Composite Beams DYB 654: ADVANCED STEEL STRUCTURES - II. Department of Earthquake and
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1 DYB 654: ADVANCED STEEL STRUCTURES - II Assoc.Prof.Bülent AKBAŞ Crown Hall at IIT Campus Chicago. Illinois Ludwig Mies van der Rohe Department of Earthquake and Structuralt Engineering i Composite Beams and Shear Studs
2 Composite Beams and Shear Studs Composite Beams Nominal Bending Strength of Fully Composite Beams Nominal Bending Strength of Fully Composite Beams Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation
3 Composite Beams
4 Composite Beams
5 Composite Beams
6 Composite Beams
7 Composite Beams
8 Composite Beams
9 Composite Beams
10 Nominal Bending (Flexural) Strength of Fully Composite Beams
11 Nominal Bending (Flexural) Strength of Fully Composite Beams b h r Y con t c =Y con h r Concrete below the top of the deck is neglected deck ribs perpendicular (beam) h r Y con t c =Y con h r /2 b average thickness can be used deck ribs parallel (girder) Figure. Effective slab depth
12 Nominal Bending (Flexural) Strength of Fully Composite Beams t c =Y con hh r h r b ' 0.85 fc a ' C = 0.85 f ba (compression) f c Y 2 d PNA (plastic neutral axis) T = f y A s e (tension) In this case the concrete compression flange thickness a is less than the slab thickness Y 2 =Y con a/2 F y PNA in concrete slab M n = Ce = Te
13 Nominal Bending (Flexural) Strength of Fully Composite Beams ' b 0.85 fc t c =Y con h r a C c = 0.85 f A (compression) ' c c h r Y 2 Y 1 C fl b f Y1 = F (compression) y d PNA (plastic neutral axis) Tb f y Ast = f y As b f Y1 = F (tension) y F y A c = ab Y 2 =Y con a/2 PNA within beamflange Y 1 = F A 0.85 f A y s 2b f F y ' c c φ M b n ' Y1 d = φb[( 0.85 fc Ac ( Y1 + Y2 ) + 2b f FyY1 ( ) + As Fy ( Y1 )] 2 2 φ = φ b
14 Nominal Bending (Flexural) Strength of Fully Composite Beams ' b 0.85 fc t c =Y con h r a C c = 0.85 f A (compression) ' c c h r Y 2 Y 1 C fl C w (compression) (compression) d PNA (plastic neutral axis) T b (tension) F y Y 2 =Y con a/2 PNA within beamweb ' f y As 0.85 fc Ac 2b f t f Fy Y 1 = + t 2t F w y f φ M b n t ' f Y1 t f d = φb[( 0.85 fc Ac ( Y1 + Y2 ) + 2b f t f Fy ( Y1 ) + 2twFy ( Y1 t f )( ) + As Fy ( Y1 )] φ = φ b
15 Nominal Bending (Flexural) Strength of Fully Composite Beams
16 Nominal Bending (Flexural) Strength of Fully Composite Beams 21 MPa 42 MPa 525 MPa (MPa) 21 MPa 70 MPa
17 Nominal Bending (Flexural) Strength of Fully Composite Beams tension area kn kn
18 Nominal Bending (Flexural) Strength of Fully Composite Beams
19 Example 2250 mm 28 MPa 82.5 mm 37.5 mm 120 mm 16x26 250MPa 4,960 mm mm 23.2 mm +Y con a/2=308mm/ 382 knm
20 Nominal Bending (Flexural) Strength of Partially Composite Beams
21 Nominal Bending (Flexural) Strength of Partially Composite Beams
22 Nominal Bending (Flexural) Strength of Partially Composite Beams
23 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation (mm) 200, MPa (kg/m 3 ) E c = 0.043w 1.5 c f ' c ( MPa) for 1.44 t/m 3 < w c < 2.5t/m 3 E 4700 f ' c (Mpa) ( MPa) c = For w c > 2.5t/m 3
24 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation
25 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation mm 2 mm 2
26 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation
27 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation
28 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation
29 Elastic Behavior and Moment of Inertia of Composite Beams for Deflection Calculation AISC , Commentary I3.1
30
31 mm 2 mm 2 Shear Connectors
32
33
34
35
36 kn kn
37 Top flange
38
39 345MPa =450MPa) 28MPa 12cm 7.5cm 4.80kN/m 2 1.0kN/m 2
40 3.65m=10.95m 12cm 12.80m 7.5cm
