How to Calculate Maximum Torsion in a Round Bar

Written by pauline gill
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How to Calculate Maximum Torsion in a Round Bar
Torque from these gears must be transmitted reliably through a shaft. (rusty gears image by steve dimitriou from Fotolia.com)

Round bars, otherwise known as shafts and axles, transmit torque and rotational power as well as carry radial and thrust loads when used as axles. Most power-transmitting shafts are composed of steel or stainless steel because of the balance of strength, rigidity, and hardness of this metal that go along with its relative economy compared to other metals. Designers of shafts transmitting torque or torsional forces must consider both the maximum and allowable yield stresses, tensile stresses, and shear stresses that a metal can withstand when selecting a shaft for a specific application.

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Instructions

  1. 1

    Define the round bar torsion application. In this example, a 1-inch-diameter axle shaft (round bar) will drive two wheels on a lawn tractor from a common drive sprocket. If the axle is composed of alloy steel with an ultimate tensile strength of 80,000 psi and a yield strength of 27216 Kilogram, you can calculate both the maximum torsion the shaft will handle before deforming or breaking, as well as the maximum allowable (operational) torsion.

    How to Calculate Maximum Torsion in a Round Bar
    A calculation of maximum torsion for this propeller shaft exists somewhere. (propeller image by cico from Fotolia.com)
  2. 2

    Determine the formula for maximum torsion the shaft will sustain without breaking. The maximum torsional stress is expressed as T max = (pi/16) x Su (sigma) x D^3, where T max is the maximum torsional stress in inch-pounds (in.-lb.), Su (sigma) is the maximum shear stress in psi, and D is the shaft or round bar diameter in inches.

    How to Calculate Maximum Torsion in a Round Bar
    Disc brakes on this train axle transmit torque to the wheels. (squelette de locomotive image by yann&Bernard; Anceze from Fotolia.com)
  3. 3

    Determine and substitute actual values for this alloy and solve for Tmax ultimate (breaking strength). The ultimate tensile strength of 80,000 psi should be multiplied by 0.75 according to the approximation formula Ssu = 0.75 x Su, where Ssu is the ultimate shear strength and Su is the ultimate tensile strength. This yields a value of 60,000 psi for ultimate shear strength Su. Substituting values, Tmax (breaking) = (pi/16) x 60,000 x D^3 = 0.1963 x 60,000 x 1 in.^3 = 11,778 in.-lb. torsion/12 in./ft. = 981.5ft.-lb. torsion.

    How to Calculate Maximum Torsion in a Round Bar
    A calibrated torque wrench can actually test smaller shafts. (torque wrench and accessories image by Christopher Dodge from Fotolia.com)
  4. 4

    Calculate the maximum torsion the shaft will sustain without permanent deformation. Multiply the tensile yield strength of 60,000 psi by 0.58 according to the approximation formula Ssyp = 0.585 Syp to yield 34,800 psi. Substituting values, Tmax (deformation) = 0.1963 x 34,800 psi x 1 inch^3 = 6821 in.-lb. torsion/12 in./ft. = 568.41ft.-lb. torsion.

  5. 5

    Calculate the maximum allowable torsion under which the shaft should be operated (for longevity and safety). Generally, the industry considers 60 per cent of the yield torsion with a 1.5 safety factor or 40 per cent of yield torsion. Therefore, 568.41ft.-lb. x 0.40 factor = 227.36ft.-lb. for the 1-inch alloy steel shaft as an operational limit.

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