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.
 

Problem 72
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is

where θ is the angle of incidence and d the distance from the source.)