CE 591 Advanced Structural Steel Design. Fall 2013 Lecture 7: Plate Girders; Design Rules of Thumb Flange-to-web weld Design Aids Design Example - PDF

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CE 591 Advanced Structural Steel Design Fall 013 Lecture 7: Plate Girders; Design Rules of Thumb Flange-to-web weld Design Aids Design Example Proportioning the Section Goals Satisfy limit states Strength
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CE 591 Advanced Structural Steel Design Fall 013 Lecture 7: Plate Girders; Design Rules of Thumb Flange-to-web weld Design Aids Design Example Proportioning the Section Goals Satisfy limit states Strength Serviceability Minimum cost assume cost proportional to weight of steel but remember that least-weight may not provide the most cost effective design! Rules of Thumb Span-Depth Ratio Salmon & Johnson, Steel Structures, 4 th ed. L d 10 to 1 b f Rules of Thumb, MSC 000 L d 15 d L Modern Steel Construction, 000 Design It Like You Are Going to Build It Karl Frank 013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/nascc013/es1.mp4 Recommendations for composite plate girders for bridges Design It Like You Are Going to Build It Karl Frank 013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/nascc013/es1.mp4 Recommendations for composite plate girders for bridges AASHTO Cross Sectional Limits Similar to AISC eq. F13- Not stable if outside limit Rules of Thumb Flange Width b f bf d 0. to 0.3 d deep section shallow section Optimum Depth (another option) Based on minimizing weight (i.e. gross cross-sectional area), supposing no depth restriction f is average stress on flange (i.e. F cr ) b w is an assumed constant h/t b w of 30 for optimum proportion A36 C 1 is a factor to account for reducing flange size at regions of lower moment C is factor to account for reducing web thickness at regions of reduced shear Optimum Depth, cont d h 3 f 3MC (3C 1 bw C 1 ) Suppose C 1 = C = 1 (i.e. no section reduction in regions of lower stress) h 3 3M bw f Rules of Thumb Flange Area b f A f M u /f d h A w C A f M fh A 6 w T Average stress on flange S x / h Rules of Thumb Plate dimensions Plate widths increments Stiffener spacing 3 multiples Rules of Thumb Plate thickness Increments (inches) Range (inches) 1/16 t 9/16 1/8 5/8 t 1-1/ 1/4 t 1-1/ Rules of Thumb Flange Plates, p. 1 Based on minimum volume (weight) and A f equation used earlier L/ M max L Groove weld A f 1 1 A f A f1 A f Rules of Thumb Flange Plates, p. L/3 L Groove weld M max A f A f A f1 A f Unless save lbs of material, added cost of weld makes flange plate transition uneconomical (Salmon et al., Steel Structures, 5 th ed.) Other flange plate recommendations If concerned about LTB, keep b f /t f at about the l p value in maximum moment regions Could then reduce flange thickness in low moment regions (reduce thickness instead of width) No LTB? Reduce width if desired slight advantage in fatigue strength Transition slope should be less than 1 in -1/ for either width or thickness change 1 in 4 to 1 in 1 recommended for change in width 013 NASCC Educator Session: Bridge Design for the Classroom media.aisc.org/nascc013/es1.mp4 Weld of flange to web Must provide for factored horizontal shear flow X X shear Vu Q flow Ix (kips/in) 1 st moment of area of flange about neutral axis Weld of flange to web, p. X X DOTs typically require SAW for these welds more thermally efficient More uniform weld cross section and strength no stops/starts and other irregularities that concentrate stress SMAW uses stick electrodes of limited length and