The RoyMech bolted joint and fastener calculator section provides engineering tools for bolt shear stress, bearing stress, plate shear, eccentric bolt group loading, preload, tightening torque, thread stress area, proof load, thread engagement, thread stripping, bolt length and fastener layout checks.
A bolted joint calculator is used to estimate stresses, forces, clearances and safety margins in bolted connections. These calculations may include bolt shear stress, tensile stress, bearing stress between the bolt and plate, plate edge shear, bolt preload, tightening torque, eccentric bolt group loading, combined tensile and shear stress, thread stress area and thread stripping capacity.
For a circular bolt in single shear, the basic shear stress formula is:
τ = 4F / πd2
For double shear, the shear stress is:
τ = 2F / πd2
Where F is the applied shear force and d is the bolt diameter.
These calculators are intended to help engineers carry out preliminary bolted joint and fastener checks using clear formulae, substituted values and worked calculations.
For background theory, loading methods and bolted joint design guidance, see the main RoyMech reference page: Bolted Joint Design and Calculations.
| Calculator | What It Calculates | Useful For | Calculator Link |
| Bolt Shear Stress Calculator | Calculates bolt shear stress for single shear and double shear loading using applied force and bolt diameter. | Checking bolts subject to transverse shear loads in simple bolted joints. | Bolt Shear Stress Calculator |
| Bolt Bearing Stress Calculator | Calculates bearing stress between a bolt and connected plate using applied force, bolt diameter and plate thickness. | Checking compressive contact stress in plates, lugs, brackets and bolted connections. | Bolt Bearing Stress Calculator |
| Bolt Plate Shear Calculator | Calculates plate edge shear stress using applied force, edge distance or shear width and plate thickness. | Checking whether the connected plate may fail in shear near the bolt hole or plate edge. | Bolt Plate Shear Calculator |
| Bolt Group Eccentric Load Calculator | Calculates direct shear, torsional load distribution and resultant bolt loads for rectangular bolt groups subject to eccentric loading. | Bracket connections, base plates, support plates and bolt groups where the applied load does not pass through the bolt group centroid. | Bolt Group Eccentric Load Calculator |
| Bolt Combined Stress Calculator | Calculates combined tensile and shear stress using the Von Mises criterion. | Bolts subject to both axial tension and transverse shear loading. | Bolt Combined Stress Calculator |
| Bolt Preload Calculator | Estimates bolt preload and clamp force from tightening torque, bolt diameter and nut factor. | Torque-to-preload estimates for preloaded bolted joints. | Bolt Preload Calculator |
| Bolt Tensile Stress Calculator | Calculates tensile stress in a bolt from axial load and bolt diameter. | Axial bolt tension checks and simple tensile load calculations. | Bolt Tensile Stress Calculator |
| Thread Tensile Stress Area Calculator | Calculates ISO metric thread tensile stress area from nominal diameter and pitch. | Threaded-section tensile stress checks where the thread is the critical section. | Thread Tensile Stress Area Calculator |
| Bolt Proof Load Calculator | Calculates proof load from proof stress and tensile stress area. | Bolt grade checks, proof load checks and recommended preload range estimates. | Bolt Proof Load Calculator |
| Bolt Tightening Torque Calculator | Calculates tightening torque from target preload, bolt diameter and nut factor. | Preload-to-torque estimates for bolt tightening calculations. | Bolt Tightening Torque Calculator |
| Thread Engagement Length Calculator | Estimates required thread engagement length for tapped holes and threaded joints. | Thread engagement, pull-out and tapped hole checks. | Thread Engagement Length Calculator |
| Thread Stripping Calculator | Checks approximate internal and external thread stripping capacity. | Nut threads, tapped holes, threaded inserts and softer material thread checks. | Thread Stripping Calculator |
| Bolt Length Calculator | Estimates required bolt length for through bolts with nuts and bolts into tapped holes. | Fastener selection, assembly planning and checking selected bolt length. | Bolt Length Calculator |
| Washer Bearing Pressure Calculator | Calculates bearing pressure under a washer, nut face or bolt head from clamp force. | Clamp load pressure checks on softer materials and washer sizing. | Washer Bearing Pressure Calculator |
| Bolt Spacing and Edge Distance Calculator | Checks bolt pitch and edge distance against selected diameter-based layout rules. | Preliminary bolted plate layout checks. | Bolt Spacing and Edge Distance Calculator |
| Bolt Hole Clearance Calculator | Calculates diametral and radial clearance between a bolt and hole. | Clearance hole, fit and assembly checks. | Bolt Hole Clearance Calculator |
| Bolt Head and Nut Clearance Calculator | Checks clearance around a bolt head or nut for spanner or socket access. | Tool access, maintenance clearance and fastener layout checks. | Bolt Head and Nut Clearance Calculator |
| Design Task | Description | Recommended Calculator |
| Check bolt shear stress | Check shear stress in a bolt shank for single shear or double shear loading. | Bolt Shear Stress Calculator |
| Check bolt tensile stress | Check axial tensile stress in a bolt from an applied tensile load. | Bolt Tensile Stress Calculator |
| Check combined tension and shear | Check bolts carrying both axial tensile load and transverse shear load. | Bolt Combined Stress Calculator |
| Check bearing stress | Check compressive bearing stress between the bolt and connected plate. | Bolt Bearing Stress Calculator |
| Check plate edge shear-out | Check whether a plate may fail by shear-out near the bolt hole or edge. | Bolt Plate Shear Calculator |
| Analyse eccentric bolt groups | Calculate bolt forces where the applied load does not pass through the bolt group centroid. | Bolt Group Eccentric Load Calculator |
| Estimate preload from torque | Estimate bolt preload and clamp force from tightening torque, diameter and nut factor. | Bolt Preload Calculator |
| Calculate torque from target preload | Estimate tightening torque needed to achieve a selected preload. | Bolt Tightening Torque Calculator |
| Calculate thread stress area | Calculate ISO metric thread tensile stress area from diameter and pitch. | Thread Tensile Stress Area Calculator |
| Check bolt proof load | Calculate proof load from proof stress and tensile stress area. | Bolt Proof Load Calculator |
| Check thread engagement length | Estimate required thread engagement length for tapped holes and threaded joints. | Thread Engagement Length Calculator |
| Check thread stripping | Check approximate internal and external thread stripping capacity. | Thread Stripping Calculator |
| Select bolt length | Estimate required bolt length for a through bolt or tapped hole joint. | Bolt Length Calculator |
| Check washer bearing pressure | Calculate bearing pressure under a washer, nut face or bolt head. | Washer Bearing Pressure Calculator |
| Check bolt spacing and edge distance | Check bolt pitch and edge distance for a preliminary bolted plate layout. | Bolt Spacing and Edge Distance Calculator |
| Check bolt-hole clearance | Calculate diametral and radial clearance between a bolt and hole. | Bolt Hole Clearance Calculator |
| Check spanner or socket access | Check clearance around a bolt head or nut for tool access. | Bolt Head and Nut Clearance Calculator |
| Formula | Meaning | Used In |
| τ = 4F / πd2 | Bolt shear stress in single shear. | Bolt Shear Stress Calculator |
| τ = 2F / πd2 | Bolt shear stress in double shear. | Bolt Shear Stress Calculator |
| σc = F / dt | