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SIMPLE STRAINS AND STRESSES 71 
$. A ferro-concrete column is 12 inches square. The principal reinforce- 
ment consists of four longitudinal steel bars placed near the angles of the 
‘column, and having an aggregate cross sectional area of 11 square inches, The 
load carried by the column is 50 tons. Determine the compressive stresses in 
the concrete and steel, in lbs. per square inch, assuming that the modulus of 
elasticity of the concrete is one-tenth that of the steel. 
4. A steel tube, 1°25 inches internal diameter, 0°104 inch thick, and 12 feet 
long, is covered and lined throughout with a r tubes 0-08 inch thick. The 
three tubes are firmly united at their ends, This compound tube is subjected 
to tension, and the stress produced in the steel tube is 9000 lbs. per square inch. 
Determine (1) the elongation of the tube, (2) the stress in the copper tubes, and 
3) the load carried by the compound tube. E=30,000,000 lbs. per square inch 
steel, and 16,000,000 lbs. per square inch for copper. 
6. The compound tube in the preceding exercise is raised in temperature 
200° F. Find the stresses in the steel and copper, and the increase in length of 
the tube. Also, what must be the magnitude of the forces, which, applied to the 
ends of the tube, will prevent its expansion? Coefficients of expansion of steel 
and copper 0°000006 and 0:0000095 respectively per degree F. 
6. If a thin circular hoop is strained and remains circular, prove that the 
circumferential strain is equal to the diametrical strain. 
7. A cylindrical steel hoop has an internal diameter 20 inches, thickness 1 
inch, and breadth 1 inch. A second steel hoop has an internal diameter 21°97 
inches, thickness 0°7 inch, and breadth 1 inch. The second hoop is expanded 
by heating and is then shrunk on to the first hoop. Determine (1) the new 
internal eter of the first hoop, (2) the tensile stress in the second hoop, and 
(3) the compressive stress in the first hoop. E=30,000,000 lbs. per square inch, 
8. Referring to the hoops of the preceding exercise. Find what must be the 
internal diameter of the second hoop so that the stress in it when it is shrunk 
on to the first will be 10,000 Ibs. per square inch. Then determine the stress 
in the first hoop and its new internal diameter. 
9. Calculate the length of a bar of uniform section whose density is 0°28 Ib. 
per cubic inch, and whose coefficient of elasticity is 28,000,000 Ibs. per square inch, 
which when hung from one end causes a maximum tensile stress in it of # ton 
persquare inch. Find also the increase in its length due to the tension. 
10. A wrought-iron bar 25 feet long is 2 inches diameter for 6 feet of its 
length, 1} inches diameter for 7 feet of its length, and 14 inches diameter for 
the remainder of its length. This bar is in tension, and the stress on the smallest 
sections is 12,000 lbs. per square inch, Taking E=28,000,000 lbs. per square 
inch, find the total elongation of the bar. . 
11. In testing to destruction a piece of mild steel, 0-937 inch diameter, in 
tension, a load-strain diagram was taken, The diagram showed the elongations 
full size, and the loads to a scale of 5 tons tolinch. The length of bar under 
observation was 10 inches. The total elongation after fracture was 2°46 inches. 
The area of the diagram, measured with a planimeter, was 7°47 square inches. 
Determine (a) the amount of work represented by the diagram, (b) the work 
done in straining the bar up to the elastic limit, taking the length as 10 inches, 
having given, load at elastic limit 9 tons, and modulus of elasticity 29,900,000 
lbs. per square inch. Also (c) express (a) as a multiple of (0). 
12. Calculate the resilience, in ft.-lbs., of a cubic inch of steel, in tension, 
taking the elastic limit at 20,000 lbs, per square inch, and the modulus of elas- 
ticity at 30,000,000 Ibs. per square inch. 
13. A steel bar 1 inch diameter and 6 feet long is put in tension by a force 
of 3 tons applied suddenly. Determine the maximum stress and the maximum 
elongation produced. E=30,000,000 Ibs. per square inch. 
14. If a bar 4 inch in diameter stretched } of an inch undera steady load of 
I ton, what stress would be produced in the rod by a weight of 150 lbs, falling 
through 3 inches before commencing to stretch the rod. The rod is initially 
unstressed, [U.L.] 
15. A steel rod, 2 inches diameter and 10 feet long when unloaded, is sus- 
pended from one end, and has a weight of 1000 lbs. threaded on to it. The 
is allowed to fall freely from a height h=1 inch on to a head formed 
on the lower end of the rod: Find the maximum stress produced in the rod. 
Also, find 4 so that the maximum stress may be 10,000 lbs. per square inch. 
E= 30,000,000 Ibs, per square inch, 