diameter Rules of Thumb Web Reasonable range for web stress f V A n w 1 to16 ksi 9 ksi? May be able to use thinner web Practical minimum web thickness (t w ) 5/16 Design Aids Shear, Stiffeners Tables 3-16a, 3-17a (without TFA) 36 ksi and 50 ksi steel Starting on AISC Manual p Tables 3-16b, 3-17b (with TFA) f v V n /A w graphed as a function of h/t w and a/h NOTE: here, A w = d t w (AISC G) ---- means exceeded practical limit on stiffener spacing a h 60 h tw a/h 3.0 k v = 5.0 Corresponds approximately to limit for vertical flange buckling Plate Girder Design Example Consider a simply supported plate girder that carries the factored uniform load and two concentrated loads as shown. Design a doubly symmetric, non-hybrid girder with A36 steel. Assume that lateral support is provided at the ends and at the concentrated loads. 1.D + 1.6L load combination controls. Factored loads shown. L/360 deflection limit (total service load). 150 k 150 k 5 k/ft A B C D 4' 4' 4' 330 k Lateral Support Lateral Support Design Example, p. 150 k 150 k 5 k/ft A B C D 4' 4' 4' Lateral Support Shear (kip) Moment (ft-kip) 330 k Design Example, p. 3a Sizing the Section, try Rule of Thumb L d 10 to1 (7 ft)(1in 1 / ft) 7 in Try h = 7 Try t w = 5/16 h tw 7 5/16 30 Design Example, p. 3b Sizing the Section, try formula for h h 3 3M f b w 3 3( M u R / pg f F ) cr b w h 3 3(6840kipft / 0.9)(1in / (1.0)(36ksi) ft)(30) 107in Design Example, p. 3c Try h = 107 Try t w = 5/16 h tw 107 5/16 34 AISC F13. for a/h 1.5 h tw max a/h 1.5 limit will be even smaller Also, web substantially heavier than for h=7 with practical minimum web thickness So, try h= ksi 36ksi 341 Design Example, p. 4 Slender Web? 5.70 E F lr lr y Table B4.1b (Case 15) Check shear stress (recommended) h tw 30 lr 9000ksi 36ksi fv A n w 1 to16 ksi V A u w 330kips (7 )( 5 ) Design Example, p. 5 Double check AISC Limitations, h/t w = 30 h t w E a 1.0 for 1.5 F h yf (F13-3) 9000ksi ksi h t w 0.40E Fy 341 for a h 1.5 (F13-4) 0.40(9000ksi) 36ksi 3 OK, Limitations satisfied Design Example, p. 6 Estimate Flange Size A f M fh A 6 w M f R b PG u F cr h A 6 w Assume R PG = 1.0, F cr = F y A f 6840 ft kip(1in / ft) (0.9)(1.0)(36ksi)(7 ) 7 (5/16 ) in Design Example, p. 7 Possible flange dimensions t f (in) b f (in) A f (in ) b f /t f b f tf Use FLB compactness limit to help choose size (optional) Table B4.1b l p E F 36 yf Flange width rule b f d 6 (7 (1.5 )) 0.34 of thumb 0.3 Design Example, p. 8a LTB Flexural Capacity; L b = 4 ft b (6 )(1.5) (1)( ) 3 f =6 r t 7. 1in 5 t (6)(1.5) (1)( ) f = t w =5/16 h c /6 =7 /6 =1 L 1. 1r p (F4-7) t E F y 9000ksi Lp 1.1(7.1in) in ft 36ksi L r r (F5-5) t E 0.7F 9000ksi Lr ( 7.1in) 757in ft 0.7(36ksi) y 150 k 150 k 5 k/ft Design Example, p. 8b L p = 18.5 ft L b = 4 ft L r = 63.1 ft F cr L L L L b p Shear Cb[ Fy (0.3Fy)( )] (kip) r p ~5% difference in M u within L b assume constant moment Moment (ft-kip) A B C D 4' 4' 4' 330 k F y (F5-3) Fcr ( 1.0)[36 (0.3(36))( )] 36ksi Fcr 34. 5ksi Lateral Support 330 Design Example, p. 9 Calculate Section Modulus, etc S x 1 5 ( in )(7 3 3 ) 7 (6)(1.5)( 7 ( 1.5 ) 1.5) 1 ( 1 )(6)(1.5 3 ) 5/16 7 hctw (7 )(5/16 ) aw a w bfctc (6 )(1.5 ) (F4-1) 10 OK Design Example, p. 10 Calculate Flexural Capacity R pg 1 aw hc E ( 5.7 ) a t F w w y (F5-6) 9000ksi 1 ( 5.7 ) (0.69) 5/16 36ksi 0.97 fm f S R F (F5-) and AISC F1 n b xc pg cr 3 0.9(60in )(0.97)(34.5ksi) 78368kip in 6531kip ft M u = 6840 kip-ft N.G. Design Example, p. 11 TRY 8 x 1.5 flange Recalculate properties: Af 4 in r t 7. 74in b t f f 8 (1.5 ) Lp 0.1 ft Lb 4 Lr Fcr 35. 