Handbook of Civil Engineering Calculations

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
   (1180.1cm^3 ).


4. Compute the shear flow
   Compute the shear flow q, using q = VQfI= 2100(72)7666 = 227 Ib/lin in (39.75 kN/m).


5. Compute the shearing stress
   Use the relation v = qlt= VQI(If), where t = width of the cross section at the given plane.
   Then v = 227/6 = 38 lb/in^2 (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 OFA SECTION

A cantilever beam carries the load shown in Fig. 3 Ia and has the transverse section

shown in Fig. 316. 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

(c) Partial plan of top flange (b) Section X-X

FIGURE 31

(a) Load on cantilever beam

Thickness