Page 65 - Handbook of Civil Engineering Calculations, Second Edition

1.48 STRUCTURAL STEEL ENGINEERING AND DESIGN

3. Determine the static moment of the cross-sectional area
Calculate the static moment Q of the cross-sectional area above the plane under consider-
ation with respect to the centroidal axis of the section. Thus, Q Ay 3(6)(4) 72 in 3
3
(1180.1 cm ).
4. Compute the shear flow
Compute the shear flow q, using q VQ/I 2100(72)/666 227 lb/lin in. (39.75 kN/m).
5. Compute the shearing stress
Use the relation v q/t VQ/(It), where t width of the cross section at the given
plane. Then v 227/6 38 lb/sq.in. (262.0 kPa).
Note that v represents both the longitudinal and the transverse shearing stress at a par-
ticular point. This is based on the principle that the shearing stresses at a given point in
two mutually perpendicular directions are equal.

LOCATING THE SHEAR CENTER OF A SECTION

A cantilever beam carries the load shown in Fig. 31a and has the transverse section
shown in Fig. 31b. Locate the shear center of the section.

Calculation Procedure:

1. Construct a free-body diagram of a portion of the beam
Consider that the transverse section of a beam is symmetric solely about its horizontal
centroidal axis. If bending of the beam is not to be accompanied by torsion, the vertical

FIGURE 31