8ksi 3 S x 385in a w 9.33 lp 10.8 compact wrt FLB ft 5/16 7 Design Example, p. 1 Recalculate Flexural Capacity, cont d. R pg 9000ksi 1 ( 5.7 ) (0.535) 5/16 36ksi fm n f S b xc R 0.9(385in 3 pg F )(0.973)(35.8ksi) 10985kip in 858kip ft cr Design Example, p. 13 Check against M u including self-weight Area 5 (8in)(1.5in) (7in)( in) 106in in Weight (490pcf ) 361lb / ft in 144 ft 361lb / ft (7 ft) 1000lbs / kip 6840kip ft kip 8 M u fm n M u flexural capacity of section is adequate ft 858 kip-ft Design Example, p. 14 Check Deflection Limits Estimate service loads 150 k 150 k 5 k/ft w w P u Shear (kip) service service Moment a A 4' B 4' C 4' D 330 k / k ft /1.5 P u 1.(0.361k / ft) 3.6k / ft 5.43k / ft / kips / kips Lateral Support 330 Design Example, p. 15 Deflection limits, cont d. I x 1 1 7 1.5 ( )(8 )(1.5 ) ()(8 )(1.5 )( ) ( )(7 ) 13,183in wserviceL 384EI 4 Pservicea 4EI (3L 4a 100kips(4 ft)(178in 3/ ft 3) (3(7 4(9,000ksi)(13,183in 4) ) ft 4 5(3.6k / ft)(7 ft )(178in 3 / ft 384(9,000ksi)(13,183in 4) ) 4(4 ft )) in 3 ) max L ft(1in 360 / ft).40in 1.5 in OK Shear (kip) Moment (ft-kip) Design Example, p k 150 k 5 k/ft Low shear demand Region BC h 30 A B C D Lateral 4' 4' 4' Support 60 C 330 k h t w v kve 5.0(9000ksi) F 36ksi yw k ve h ( ) Fy t w 330 t w 1.51(5)(9000ksi) (30 )(36ksi) (G-5) 60 is limit for unstiffened girders (F13.); stiffeners not required unless needed for capacity 0.1 Design Example, p. 17 Shear Capacity Region BC fvn 0.9(0.6 Aw FyCv ) 5 0.9(0.6)(75 )( )(36 ksi)(0.1) 54.6kips 16 a h 60 h tw a 1.8h 1.8(7 ) (G-1) and AISC G1 V u = 60 kips w/o self-weight N.G. a = 90 a/h=1.5 Design Example, p. 18 Shear Capacity Region BC k v k 5 8. ( a / h) (1.5) v kve 8.(9000ksi) h F 36ksi t y w 30 C v (G-5) 1.51k ve h ( ) F t w yw 1.51(8.)(9000ksi) (30 )(36ksi) 0.19 Design Example, p. 19 Shear Capacity Region BC fv n 0.9(0.6A w F y )( C v C v 1 ( a / h) ) (G3-) (0.6)(75 )( )(36 ksi)(0.19 ) kips V u = 60 kips OK By inspection, adequate for V u including self-weight 4 ft(1in / ft) 90in / panel 3. panels 4 ft(1in / ft) a 7 a 7in; spaces h 7 Small adjustment needed later since a is clear distance between stiffeners Design Example, p k 150 k 5 k/ft Shear Capacity Regions AB and CD Shear (kip) Moment (ft-kip) A B C D 4' 4' 4' 330 k Lateral Support 330 Design End Panels first NO TFA Permitted 361lb / ft (7 ft) 1000lbs / kip V u kips kips 6840 Required Stress 346kips (75 )(5 /16 ) 14.8 ksi Design Example, p. 1 Shear Capacity, End Panels Use Table 3-16a (No TFA) for estimate Will need a/h 0.5 fvn Vu 346kips Requires: C v 0.791 k v 34.4 a/h 0.41 a 9.5 Design Example, p. Shear Capacity, End Panel k v Try a = 7 ; a/h = ( a / h) (0.375) kve 40.6(9000ksi) h Fy 36ksi tw 1.10 kve 40.6(9000ksi) h F 36ksi t y 1.10 kve Fy 1.10 (40.6)(9000ksi) (36ksi) Cv 0.86 h tw 30 5 Vn 0.9(0.6 Aw FyCv ) 0.9(0.6)(75 )( )(36 ksi)(0.86) 39 kips 16 OK w Design Example, p k 150 k 5 k/ft Shear Capacity Regions AB and CD Shear (kip) Moment (ft-kip) A B C D Lateral After End Panels 4' 4' 4' Support TFA Permitted? 330 k ~7 Aw ( Afc A ft ) (7 )(5 16 ) (8 )(1.5 ) h b fc h b ft 330 7 8 Check AISC G3.1 (a) and (b) satisfied; (c) and (d)?? .5 TFA OK! 6.0 TFA OK! Design Example, p k 150 k 5 k/ft Shear Capacity Regions AB and CD Shear (kip) Moment (ft-kip) A B C D 4' 4' 4' 330 k ~ Lateral Support 330 After End Panels TFA Permitted V u 334kips Including self-weight Required Stress kips (75 )(5 /16 ) 14. ksi Design Example, p. 5 Shear Capacity, after End Panels Use Table 3-16b (with TFA) for estimate Based on required stress, try a/h = 0.80? Design Example, p. 6 Shear Capacity, after End Panel, with TFA 5 5 k v 5 ( a / h) (0.78) Try a = 56 ; a/h = kve 13.