WORLD FOR CIVIL

Topic 6.3a: Power Transmission - Example 1

Example 1:
A solid steel shaft, shown in Diagram 1, has a 1 inch diameter and an allowable shear stress of 12,000 lb/in². What is the largest amount of power which could safely be transmitted down the shaft if it is to rotate at 2400 rpm?

Solution:
Step 1: First, using the maximum allowable shear stress, we determine the largest torque which may be applied to the shaft. The formula for the shear stress in a shaft is:
= T r / J ; then solving for the torque: T = J / r ; where
J = (3.1416) d⁴ / 32 = .098 in⁴; r = .5 inch; and = 12.000 lb/in², (We use the allowable shear stress as the maximum stress in the shaft.) Putting values into the equation and solving:
T = 12,000 lb/in² * .098 in⁴ / .5 in = 2356 in-lb = 196 ft-lb.

Step 2: Now that we have the maximum torque we can safely apply, we can determine the largest amount of power we can transmitted from the horsepower equation.
P_hp = 2 pi T n/ 550 = 2 (3.1416) 196 ft-lb. (40 rev/s)/ (550 ft-lb/s/hp) = 90 hp