Bolted Joint Design | Bolt Shear, Bearing Stress & Preload

Q: How do you calculate bolt shear stress?

For single shear, bolt shear stress may be estimated using tau equals 4F divided by pi d squared. For double shear, the shear stress is approximately half the single shear value, assuming equal load sharing between two shear planes.

Q: How is bolt bearing stress calculated?

Bearing stress is commonly estimated using sigma c equals F divided by d times t, where F is the applied force, d is the bolt diameter and t is the plate thickness.

Bolted joints are widely used in mechanical and structural design because they provide strong, removable connections between components. This page covers bolt shear stress, bearing stress, eccentric loading, combined stresses, preload and practical design guidance for bolted joint calculations.

Engineering note: The formulae on this page are intended for general engineering guidance and preliminary design calculations. Final bolted joint design should consider bolt grade, preload, thread engagement, friction, fatigue, joint stiffness, bearing stress, prying action and the relevant design standards.

Introduction to Bolted Joints

Bolted joints are widely used to fasten mechanical components because they provide strong connections that can be disassembled for maintenance or inspection. A good bolted joint design considers assembly, positional accuracy, load resistance, disassembly requirements and long-term retention.

Common fastening methods include bolts and screws, rivets, pins, keys, welding, brazing, adhesives and mechanical locking methods. This page focuses on bolted joints using bolts, nuts and hex-head screws.

Design Considerations

Ease of assembly and disassembly
Positional accuracy and alignment
Ability to hold components rigidly against expected loads
Freedom to separate components for service
Resistance to loosening over time
Suitability of bolt grade, thread length and joint material

Types of Bolt Loading

Bolts are typically loaded in one or more of the following ways:

Tension — axial load along the bolt shank, usually associated with clamping action.
Shear — transverse load across the bolt shank, in either single shear or double shear.
Combined shear and tension — axial and transverse loads acting together.
Preload — initial tensile force introduced by tightening the bolt.

Bending loads on bolts should be avoided where possible. If significant lateral loads exist, dowels, locating pins, fitted bolts or shear keys may be preferable to relying on the bolt shank alone.

HSFG bolts, or high strength friction grip bolts, are tightened to a defined preload so that load transfer occurs through friction between the plates rather than direct shear through the bolt shank.

Bolt Shear Strength and Bearing Stress

The following formulae assume no friction between clamped plates. This is conservative for ordinary bearing-type joints, because the bolt is assumed to resist the applied shear directly.

Single Shear

Diagram of single and double shear loading in a bolted joint

Shear stress in single shear:

τ = 4Fπd²

Bearing compressive stress:

σ_c = Fdt

Plate shear stress at edge:

τ_plate = F2ct

Double Shear

Shear stress in double shear:

τ = 2Fπd²

Bearing compressive stress:

σ_c = Fdt

Plate shear stress at edge:

τ_plate = F2ct

Symbol	Meaning
F	Applied force
d	Bolt diameter
t	Plate thickness
c	Edge distance or shear plane width used for plate shear check
τ	Bolt shear stress
σ_c	Bearing compressive stress

For an interactive check, use the Bolt Shear Stress Calculator, Bolt Bearing Stress Calculator or Bolt Plate Shear Calculator.

Shear from Torsion and Eccentric Loading

When a bracket carries an offset load, the applied force creates both direct shear and a moment about the bolt group centroid. Bolts arranged around the centroid share the direct shear and also receive additional torsional force components.

Bolt group layout showing centroid and torsional loading distribution

Direct vertical force per bolt:

F_nv = Fn

Torsional force at bolt n:

F_nm = F R r_n∑ r_i²

Horizontal component of torsional force:

F_th = F_nm v_n√(h_n² + v_n²)

Vertical component including direct shear:

F_tv = F_nv + F_nm h_n√(h_n² + v_n²)

Resultant force at bolt:

F_t = √(F_th² + F_tv²)

Shear stress from resultant force:

τ_t = F_tA

For an interactive calculation of rectangular bolt groups, use the Bolt Group Eccentric Load Calculator.

