+Ln)/(Dn/Ln+l)] Du + In'::' (1.2D /L + 1.6)/[ (D /L + 1)] n n n n (3) Frm Eq. (3), the factr f safety against the nminal resistance used in the LRFD criteria is as fllws: 1.2D /L n n (4) (F. S. )LRFD (Du /Lu + 1) The allwable lad fr ASD is based n a factr f safety f the nminal resistance as shwn in Eq. (5). D n +L n R n <--- - (F.S.) ASD (5) Therefre, based n Eqs. (3) and (5), the.. allwable lad rati is as fllws: (Pa)LRFD (Pa ) ASD (F. S.) ASD D /L + 1 n n 1. 2D nil n (6) Equatin (6) was used in this study t cmpare the AISI Specificatin (Ref. 1) fr allwable stress design and the prpsed recmmendatins n the LRFD criteria (Ref. 9). This equatin wuld nly be applicable t structural members with ne type f lad. It des nt apply t the cmbined bending and shear, cmbined bending and web crippling, and beam-clumn criteria where design frmulas are interactin equatins. Tables 1 and 2 list the ASD safety factrs, the LRFD resistance factrs, and the allwable lad ratis fr D/L = 1/3 fr structural members and cnnectins, respectively. Figure 1 shws a graph f the allwable lad rati versus dead-t-live rati fr tensin members and flexural members. Curves fr ther structural members r cnnectins listed in Tables 1 r 2 wuld be similar except that they wuld be shifted up r dwn depending n the design factrs listed. As shwn in the figure and tables, the LRFD criteria is slightly cnservative fr dead-t-live lad ratis less than 1/3.

5 546 SEVENTH SPECIALTY CONFERENCE COMBINED LOADS When a structural members has t be designed fr a cmbinatin f lads r lad effects, an interactin equatin is used in bth the AISI Specificatin (Ref. 1) and the Tentative Recmmendatins fr LRFD (Ref. 9). Due t the cmplexity f the design equatins fr cmbined lads, specific examples were chsen fr cmparisn. Fr cmbined bending and shear design f webs, different examples were investigated varying the thickness, yield strength, and depth f the beams. The lad case chsen was a unifrmly laded three span cntinuus beam. The allwable lad rati versus deadt-live lad rati curves were all within 2% f the curve shwn in Figure 1. Fr cmbined bending and web crippling design, the same prcedure was used but nly a simple beam with a cncentrated lad at midspan was investigated. Figures 2 thrugh 5 shw typical allwable lad rati curves fr specific examples. Unlike cmbined bending and shear, bending and web crippling results in a wide range f allwable lad ratis fr a given dead-t-live lad rati. Figures 3 and 5 shw a decrease in allwable lad rati with increasing span length fr this example. Fr cmparisn f dubly-symmetric beam-clumns, nly bending abut the y-axis was cnsidered. A typical design example was a beam-clumn with equal mments applied t each end s that the member was bent in single curvature. Since the end mments are independent f the axial lad, the rati f the unfactred applied mment t the ultimate mment capacity based n sectin strength, MT/Mus ' was cnsidered t be a parameter. The slutin f the interactin equatins fr flexural failure at midlength which includes the effects f secndary mments required a cmputer prgram t calculate allwable axial lads fr varius lengths, end mment ratis, and dead-t-live lad ratis. The interactin design equatins based n failure at braced pints in the beam-clumn yielded similar results as the equatins based n failure at midspan which wuld be the gverning equatins fr this example. Figures 6 thrugh 9 illustrate the results f typical dublysymmetric beam-clumns. Figures 6, 8, and 9 shw similar shaped curves as shwn in previus examples except that the slpe f the curves increase with increasing end mment ratis. The relatinship between allwable lad rati and slenderness rati is shwn in Figure 7. As shwn in the figure, allwable lad rati increases with increasing slenderness rati f the beam-clumn. The dashed line curves shwn in Figure 8 represent the beamclumn subject t jint translatin r transverse lading between its supprts where Cm = As shwn in the figure, the effect f

