§7.3 Shear Stress Distribution 159 7.3.1.Vertical shear in the web The distribution of shear stress due to bending at any point in a given transverse cross- section is given,in general,by eqn.(7.3) d/2 0 T= ydA Ib In the case of the I-beam,however,the width of the section is not constant so that the quantity dA will be different in the web and the flange.Equation (7.3)must therefore be modified to h/2 d/2 t= 0 It tydy+ h/2 「h2 274 小 As for the rectangular section,the first term produces a parabolic stress distribution.The second term is a constant and equal to the value of the shear stress at the top and bottom of the web,where y =h/2, i.e. tA=T8= 0b「d2h2] 2lt44 (7.7) The maximum shear occurs at the N.A.,where y=0, Qh2,2b「d2h27 81+2m4-4 (7.8) 7.3.2.Vertical shear in the flanges (a)Along the central section YY The vertical shear in the flange where the width of the section is b is again given by eqn.(7.3) as d/2 T= d/2 (7.9) The maximum value is that at the bottom of the flange when yi=h/2, (7.10 this value being considerably smaller than that obtained at the top of the web.$7.3 Shear Stress Distribution 159 7.3.1. Vertical shear in the web The distribution of shear stress due to bending at any point in a given transverse cross￾section is given, in general, by eqn. (7.3) dl2 .=-I Q ydA Ib Y In the case of the I-beam, however, the width of the section is not constant so that the quantity dA will be different in the web and the flange. Equation (7.3) must therefore be modified to hl2 di2 T =e It [ tydy+g I by,dy, Y hi2 As for the rectangular section, the first term produces a parabolic stress distribution. The second term is a constant and equal to the value of the shear stress at the top and bottom of the web, where y = hl2, i.e. The maximum shear occurs at the N.A., where y = 0, Qh2 Qb d2 h2 ‘Fmax=-+- --- 81 21t[4 41 (7.7) 7.3.2. Vertical shear in the flanges (a) Along the central section YY The vertical shear in the flange where the width of the section is b is again given by eqn. (7.3) as di2 Q Ib T = - y,dA Yl di2 = gj y,bdy, = lb Yl The maximum value is that at the bottom of the flange when y, = h/2, (7.9) (7.10) this value being considerably smaller than that obtained at the top of the web