Bending Forces and Combined Loads

Bolted joint under bending showing shear and tensile force distribution

Bolted joints subject to offset loads may experience both shear and tensile forces. In simplified calculations, shear may be distributed across the bolts, while tensile load from bending is distributed according to bolt position and lever arm.

Direct shear per bolt:

F_s = F_vn

Shear stress:

τ_n = F_sA

Tensile force from bending:

F_nt = ((F_v R_v) + (F_h R_h)) V_n∑ V_i²

Tensile stress:

σ_n = F_ntA

Where F_v and F_h are vertical and horizontal components, R_v and R_h are eccentric radii and V_n is the lever arm for each bolt.

Combined Stresses and Failure Criteria

For ductile bolts subject to combined tensile and shear stresses, the Von Mises criterion is commonly used. This converts the combined tensile and shear stress state into a single equivalent stress.

Von Mises equivalent stress:

σ_vm = √(σ_x² + 3τ_xy²)

Factor of safety:

FoS = S_y√(σ_x² + 3τ_xy²)

Include preload, residual torque and service loads when evaluating the combined stress state, because these can significantly change the safety margin.

For an interactive check, use the Bolt Combined Stress Calculator.

Preloaded Bolts

Preloading, or tensioning, a bolt changes the initial stress state and creates clamp force between the connected parts. Preload can improve joint performance, reduce slip and help maintain contact between plates.

Approximate torque-preload relationship:

T = KFd

Estimated preload:

F = TKd

Where T is tightening torque, K is the nut factor, F is preload and d is bolt diameter.

For an interactive calculation, use the Bolt Preload Calculator.

For more detailed preload guidance, see the bolt preload calculations and theory page.

Practical Bolted Joint Design Guidance

Keep bolts primarily in tension where possible.
Avoid putting threads in the shear plane where possible.
Use the plain shank through the shear plane for higher shear capacity.
Check bolt shear, plate bearing and plate shear-out separately.
Consider eccentric loading where the applied force does not pass through the bolt group centroid.
Use preload carefully where slip resistance, fatigue or sealing is important.
Account for fatigue where loads are cyclic.
Consider loosening resistance, locking methods and maintenance access.

Frequently Asked Questions

What is a bolted joint used for?

A bolted joint is used to clamp components together using a bolt and nut. It provides a strong mechanical connection that can usually be disassembled for maintenance, inspection or replacement.

How do you calculate bolt shear stress?

For single shear, bolt shear stress may be estimated using τ = 4F / (πd²). For double shear, the shear stress is approximately half the single shear value, assuming equal load sharing between the two shear planes.

What is the difference between single shear and double shear?

In single shear, the bolt is cut by one shear plane. In double shear, the bolt is cut by two shear planes, so the applied load is shared across two shear areas.

How is bolt bearing stress calculated?

Bearing stress is commonly estimated using σ_c = F / (dt), where F is the applied force, d is the bolt diameter and t is the plate thickness.

Should bolts carry shear loads?

Bolts can carry shear loads, but where possible lateral forces should be resisted by friction, dowels, fitted bolts, keys or other locating features rather than relying on threads in shear.

What happens if bolt threads are in the shear plane?

The thread root has reduced cross-sectional area compared with the plain shank, so shear capacity is reduced. Where possible, the plain shank should pass through the shear plane.

How do HSFG bolts work?

High strength friction grip bolts are tightened to a specified preload so that load transfer occurs through friction between the connected plates rather than direct shear through the bolt.

Should preload be included in bolt stress calculations?

Yes. Preload and residual torque can affect the bolt stress state and should be included where accurate service stress, fatigue or joint slip calculations are required.

What failure theory is commonly used for combined bolt stresses?

For ductile bolts, the Von Mises criterion is commonly used to combine tensile and shear stresses into a single equivalent stress.

Bolted Joint Design and Calculations