160 APPLIED MECHANICS 
the maximum value of x so that there shall be no crushing stress in the~ 
link. 
3. A short cylindrical block of diameter d pe 
is subjected to crushing by a load whose line 77 
of action is parallel to the axis of the block, P = EA ‘Se P 
and at a@ distance # from it. Find the maxi- C2729 
mum value of x, in terms of d,so that there K2 
shall be no tensile stress in the block. 
4. Show that there will be no tensile stress Fig. 224. 
at the joints of a masonry arch if the resultant 
thrust between two adjacent blocks falls within the middle third of the joint. 
5. The crane hook shown in Fig. 225 has at the level AB a circular cross 
section 24 inches in diameter, and & the distance of B from the line of action 
of the load W is 2 inches. Find W, in tons, when the tensile stress at B is 
4 tons per square inch. Find also the nature and intehsity of the stress at A. 
6. Referring to the crane hook shown in Fig. 225, if d is the diameter of the 
section at AB, and k= “a, find d in terms of W, where W is in tons and the 
tensile stress at Bis 5 tons per square inch, What is the nature and intensity 
of the stress at A? ‘ 
7. A beam 3 inches deep and 2 inches wide projects from a wall and carries 
a load P, which acts as shown in Fig. 226. The maximum tensile stress in the 
Fia. 225. Fig. 226. Fig. 227. 
beam is to be 10,000 lbs. per square inch, Find the magnitude of P, in lbs., 
(a) when h=1} inches ; (6) when h=44 inches. 
8. In the crane hook shown in Fig. 227 the dimensions are given in terms of 
an unknown unit, and the section at AB is to be assumed as having the form 
shown in the lower part of the figure. Determine the unit for the dimensions in 
terms of W the load in tons, so that the total tensile stress at B shall be 5 tons 
per square inch, 
9. A built-up crane jib is in the form ofa curved girder, and a horizontal 
section near the base is a hollow rectangle. The outside dimensions of the 
rectangle are 54 and 36 inches, and the longer and shorter sides are 1 inch and 
2 inches thick respectively. Find the maximum tensile and compressive stresses 
induced in the material when a load of 25 tons is suspended from the end of the 
crane, the horizontal distance of the load from the centre of the section being 
50 feet. Show by a sketch how the intensity of stress varies across the 
section, [U.L.] 
10. A cylindrical masonry column of diameter d feet is subjected to a 
horizontal force due to the wind pressure. Prove that no tensile stress will be 
produced in the basal cross section of this column, if the resultant of the wind 
pressure and the weight of the column fall inside a circle concentric to the 
circular cross section of the column, and of diameter =} of the diameter of the 
column. Hence find the greatest height to which a column of granite 6 feet in 
diameter can be safely built, if the maximum intensity of the horizontal wind 
cer. . 40 lbs. per square foot, the weight of the granite being 160 lbs. per 
cubic foot. 
