Bolt Stretching and Tensile Stress
Tensile stress and Hooke's Law.
Elongation
Bolt stretching according Hook's Law can be calculated as
dl = F L / E A (1)
where
dl = change in length of bolt (inches, m)
F = applied tensile load (lb, N)
Leff = 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)
where
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)
where
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
