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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.)

Solution:

Problem 69

A man on an island 12 miles south of a straight beach wishes to reach a point on shore 20 miles east. If a motorboat, making 20 miles per hour, can be hired at the rate of $2.00 per hour for the time it is actually used, and the cost of land transportation is $0.06 per mile, how much must he pay for the trip?

Problem 66

Find the largest right pyramid with a square base that can be inscribed in a sphere of radius a.

Problem 64

A sphere is cut to the shape of a circular cone. How much of the material can be saved? (See Problem 63)

Problem 62

Inscribe a circular cylinder of maximum convex surface area in a given circular cone.