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# 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/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
• 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

## Related Topics

• Fasteners - Bolts, nuts and threaded rods - torque, tension and loads

## Tag Search

• en: bolt stretching thightening tensile strengt stress modulus elasticity

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## Citation

• Engineering ToolBox, (2008). Bolt Stretching and Tensile Stress. [online] Available at: https://www.engineeringtoolbox.com/bolt-stretching-d_1164.html [Accessed Day Mo. Year].

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