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STRENGTH OF MATERIALS. 221
/= Thickness of cylinder head in inches.
P = Radius of cylinder head in inches.
P = Pressure in pounds per square inch.
d = Depth in inches of dishing of the head at its center.
Si = Allowable working stress in the material, which may
be the same as given above.
This formula was used to calculate the thickness of a cast
iron head 44 inches in diameter, dished 7 inches, steam pressure
75 pounds per square inch.
Note.—In these examples the radius of the bolt circle
should be considered as the radius of the head when calculat-
ing the thickness.
The diameter of the bolts ought to be so large that the
strain on the bolts will not exceed 3000 to 5000 pounds per
square inch calculating the area of the bolt at the bottom of the
thread, and the distance from center to center of the bolts
ought not to exceed six times their diameter.
The above formula may also be used for dished cylinder
heads of wrought iron or steel, by allowing the proper value for
Si. For soft steel Si may be 9000 to 12,000 pounds, and for
wrought iron 5000 to 8000 pounds.
Caution.—Cast iron is not a desirable material to use for
large unribbed cylinder heads; either flat or dished wrought
iron or steel is far superior.
Strength of a Hollow Sphere Exposed to Internal
Pressure.
d2 7r
The pressure acts on a surface equal to
—t— and it is re-
D + d
sisted by a metal area equal to —~— X tt X A
D = External diameter.
d = Internal diameter.
/ = Thickness of metal.
When the difference between inside and outside diameter
is small it need not be considered in practice, and the formula
will be
:
d*TT
P X —4— = dX 7v X/X^i
which reduces to
„ 4X/X^i P X d
J
’^—d t = -±sT
Si — Allowable tensile stress in the material.
Note.—This formula only allows for tensile strength ; if it
is used for calculating the thickness of the body of a globe
valve or anything similar a liberal amount of metal must be
added, in order to obtain good results when casting.
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