A cylindrical bar made of phenolic must withstand 106 cycles

A cylindrical bar made of phenolic must withstand 106 cycles of an axial load of P = 218 lbs at 1800 cpm. Find the diameter of the bar required (let Sallowable=5.4 ksi).

Solution

S_e   = 5.4 ksi

S_u   = 7 ksi

Using Basquin\'s equation

B = log(Se) - log(0.9*S_u) / 3     = log(5400) - log(0.9*7000)   / 3   = -0.0223156

A = S_e / 10^(6*B)    = 7350

Therefore   Sr    = A * N^B    = 7350 * N^(-0.0223156)

                 for N = 106 cycles

                Sr   = 6.623 ksi

4 * P / pi * d^2   = 6.623 * 10^3

diameter = 0.2047 inches