# 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)

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

E = Young's Modulus of Elasticity (psi, N/m^{2})

A = tensile stress area of the bolt (square inches, m^{2})

### 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/m ^{2} (Pa))*

### Example - Bolt Stretching - Imperial Units

- stud diameter :
*7/8 inches* - thread pitch :
*9* - Young's Modulus steel :
*30 10*^{6}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 (in^{2})

The elongation can be calculated as

dl = (10000 lb) (5 in) / ((30 10^{6}psi) (0.46 in^{2}))

= 0.0036 (inches)

The tensile stress can be calculated as

*σ = (10000 lb) / (0.46 in ^{2})*

* = 21740 psi*