Bolt Diameter

Calculate the required bolt thread major diameter under axial, combined, or shear loading conditions.

Inputs

W

Load

\sigma

Tensile Stress

MPa

Formula Interpretation

Axial Tensile Load

d = \sqrt{\dfrac{2W}{\sigma}} \quad \text{(mm)}

$W$ is the applied axial load (N); $\sigma$ is the allowable tensile stress (MPa). Pure tension — only normal stress acts on the bolt cross-section.

Axial Load + Torsion

d = \sqrt{\dfrac{8W}{3\sigma}} \quad \text{(mm)}

When torsional load accompanies the axial load (e.g., pre-tightening torque), both normal and shear stresses act simultaneously. The coefficient 8/3 accounts for this combined effect.

Shear Force ⊥ Bolt Axis

d = \sqrt{\dfrac{4W}{\pi\tau}} \quad \text{(mm)}

$\tau$ is the allowable shear stress (MPa). The shear acts on the bolt shank cross-section; the threaded portion should be kept outside the shear plane.

Knowledge: Bolt Sizing

Because the loads on a bolt are typically a complex combination of forces in various directions, it is difficult to accurately characterize the stress state and determine dimensions. Bolt sizing is generally performed by calculating the size for each individual load type: axial load alone, combined axial and torsional load, and shear force perpendicular to the axis. The bolt size is expressed by the major (outer) diameter d of the external thread. The minor diameter d₁ ≈ 0.8d for reference.

Worked Example

Find the bolt diameter required to carry a tensile load of $30\,\text{kN}$ . The allowable tensile stress is $60\,\text{MPa}$ .

Step 1 — Apply Formula ① (axial load only)

d = \sqrt{\dfrac{2W}{\sigma}} = \sqrt{\dfrac{2 \times 30\,000}{60}} = \sqrt{1000} \approx 31.6 \text{ (mm)}

Step 2 — Select standard diameter

d_{\text{select}} = 32 \text{ mm (M32)}

Therefore, select a bolt with major diameter $32\,\text{mm}\;(\text{M32})$ .

Extended Knowledge

•Triangular (V-form) threads are preferred for fastening connections; square threads are preferred for power-transmission screws under heavy loads.
•When a bolt is subjected to shear, the shear stress acts on the minor diameter d₁. For calculation purposes, d₁ = 0.8d.
•In practice, select the next standard M-series diameter above the calculated value to ensure a safety margin.