To determine the load capacity or the size of beam section, it must satisfy the allowable stresses in both flexure (bending) and shear. Shearing stress usually governs in the design of short beams that are heavily loaded, while flexure is usually the governing stress for long beams. In material comparison, timber is low in shear strength than that of steel.
 

Problem 577
A plywood beam is built up of 1/4-in. strips separated by blocks as shown in Fig. P-577. What shearing force V will cause a maximum shearing stress of 200 psi?
 

Problem 576
Rework Prob. 575 assuming that the web is 200 mm instead of 160 mm.
 

Problem 575
Determine the maximum and minimum shearing stress in the web of the wide flange section in Fig. P-575 if V = 100 kN. Also, compute the percentage of vertical shear carried only by the web of the beam.
 

The lateral area of frustum of a right circular cone is given by the formula
 

where
R = radius of the lower base
r = radius of the upper base
L = length of lateral side
 

Problem 574
In the beam section shown in Fig. P-574, prove that the maximum horizontal shearing stress occurs at layers h/8 above or below the NA.
 

Problem 573
The cross-section of a beam is an isosceles triangle with vertex uppermost, of altitude h and base b. If V is the vertical shear, show that the maximum shearing stress is 3V / bh located at the midpoint of the altitude.
 

Problem 572
The T section shown in Fig. P-572 is the cross-section of a beam formed by joining two rectangular pieces of wood together. The beam is subjected to a maximum shearing force of 60 kN. Show that the NA is 34 mm from the top and the I_NA = 10.57 × 10⁶ mm⁴. Using these values, determine the shearing stress (a) at the neutral axis and (b) at the junction between the two pieces of wood.
 

Problem 571
For a beam with the same cross section as that in Prob. 570, plot the shearing stress distribution across the section at a section where the shearing force is V = 1800 lb.
 

Problem 570
A uniformly distributed load of 200 lb/ft is carried on a simply supported beam span. If the cross-section is as shown in Fig. P-570, determine the maximum length of the beam if the shearing stress is limited to 80 psi. Assume the load acts over the entire length of the beam.