ABSTRACT
Vv EDED = (13.1) where d = effective depth of the slab u = perimeter of the portion of the slab considered Similarly, consider a portion of the slab along with an isolated column as shown in Fig. 13.2b. If MED is the moment in the column due to loads acting on the slab at
vED
VED
Fig. 13.2b Shear stress distribution due to moment the ultimate limit state, the column moment is resisted by shear stresses vED distributed around the edges of the slab. Similar to bending stresses the shear stress vED changes sign on the two symmetrical halves of the slab. In general the magnitude of the shear stress is not constant, but for design purposes, it is taken as constant. The shape of the slab considered for calculation of the shear stress varies depending on the shape of the column and the presence of local thickening of the slab near columns known as column capitals. The perimeter of the portion of the slab considered is known as the critical perimeter. 13.3 CRITICAL SHEAR PERIMETER The basic control perimeter is at a distance of two times the effective depth of the slab from the face of the column as shown in Fig. 13.3. The effective depth d can be taken as the average of the effective depths in two orthogonal directions. Depending on the shape of the column cross section, the shape of the critical perimeter in plan varies as shown in Fig. 13.4. i. In the case of a circular columns, the critical perimeter U1 is of the same shape as the column and is equal to u1 = π (D + 4d) (13.2) where D is diameter of the column ii. In the case of rectangular columns, the critical perimeter is similar to the shape of the column, except with rounded corners and is equal to u1 = 2(C1 + C2) + 4π d (13.3) where C1 and C2 are side dimensions of the column For other than circular and rectangular columns, the basic idea of the critical perimeter being at a distance of twice the effective depth of the slab from the sides of the column and rounded at the corners as shown in Fig. 13.5 is adopted.
