This simple bolt stress calculator takes bolt geometry and load inputs, and outputs various bolt stresses. The thread shear stress and Equivalent von-Mises stress can be compared with the allowable stress limits (Typically 0.5*Yield Strength and 0.66*Yield Strength respectively, but varies based on design codes.)

Assumptions and Notes

For these calculations, the coordinate system is oriented as shown below – Z direction is parallel to the shaft of the bolt.

• If you have an “accurate” structural model where the fastener is physically modeled, then the analysis results should supersede this calculation.
• This calculator is as good as the inputs. Load reactions from a structural analysis where a bolt is not physically modeled can vary significantly based on the bolted joint modeling method (Bonded contact vs Beam, Preload application method, boundary conditions etc.)
• The equivalent stress computed is stress at a point which is at the outermost fiber on the bolt shaft and is not in a region of stress concentration. In real life, the average stress through the cross section of the bolt shaft will be lower than the value computed by this calculator. This makes the calculated equivalent stress conservative for static load qualification.
• Stress concentrations are not accounted for by this calculator. Therefore, fatigue load qualifications should not be performed using the calculated von-Mises stress.

Calculation Method

Three types of stresses are considered for this calculation:

Maximum Tensile Stress within the Bolt Shaft

This is the sum of the tensile stress resulting from:

• Bolt Preload (Fp / A)
• Axial Load (Fz / A)
• Bending Moment about the X axis (32*Mx / pi*d^3)
• Bending Moment about the Y axis (32*My / pi*d^3)

Maximum Shear Stress within the Bolt Shaft

This is the sum of the shear stress resulting from:

• Direct Shear Stress due to Force along the X axis (Fx / A)
• Direct Shear Stress due to Force along the Y axis (Fy / A)
• Torsional Shear Stress (16*Mz / pi*d^3)

Maximum Shear Stress within the Bolt Threads

This is the sum of the shear stress resulting from:

• Direct Shear due to Preload (Fp / At)
• Direct Shear due to Force along Z axis (Fz / At)

The total tensile and shear stress can be used to calculate the equivalent von-Mises Stress. You can read more on this calculation in this article : How to calculate bolt stress.

Calculator Verification

The preloaded values in the calculator are for a test case as shown below:

The following forces and moments are applied:

(Fx, Fy, Fz) = (25, -60, -80) N

(Mx, My, Mz) = (250, -20, 10) N.mm

The load reactions computed at the fixity are as follows:

(Fx, Fy, Fz) = (-25, 60, 80) N

(Mx, My, Mz) = (-1300, -418, -10) N.mm

This results in an Equivalent von-Mises Stress of 116 MPa as follows:

The stress result is shown below. As stated previously the stress at the stress concentration is not considered by the calculator. The calculated VMS of 116 MPa occurs at a distance between one and two elements away from the peak stress as show in Figure 3 below.