# Allowable Stress

If a member is loaded beyond its ultimate stress, it will fail or rupture. In engineering structures, it is essential that the structure not fail. Thus, the design is based on some lower value called allowable stress or design stress. If, for example, a certain type of steel is known to have an ultimate strength of 110,000 psi, a lower allowable stress would be used for design, say 55,000 psi. This allowable stress would allow only half the load the ultimate stress would allow. Allowable stress values are different for different materials, and they are tabulated and recommended by the International Building Code Association.
The ratio of the ultimate stress to the allowable stress is known as the factor of safety.

factor of safety = ultimate strength / allowable stress
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Example
Determine the required size for a steel rod to support a tensile load of 50,000 lb if the allowable tensile stress of the steel is 25, 000 psi.

Solution
σ = F/A
or
A = F/σ = 50, 000lb/25, 000psi = 2in2
A = πD2/4 = 2in2
Solving for D, we have:
D = 1.6 in