COMPOUND STRAINS AND STRESSES 161 
Note.—You may assume that the wind pressure on the cylindrical surface is 
area to a pressure of half the given intensity on an area equal to the 
eter of the column multiplied by its height. (U.L.] 
11. Using the method of Art. 150, p. 154, show that if the cross section 
_ of the ring is a square whose sides are equal to s, then s=} af 7 (Gn 1). 
4 12. A steel bar 20 feet long and 2 inches square is elongated by a load of 
_ 20,000 lbs. Find by how much the volume of the bar is increased. Take 
_ ¢=0°27 and E=30,000,000 lbs. per square inch, 
13. A piece of cast iron 5 inches long and 1 inch square is subjected to com- 
ora in the direction of its length by a load of 10 tons. What must be the 
intensity, in tons per square inch, of the lateral external pressure which must be 
7 ed to the piece to prevent lateral strain, and what will then be the alteration 
in length? ‘Take o=0:25 and E=7000 tons per square inch. 
; 14. The shell of a cylindrical steam boiler is 8 feet 4 inches in diameter and 
1 inch thick, and the effective steam pressure is 200 lbs. per square inch. Find 
_ the circumferential strain produced, (a) neglecting the longitudinal strain, (5) 
taking the longitudinal strain into account. Take o=0°26 and E=30,000,000 lbs. 
square inch. 
15. A bar of mild steel 1 inch in diameter twists through an angle of 2:2 degrees 
in a 20-inch length when subjected to a twisting moment of 2200 inch-lbs. An 
_ exactly similar bar of the same material deflects 0°03 inch when supported 
horizontally at two points 20 inches apart and loaded at the centre of the span 
with a load of 264 lbs. Calculate the Modulus of Elasticity (E), Modulus of 
_ ‘Transverse Elasticity (C), Modulus of Elasticity of Bulk (K), and Poisson’s ratio 
_ for the material. (U.L.] 
y 16. The cylinder of an hydraulic press has an internal diameter of 10 inches, 
and the water pressure is 1500 lbs. per square inch. Find the thickness of the 
_ metal of the cylinder so that the maximum stress may be 2500 lbs. per square 
inch. What will be the stress in the metal at the outside of the cylinder? 
17. Find the safe internal pressure, in Ibs. per square inch, for the cylinder 
_ of an hydraulic press which has an internal diameter of 5 inches and an external 
_ diameter of 7 inches, when the maximum safe stress is 3000 lbs. per square inch. 
18. The internal diameter of a thick hollow cylinder is 54 inches, the internal 
eno is 1120 lbs. per square inch, and the maximum stress produced is 
Ibs. per square inch. Find the thickness of the metal. 
19. The internal and external radii of a thick hollow cylinder are 5 inches 
and 9 inches respectively. If the tensile stress in the metal at the inner surface 
_ of the cylinder is 3000 lbs. per square inch, what is the internal pressure? 
_ Calculate the values of the tensile stress in the metal, in lbs. per square inch, 
at radii 6, 7, 8, and 9 inches, and plot the stresses on the thickness of the 
_ cylinder asa base. Linear scale, full size, Stress scale, 1 inch to 1000 lbs. per 
_ Square inch. 
20. In a thick hollow cylinder, show that if the stress f at radius r is 
inversely proportional to r, or that fr?=constant, then p,r3;=f,t (Barlow's 
3 ), where p, is the internal pressure, f, the stress at the inner surface, 
_ 1% the external radius, and ¢ the thickness of the metal. The external pressure 
is assumed to be zero. 
' 21. The internal pressure in a thick hollow cylinder is 3 tons per square inch. 
_ The internal and external radii of the cylinder are 5 inches and 10 inches 
respectively. Calculate the values of the stress at radii 5, 6, 7, 8, 9, and 10 inches, 
_ (a) by Lamé’s formula ; (6) by Barlow's formula (see preceding exercise). Plot 
the results. Linear scale, full size. Stress scale, 1 inch to 2 tons per square inch. 
y 22. Same as preceding exercise, except that there is an initial stress in the 
_ material which varies uniformly from 2 tons per square inch compression at the 
_ inner surface to 2 tons per square inch tension at the outer surface. . 
