Machinery's Handbook, 31st Edition
Shafts
295
SHAFTS Shaft Calculations Torsional Strength of Shafting.— In the formulas that follow, α = angular deflection of shaft in degrees c = distance from center of gravity to extreme fiber D = diameter of shaft in inches G = torsional modulus of elasticity = 11,500,000 pounds per square inch for steel J = polar moment of inertia of shaft cross section (see table) l = length of shaft in inches N = angular velocity of shaft in revolutions per minute P = power transmitted in horsepower S s = allowable torsional shearing stress in pounds per square inch T = torsional or twisting moment in inch-pounds Z p = polar section modulus (see table page 252 ) The allowable twisting moment for a shaft of any cross section such as circular, square, etc., is: (1) For a shaft delivering P horsepower at N revolutions per minute the twisting moment T being transmitted is: (2) The twisting moment T as determined by Formula (2) should be less than the value determined by using Formula (1) if the maximum allowable stress S s is not to be exceeded. The diameter of a solid circular shaft required to transmit a given torque T is: (3a) or (3b) The allowable stresses that are generally used in practice are: 4000 pounds per square inch for main power-transmitting shafts; 6000 pounds per square inch for lineshafts carrying pulleys; and 8500 pounds per square inch for small, short shafts, countershafts, etc. Using these allowable stresses, the horsepower P transmitted by a shaft of diameter D , or the diameter D of a shaft to transmit a given horsepower P may be determined from the following formulas: For main power-transmitting shafts: (4a) or (4b) For lineshafts carrying pulleys: (5a) or (5b) T S Z s p # = , N P 63 000 T = . D S T 51 s 3 = , D NS 3 = P 321 000 s P D N 80 3 = D N P 80 3 = . D N P 535 3 =
. P D N 535 3 =
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