6 COMPARATIVE STUDY OF DESIGN METHODS 547 the cefficient, C, n the allwable lad rati is. related t the end mment rati. min Figure 9, the dashed line curves represent the beam-clumn fabricated with a steel pssessing a higher yield pint. The influence f the yield pint n the allwable lad rati versus dead-t-1ive lad rati curves fr varius end mment ratis is similar but ppsite t that f the effect f the cefficient, C, shwn in Figure 8. These effects are negligible fr small end m mment ratis. Fr singly-symmetric beam-clumns, the directin f the mment r lcatin f the eccentric axial lad can be imprtant s eccentricity was used as a parameter instead f end mment rati and the allwable eccentric axial lads were slved fr with a similar cmputer prgram. Since the mment is nw directly prprtinal t the axial lad, the eccentricity r end mment did nt affect the slpe f the allwable lad rati curves as shwn in Figure 10. Figure 11 shws the a110wabe 10ad,rati versus eccentricity fr tw different yield pint materia1s Figures 10 and 11 bth shw an increase in allwable lad rati with a decrease in eccentricity. Higher yield pint materials will als result in a slight increase in allwable lad rati. The relatinship between allwable lad rati and slenderness rati at a given dead-t-1ive lad rati is illustrated in Figure 12 fr tw different yield pint materials. The figure shws an increase in allwable lad rati as the slenderness rati increases. CONCLUSIONS This investigatin cmpares the AlSI Specificatin which is based n allwable stress design with the pt6psed recmmendatins n the lad and resistance factr design fr c1dfrmed steel structures. It was fund that the dead-t-1ive lad rati had a significant effect n the degree f cnservatism f the LRFD criteria. In general, the allwable lad rati, (Pa)LRFD!(Pa)ASD' increases as the dead-t-1ive lad rati increases. Because c1dfrmed steel members are usually thin, the dead-t-live lad ratis f such light weight members are expected t be lwer than the ratis used fr ther building materials. In view f this and the fact that the lad factr used fr live lad is larger than the lad factr fr dead lad, the LRFD criteria were fund t be cnservative in mst cases, ACKNOWLEDGMENTS This prject was spnsred by the American Irn and Steel Institute. The technical guidance prvided by the AISI Task Grup n Lad and Resistance Factr Design under the chairmanship f Mr. Karl H. Klippstein and the AISI Staff. Dr. Albert L. Jhnsn. is gratefully acknwledged.

7 548 SEVENTH SPECIALTY CONFERENCE APPENDIX I - REFERENCES 1. American Irn and Steel Institute, "Specificatin fr the Design f Cld-Frmed Steel Structural Members," American Institute f Steel Cnstructin, "Prpsed Lad & Resistance Factr Design Specificatin fr Structural Steel Buildings," September 1, Rang, T. N., Galambs, T. V., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," First Prgress Reprt, submitted t American Irn and Steel Institute, January Rang, T.N., Galambs, T.V., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," Secnd Prgress Reprt, submitted t American Irn and Steel Institute, January Rang, T.N., Galambs, T.V., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," Third Prgress Reprt, submitted t American Irn and Steel Institute, January Rang, T.N., Galambs, T. V., and Yu, W. W., "Lad and Resistance Factr Design :f Cld-Frmed Steel," Furth Prgress Reprt, submitted t American Irn and Steel Institute, January Suprnsilaphachia, B., Galambs, T.V., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," Fifth Prgress Reprt, submitted t American Irn and Steel Institute, September Galambs, T.V., and. Yu, W. W., "Lad. and Resistance Factr Design f Cld-Frmed Steel," Sixth Prgress Reprt, submitted t American Irn and Steel Institute, March Galambs, T.V., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," Seventh Prgress Reprt, submitted t American Irn and Steel Institute, September Snyder, B.K., Pan, L.C., and Yu, W. W., "Lad and Resistance Factr Design f Cld-Frmed Steel," Eighth Prgress Reprt, submitted t American Irn and Steel Institute, September 1983.

