8.3 CHECK FOR SHEAR

Item 1.0 8.0

Chainage of Section from left support 0.00 12.50

Details of prestressing1 Net prestressing force in Stage 1 prestressing (t) 393.2 433.42 No of Tendons in Stage-1 prestressing 34 343 Net prestressing force in Stage 2 prestressing (t) 121.5 130.64 No of Tendons in Stage-2 prestressing 10 105 Total No of strands 44 446 Distance from bottom of Stage 1 prestressing (m) 0.555 0.1207 Distance from bottom of Stage 2 prestressing (m) 1.170 0.1208 Net eccentricity from bottom (m) 0.700 0.2019 Vertical Component of Prestress Stage 1 Prestressing (t) 46.9 0.0

10 Vertical Component of Prestress Stage 2 Prestressing (t) 20.7 0.011 Total Vertical Component of Prestress (t) 67.6 0.0

Section Properties12 Width of deck slab (m) 3.000 3.00013 Width of Bottom Bulb (m) 0.800 0.80014 Width of web Bw (m) 0.800 0.30015 Duct Dia Dduct (m) 0.090 0.09016 Effective width of Web (Bw-1.2*Dduct) (m) 0.755 0.17917 Depth of beam only (m) 1.500 1.50018 Depth of deck only (m) 0.225 0.22519 Depth of Bottom Flange (m) 0.250 0.25020 Over all depth (m) 1.725 1.72521 Area of simple section (m2) 1.270 0.79822 Area of composite section (m2) 2.045 1.57523 C.G. of simple section from bottom (m) 0.786 0.77424 C.G. of composite section from bottom (m) 1.121 1.21525 Moment of inertia-simple section, Ip (m4) 0.538 0.22026 Moment of inertia-composite section, Ic (m4) 0.634 0.25027 fck (Mpa) 40 40

Sr. No UNITS

8.3 CHECK FOR SHEAR

Item 1.0 8.0

Chainage of Section from left support 0.00 12.50Sr. No UNITS

Shear Forces28 Due to Self Weight of beam (t) 62.9 030 Due to S.I.D.L.+WC (t) 39.8 2.731 Due to Live Load (Positive Moment) (t) 80.8 6.932 Due to Footpath live Load (t) 58.8 4.433 Ultimate Shear force (t) 242.3 13.6

Ultimate Shear force (corr. To Negative moment) (t) 915.16 151.06

Corr. Bending Moments34 Due to Self Weight of beam (tm) 0.5 -361.736 Due to S.I.D.L. (tm) 0.2 -238.037 Due to Footpath live Load (tm) 0.0 -33.838 Due to Live Load (Positive Moment) (tm) 0.0 22.0

Ultimate Moment (Positive moment) (tm) 0.1 22.0Ultimate Moment (Negative moment) (tm) 0.0 -437.2

39 ultimate moment (max of positive and negative) (tm) 0.1 437.240 db (m) 1.38 1.38

Grade of deck slab 40.00 40.00Grade of girder 40.00 40.00Modulus of elasticity of deck slab concrete 33.35 33.35Modulus of elasticity of girder concrete 33.35 33.35

41 Width of equivalent Compression Flange Bf (m) 3.0 0.8042 Depth of Compression Flange t (m) 0.23 0.0043 Stress at extreme fibre t/m2 577.86 3636.0244 fctk0.05/ym t/m2 -156.40 -156.4045 Cracked/Uncracked Uncracked Uncracked

Cracked shear capacity of the section57 K =1+√200/d ≤ 2 1.3 1.3

58 Vmin =0.031K3/2fck1/2 Mpa 0.3 0.3

59 Axial Stress( σcp ) MPa 2.517 3.57360 VRd.c 1 =(vmin+0.15σcp)bw.d T 86.4 25.258 Area of longitudinal reinforcement mm2 452.4 452.459 row1= Asl/(bwd) 0.000 0.00260 Vrd,c 2 T 65.8 23.161 Vrd, c (Max of Vrd,c 1 and Vrdc 2) T 86.4 25.2

UnCracked shear capacity of the section62 Moment of Inertia of section (I) (m4) 0.634 0.25063 fctd =fctk/γm Mpa 1.5 1.5

8.3 CHECK FOR SHEAR

Item 1.0 8.0

Chainage of Section from left support 0.00 12.50Sr. No UNITS

64 Flexural tensile stress at the location due to applied loads Mpa 0.0 2.565 S1 - Top flange m3 0.0378 0.020566 S2- Top Haunch m3 0.0046 0.002467 S3- Web m3 0.0027 0.002768 (Ay)p-first moment of inertia between composite centroidal axis and top of

girderm3 0.0451 0.0256

69 S1-Deck m3 0.332 0.26870 S2-Top Flange m3 0.038 0.020571 S-3 Top Haunch m3 0.005 0.001572 S-4 Web m3 0.003 0.0025

73(Ay)c-first moment of inertia between centroidal axis and compression fibre

m3 0.3769 0.2928

74 Vc1 T 186.1 -0.575 Stress at composite centroid due to Vc1, fs T/m2 20.7 -0.4

76 Stress at Composite centroid due to ultimate design moment acting on the precast section alone, fc,m T/m2 0.4 -447.6

77 Stress at composite centroid due to prestress, fcp T/m2 377.8 58.678 fcp T/m2 302.7 -400.879 Vc2 T 314 4580 Vrd,c = Vc1+Vc2 T 500.1 44.6

81Shear Capacity of the Section, Vrd,c

T 500.1 44.6

74 VRd.c =Ibwc/s x sqrt(fctd2+k1σcpfctd) T N.A 42.8

82 V-Vp, ton T 309.9 13.6

83 Shear Reinforcement Check No Shear Reinf. Is Required

No Shear Reinf. Is Required

84 Assuming theta 45.0 45.085 Provided dia of reinforcement 10.0 10.086 Spacing mm 200 20087 Area of Steel Provided per running meter mm2 785.4 785.488 Grade of steel 500 50089 Vrd,s T 28.5 42.490 fcd T/m2 1822.4 1822.491 fcp/fcd 0.21 0.0392 alpha, cw 1.21 1.0393 Vrd.max T 510.7 154.0

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94 Minimum Shear Reinforcement mm2 728.589 273.221OK OK