(9000ksi) h F 36ksi t y 1.51k ve 1.51(13.)(9000ksi) Cv h ( ) F (30 )(36ksi) y tw 1 Cv Vn 0.9(0.6 Aw Fy )( Cv ) ( a/ h) 5 w (0.6)(75)( )(36)(0.304 ) 356kips 334 kips OK Design Example, p k 150 k 5 k/ft Shear Capacity Regions AB and CD Shear (kip) 7 Moment (ft-kip) A B C D 4' 4' 4' 330 k Lateral Support 330 After first panels; TFA permitted V u 309kips Including self-weight Required Stress kips (75 )(5 /16 ) 13. ksi Based on Table 3-16b, repeat a/h= 0.78 Design Example, p. 8 7 Repeat process for next panel(s); determine stiffener layout (another layout might be more efficient) C L sym Note: a dimension used for stiffener spacing; therefore, actual a (clear distance) will be smaller (May also modify to get multiples of 3 for spacing) Design Example, p.9 Size flange-to-web weld Q A f h t f ( ) 7 1.5 8 (1.5 )( ) 1544in 3 X X shearflow VuQ I x 346kips(1544in 4 13,183in 3 ) 4.34kips / in Design Example, p. 30 Flange-to-web welds, cont d AISC Table J.4 minimum size 3/16 fillet for 5/16 plate (thinner part joined) Assume Submerged Arc Weld (SAW) Try w=1/4 Use matching weld electrode, 70ksi X X Design Example, p. 31 Flange-to-web weld, cont d. fr Weld Metal (AISC J) n f( 0.6FEXX ) Aw 0.75()(0.6)(70ksi) (0.5 ) 11.1kips / in Base Metal Shear Yield (AISC J4.) fr n f( 0.6F ) A 1.0(0.6)(36ksi)(0.315 ) y g 6.75kips / in Base Metal Shear Rupture (AISC J4.) fr n f( 0.6F ) A 0.75(0.6)(58ksi)(0.315 ) 8.kips / in u nv CONTROLS 4.34 kips/in OK Design Example, p. 3 Intermediate Transverse Stiffeners Assume single-plate A36 stiffeners Design stiffener between end panel and first panel with TFA End panel a/h = 0.375; adjacent panel (TFA) a/h = 0.78 Design Example, p.33 bst 8 5 16 13.8 Try b st = 8 b t 8 t tst st st E F yst (G3-3) b st 5/16 7 Try t st = 9/16 Design Example, p. 34 Intermediate Transverse Stiffeners, cont d. (adequate stiffness for web buckling; AISC G.) End panel a/h = 0.375; adjacent panel (TFA) a/h = 0.78 j ( a / h) I st bt 3 w j ( 7 )( ) (15.7) 1.9in for adjacent panel a/h = 0.78, I st = 3.61 in 4 Check 8 x 9/16 Ist 0.565 (8 ) in 4 OK Design Example, p. 35 I Intermediate Transverse Stiffeners, cont d. I st Adequate stiffness for TFA I h st Vu Vc 1 ( Ist Ist1) Vc V st Fyw E Ist 1.9 ( ) in 8.6in OK 1 c1 (G3-4) st 9. 4in 9000 (G3-5) Check other stiffeners Design Example, p. 36 Size welds for stiffeners f nv 0.045h F 3 yw E 0.045(7 ) 3 36ksi 9000ksi 4.1kips / in Try minimum weld size for 5/16 plate (thinner plate) AISC Table J.4 w=3/16 Assume SMAW Use matching electrode, 70 ksi Design Example, p. 37 Stiffener welds, cont d. fr n Weld Metal (AISC J) f( 0.6F ) A 0.75()(0.6)(70ksi)(0.707)(0.1875 ) EXX w 8.35kips / in Base Metal Shear Yield (AISC J4.) fr n fr n f( 0.6F ) A 1.0(0.6)(36ksi)(0.565 ) 1.kips / in y g Base Metal Shear Rupture (AISC J4.) or f( 0.6F ) A 0.75(0.6)(58ksi)(0.565 ) 14.7kips / in fr n u nv CONTROLS f( 0.6F ) A 0.75(0.6)(58)()(0.1875 ) 9.79kips / in u nv 4.1 kips/in OK Design Example, p. 38 Stiffener welds, cont d. 3/16 Use nominal weld size (Table J.4) to connect to compression flange (to prevent uplift of flange single stiffener) 3/16 4t 6t w w 5 4( ) ( ) 1.88 USE 1.5 Design Example, p. 39 Bearing Stiffeners Typically make full depth; check capacity of intermediate transverse stiffeners for BEARING Check LWY, LWC, etc. (given bearing length of support) Design bearing stiffener as needed Design Example, p. 40 Bearing Stiffeners Will design / check for homework Use pairs of stiffeners (as shown to left) Use full depth
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