8 COMPARATIVE STUDY OF DESIGN METHODS 549 APPENDIX II - NOTATION C m c D n D/L e (F.S )ASD bending cefficient used in beam-clumns distance frm the centridal axis t the fiber with maximum cmpressin stress, negative when the fiber is n the shear center side f the centrid nminal dead lad dead-t-live lad rati eccentricity f the axial lad with respect t the centridal axis, negative when n the shear center side f the centrid factr f safety against failure based n allwable stress design (F.S \RFD F Y K L factr f safety against failure based n lad and resistance factr design yield pint effective length factr = member length nminal live lad ttal unfactred applied mment M us N (P a> ASD beam strength as determined frm sectin strength actual length f bearing allwable unfactred lad based n allwable stress design allwable unfactred lad based n lad and resistance factr design nminal lad effect nminal resistance r y x x a radius f gyratin f crss-sectin abut centridal principal axis distance frm shear center t web face distance frm shear center t centrid alng the principal x-axis lad factr resistance factr

9 550 SEVENTH SPECIALTY CONFERENCE TABLE 1 FACTORS FOR DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS Member Failure Mde (F.S.) ASD <PLRFD (Pa)LRFD!(Pa)ASD fr D/L = 1/3 Tensin Yielding Flexural Yielding Lcal buckling Lateral buckling Flexural Shear yielding (Web) Inelastic shear buckling Elastic shear buckling Lcal buckling under bending Crippling (single webs) Crippling ( 1- Sectins) Q67 Cmpressin Flexural buckling Trsin-flexural buckling Trsinal buckling

10 COMPARATIVE STUDY OF DESIGN METHODS 551 TABLE 2 FACTORS FOR DESIGN OF CONNECTIONS FOR COLD-FORMED STEEL Type Failure Mde (F.S.) ASD LRFD Arc Spt Shear Weld Sheet tearing (Pa)LRFD/(Pa)ASD fr D/L = 1/ Arc <Seam Shear Weld Sheet tearing Fillet Weld Weld failure Sheet tearing Flare Weld failure Grve Weld Sheet tearing Resistance Shear Weld Min. Blt Sheet Shearing Edge Distance Tensin n Sheet tearing ,.0.65 Blted C:nn ' Bearing in Sheet piling up Blted Cnn ,036

11 552 SEVENTH SPECIALTY CONFERENCE Q UJ <: '""'<\I t- '- Q '" po...l '""'<\I t-,; ''';.., <\I po "0 <\I 0...l <J) r-l.0 <\I 0 r-l r-l <: Dead-T-Live Lad Rati, D/L Figure 1. Allwable Lad Rati vs. D/L Rati fr Tensin and Flexural Members

12 COMPARATIVE STUDY OF DESIGN METHODS x 0.105" 3" x 1. 75" x 0.105" 'M..: 1.00 "Cl Channels With...:I Stiffened Flanges OJ «0.95 L N 60 in 6 in F = 33 ksi y 0.90 Ntes: 1 in mm 1 ksi MPa Dead-T-Live Lad Rati, D/L 3.0 Figure 2. Allwable Lad Rati vs. D/L Rati fr Cmbined Bending and Web Crippling

13 554 SEVENTH SPECIALTY CONFERENCE ' r-- 5" x 2" x 0.105" Channel With Stiffened Flanges D/L 1/ N 6 in ksi 0.95 Ntes: 1 in 25.4 mm 1 ksi MFa Length f Span, L, in. Figure 3. Allwable Lad Rati vs. Span Length fr.cmbined Bending and Web Crippling

14 COMPARATIVE STUDY OF DESIGN METHODS r------r------r l.0r "x2.5" x 0.105" 0.9 3" x 2.25" x 0.105" I-Sectins With Unstiffened Flanges L N F y 60 in. 6 in. = 33 ksi 0.8 Ntes: 1 in. 1 ksi 25.4 mm MFa Dead-T-Live Lad Rati, D/L Figure 4. Allwable Lad Rati vs. D/L Rati fr Cmbined Bending and Web Crippling

15 556 SEVENTH SPECIALTY CONFERENCE " x 2.5" x 0.105" I-Sectin With Unstiffened Flanges D/L = 1/3 N = 6 in. q til..,; 1.20 Ntes: 1 in. 1 ksi 25.4 rm MPa F y 50 ksi = 33 ksi r- 0.90L- L Length f Span, L. in. Figure 5. Allwable Lad Rati vs. Span Length fr Cmbined Bending and lveb Crippling

