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Bolt Stretching and Tensile Stress

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Bolt stretching according Hook's Law can be calculated as

dl = F L / E A                      (1)


dl = change in length of bolt (inches, m)

F = applied tensile load (lb, N)

L = effective length of bolt where tensile strength is applied (inches, m)

E = Young's Modulus of Elasticity (psi, N/m2)

A = tensile stress area of the bolt (square inches, m2)

Stress Area

The tensile stress area can be calculated as

A = (π / 4) (d - 0.9743 / n)2                       (2)


d = nominal diameter of bolt (in)

n = 1 / p = number of threads per inch

p = pitch, length per thread (in)

Tensile Stress

Tensile stress can be calculated as

σ = F / A                      (3)


σ = tensile stress (psi, N/m2 (Pa))

Example - Bolt Stretching - Imperial Units

  • stud diameter : 7/8 inches 
  • thread pitch : 9
  • Young's Modulus steel : 30 106 psi
  • designed bolt load : 10000 lb
  • effective length : 5 inches

The tensile stress area can be calculated as

A = 0.7854 ((7/8 in) - 0.9743 / 9)2

    = 0.46 (in2)

The elongation can be calculated as

dl = (10000 lb) (5 in) / ((30 106 psi) (0.46 in2))

    = 0.0036 (inches)

The tensile stress can be calculated as

σ = (10000 lb) / (0.46 in2)

   = 21740 psi

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