41 3.2m 12cm 3.60kN/m 2 7.5cm 0.40kN/m 2 =4.50kN/m kN/m kN/m m =4.50x3.65=16.43kN/m =4.80x3.65=17.52kN/m =( )x3.65=14.60kN/m 65=14 60kN/m =(1.00)x3.65=3.65kN/m
42 =1.2x x17.52 =47.75kN/m75kN/m 47.75* = knm = =33.95kN/m 33.95* = knm 47.75*12.80=305.6 kn 33.95*12.80= kn
43 28MPa =345MPa =450MPa) mm
44 345 x x 28 x 3200 {12.80/4, (3.65/2+3.65/2)}=3.20m = 39.45mm = 120mm
45 mm 345 x x = 1216 knm 0.9 x / knm > knm knm > knm
46 1.5 ' kg / m 1.5 Ec = 0.043wc fc = 0.043(2400 ) 28 = 26, 753MPa E s = 200, 000MPa 3 n E = s E c = * / 2 + (120* 430)( / 2) y b = = mm (120*430) b mm / n = m / 7.46 = mm eff mm 120mm I tr = [2.964 x ( / 2) 2 ] 75mm 430x120 + [ x430x ] y b = mm d = mm I tr = x10 mm I tr = x 10 mm
47 mm L mm x x x I E L w mm N L , ) ( )(1 12, ) 75 ( / 4 = = < = = = Δ O.K. x I E tr ) (200,000)(1.011 ) (
48 =1.2x x3.65 =23.36kN/m 23.36* = knm = =18.25kN/m 18.25* = knm 09(FZ 0.9(F mm 3 y x )=0.9(345x1,486,307mm ) =461.5kNm<478.41kNm (F y Z x )/1.67=(345x1,486,307mm mm 3 )/167 )/1.67 =307.1kNm<373.76kNm
49 mm
50 345 x 10,451,59 = 47.35mm < t = 120mm 0.85 x 28 x mm 345 x 10,451. x =1,447.2 knm
51 0.9 x 1, ,447.2/1.67 1,302.5 knm > knm knm > knm
52 0.85x28x3200x47.35=3,606kN 10, (345)==3,606kN 1, (33% over strength)
53 977.92kNm kNm
54 kn kn partially composite beam
55
56
57
58 try to make kNm Also assume 55% composite action A s F y = ( 10452)(345) ) = 3, 606 kn for a W18x55 beam Q n = 0.55(3,606) = 1, 983 kn N Q a ' n 1,983,000 = = 0.85 f ' b 0.85(28)(3, ) = c eff ) 26.04mm a' Y 2 = Y con = 195 = mm 2 2
59 Assume that Y 1 is within the top flange of the beam: ' F y As 0.85 fc Ac 345(10,452) 0.85(28)(3200 x26.04) Y1 = = = mm < t f = mm O. K. 2b F 2(191.26)345 f y M n = [( 0.85(28)(3200x26.04)( ) + 2(191.26)(345)(12.30)( ) + (10,452)(345)( 12.30)] 2 2 M n =1, 179kNm 1,061kNm > kNm 706 knm > kNm φ = 0.90 Ω = b Ω b
60 1.5 ' kg / m 1.5 Ec = 0.043wc fc = 0.043(2400 ) 28 = 26, 753MPa 3 E s = 200, 000MPa n = E s E c = 7.46 x x y 10, / 2 + ( )( / 2) = = mm b 10,452 + (120x430 ) b mm / n = m / 7.46 = mm eff 430 I tr = [3.704x ,452( / 2) 2 ] 61.5mm 120mm 75mm 430x120 + [ x430x ] y b = mm y b d = 460mm I tr = x10 mm I tr = 1.193x10 mm
61 mm L mm x x x I E L w mm N L , ) ( )(1 12, ) 75 ( / 4 = = < = = = Δ O.K. x I E tr ) (200,000)(1.193 ) (
62 W 18x55 =1.2x x3.65 =23.36kN/m 23.36* = knm W 18x55 09(FZ 0.9(F 351mm 3 y x )=0.9(345x1,835,351mm ) =570kNm<478.41kNm = =18.25kN/m 18.25* = knm (F y Z x )/1.67=(345x1,835,351mm 351mm 3 )/167 )/1.67 =379kNm<373.76kNm Δ = 4 N / mm 4 5wLL 5x3.65 x12,800 L 12,800 = = 17.22mm < = = mm 8 384E( I ) 384(200,000)(3.704x10 ) x O.K.
63 mm 19 28MPa concrete Q n = 76. 5kN (See the next slide) Q n =1, 983 kn 1, = 25.9 (use 26) 26 x2 = 52 mm mm 150 ( 150 apart) m mm ) ( apart 6 x19 = 114 mm 8 x120 = 960 mm upper flute lower flute Note: usual rib (deck flute) spacing is about 150mm
64 2 (19) A sc = π = 283.5mm ' kg / m 1.5 Ec = 0.043wc fc = 0.043(2400 ) 28 = 26, 753MPa 3 Q n = 0.5(283.5) 28(26,753) = 122.7kN (1.0)(0.6)(283.5)(450) = 76. 5kN
65 CL mm = 12,600 mm mm 150 ribspacing 4650mm ( everytwoflute) 3300mm( everyflute) 4650mm( everytwoflute) 20@150mm 16@150150mm mm
66 0.6(345)(9.91)(460) = 0.9(944) = 850kN 305.6kN 944 /1.67 = 565kN kN 944kN F y = 345MPa mm fiftytwo 19
67 Non Composite Design of the Beam: =1.2x x17.52 =47.75kN/m75kN/m 47.75* = knm = =33.95kN/m 33.95* = knm 47.75*12.80=305.6 kn 33.95*12.80= kn x10 0.9(345) Z x, req = = 3,150x10 mm x10 Z x, req = = 3,366x10 mm (345/1.67) use W18x97 Z x = 3 3,450x10 mm 3
68 References Shen, J., Advanced dsteel Structures, Class Notes, IIT, 2009.
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