16 0.80 I I I I I Dead-T-Live Lad Rati, D/L Figure 6. Allwable Lad Rati vs. D/L Rati fr Beam-Clumns (") a:: j <: t:'j r:n 6 t::j ><: >%j t::j t:'j r:n... z a:: t:'j >-3 ::t: t::j r:n l Ntes: 1 in mm ksi MPa 1.10 M tel T us p <I; '" C --- p r-'1 P-< N 1M T us " x 4" x 0.105" I-Sectin With Stiffened Flanges F = 33 ksi y L = 48 in.

17 Figure 7. Allwable Lad Rati vs. Slenderness Rati fr Beam-Clumns r:n t.:i:j ;3 r:n Z t.:i:j 1.20 I I 3.5" x 4" x 0.105" I-Sectin With Stiffened Flanges /M = us L F = 33 ksi y nil 1.0 CI) <>: t- It"....,::...:I iii t- 0.90L ---- "'---nil 1/3 0.80' Ntes: 1 in. 1 ksi 25.4 mm MPa 20 Slenderness Rati, KL/r y

18 Figure 8. Allwable Lad Rati vs. D/L Rati fr Beam-Clumns I 3.0 a i rn d t::j t-<: I'%j t::j t:j a::: t:j t::j rn 81 t P til «: '" -... <>:,...l t\j JT N /H = 0.1 us C 1.0 m - C 0.85 m 1 in It 1 ksi 25.4 mm MPa 6" x 5" x 0.105" I-Sectin With Stiffened Flanges F ksi y L 60 in I I Dead-T-Live Lad Rati, D/4.

19 w tz:j -< tz:j Z >-3 ::r: w "t! tz:j ( :: (1 Z "".:I tz:j Z (1 tz:j 1.20 Vl.,,; r 2:;, :l 2:;, MT/M ' us 0.2 I.r/Hus Fy ---F y ksi 50 ksi 6" x 3" x 0.105" I-Sectin With Unstiffened Flanges L 60 in. Ntes: 1 in = 25.4 nnn 1 ksi = MPa Dead-T-Live Lad Rati, D/L Figure 9. Allwable Lad Rati vs. D/L Rati fr Beam-Clumns

20 is: e = x -0.77" "'d 1.10 I./ "- > e = c = ± 1.73" Figure 10. Allwable Lad Rati vs. D/L Rati fr Beam-Clumns en en I-' Ntes: 1 in L 1 ksi MPa (") e = 0 0 Cl x = -1.91" 0 >-< Ul -<: t':j ;., p.. 00 "- Cl 6" x 2.5" x 0.105" Channel LOl c::: With Unstiffened Flanges t:1...:i ><: ttl ::0 0 I-.:j t: I 1/ t':j 00 >-< 0 Z / F = 33 ksi y is: t':j L = 60 in. ::t: 0 t:1 00 Dead T-Live Lad Rati, D/L

21 Figure 11. Allwable Lad Rati vs. Eccentricity fr Beam-Clumns 01 rn. tr:l <: tr:l Z ::I: rn. "d tr:l Z "':l tr:l ::0 tr:l Z tr:l 1.10 I I I I F = 33 ksi - f- y ---F = 50 ksi y Q (fl..; tii 1.05 f "' :: \ "- Q 1.00 H til Ntes: 1 in. = 25.4 mm 1 ksi = MPa x 0 4" X 2" x 0.105" Channel With Stiffened Flanges I! D/L = 0.5 J L = 60 in I I I I Eccentricity, e, in.

22 25.4 mm MPa Figure 12. Allwable Lad Rati vs. Slenderness Rati fr Beam-Clumns (1 is: < trj r:n d t;j t-<: "l:j t;j trj r:n... is: trj ::t: t;j r:n 01 m c.:l " x 2" x 0.105" Channel With Stiffened Flanges Ntes: 1 in. 1 ksi Cl Ul.0: a..'" "- Cl H C1l t:! F 33 ksi y 0.95 e = 1.29 in. D/L 1/3 Slenderness Rati, KL/r y

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