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STRENGTH OF MATERIALS. 21
5
especially so with regard to its tensile strength. Generally-
speaking, we may say that for cast iron the
Modulus of elasticity is 12,000,000 to 15,000,000 pounds.
Tensile strength at limit of elasticity, 5,000 to 10,000 pounds.
Ultimate tensile strength, 10,000 to 20,000 pounds.
Elongation Under Tension.
The total stretch or elongation of any specimen when
exposed to tensile stress within the elastic limit is directly pro-
portional to the length of the specimen, but it is inversely
proportional to the modulus of elasticity and the cross sectional
area of the specimen. The following formulas may, therefore,
be used in such calculations
:
E- P X L
s X A
p _ E X s X A
. _^ X L
EX A
T
_E X sX A
A -PXL
s X.E
p
E = Modulus of elasticity in pounds per square inch.
P = Load or force in pounds acting to elongate the specimen.
s = Total stretch of specimen in inches in the length L.
L = Original length of specimen in inches before force is
applied.
A = Cross-sectional area of specimen in square inches.
Example.
From experiments it is known that the modulus of elasticity
for a certain kind of wrought iron is 28,000,000 ; what will then
be the total stretch or elongation in a round boiler stay, 1%
inches in diameter and 6 feet long, when exposed to a stress of
5000 pounds?
Solution
:
1% inches diameter = 1.227 inches area (see table, page 209)
6 feet long = 72 inches.
s= P X L
E X A
s
_ 5000 X 72
28000000 X 1227
s = 0.0105 inches = total stretch in the stay.
Note. — As already stated, wrought iron can not be
stretched as much as one-thousandth part of its original length
without danger of destroying its elasticity; thus, for this stay,
which is 72 inches, the limit of elasticity will be at a stretch of
0.072 inches; therefore the stretch produced by a load of 5,000
pounds, which is calculated to be 0.0105 inches, is well within
the safe limit.
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