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Bridges & Structures Comprehensive Design Example for Prestressed Concrete (PSC) Girder Superstructure Bridge Design Step 5 Design of Superstructure Design Step 5.7 Shear Design (S5.8) Shear design in the AASHTO-LRFD Specifications is based on the modified compression field theory. This method takes into account the effect of the axial force on the shea r behavior of the section. The angle of the shear cracking, θ, and the shear constant, β, are both functions of the level of applied shear stress and the axial strain of the section. Figure S5.8.3.4.2-1 (reproduced below) illustrates the shear parameters. Figure S5.8.3.4.2-1 - Illustration of Shear Parameters for Section Containing at Leas t the Minimum Amount of Transverse Reinforcement, V p = 0. The transverse reinforcement (stirrups) along the beam is shown in Figure 5.7-1. Table 5.7-1 lists the variables required to be calculated at several sections along the beam for shear analysis.  A sample calculation for shear at several sections follows the table. Notice that many equations contain the term V  p, the vertical component of the prestressing force. Since draped strands do not exist in the example beams, the value of V  p is taken as 0. Table 5.7-1 Shear Analysis at Different Sections Dist. (1) (ft.) A ps (in 2 ) A s (3) (in 2 ) CGS (4) (in.) d e (5) (in.) c (Rectangular behavior) (6) (in.) c (T-section behavior) (7) (in.) d e - β 1 c/2 (in.) 0.9d e (in.) d v (8) (in.) V u (9) (kips) V p (9,10) (kips) v u  /f′ c (11) M u (9,12) (kip-ft) M u  /d v (kips) 7.00 4.90 5.375 74.13 4.06 #N/A 72.40 66.71 72.40 340.4 0.00 0.1088 2,241 371.4 11.00 5.26 5.279 74.22 4.35 #N/A 72.37 66.80 72.37 315.1 0.00 0.1008 3,393 562.6 16.50 5.81 5.158 74.34 4.80 #N/A 72.30 66.91 72.30 280.7 0.00 0.0899 4,755 789.2 22.00 5.81 5.158 74.34 4.80 #N/A 72.14 66.91 72.14 246.7 0.00 0.0790 5,897 978.7 27.50 6.73 5.000 74.50 5.55 #N/A 72.14 67.05 7 2.14 213.4 0.00 0.0685 6,821 1,134.6 33.00 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 180.6 0.00 0.0579 7,535 1,253.3 38.50 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 148.3 0.00 0.0476 8,063 1,341.2 44.00 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 116.7 0.00 0.0374 8,381 1,394.1 49.50 6.73 5.000 68.37 5.55 #N/A 72.1467.0572.14 85.7 0.00 0.0275 8,494 1,412.9 54.50 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 118.4 0.00 0.0380 8,456 1,406.5 55.00 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 121.3 0.00 0.0389 8,440 1,403.9 60.50 6.73 5.000 68.37 5.55 #N/A 72.146 7.057 2.14 153.5 0.00 0.0492 8,163 1,357.8

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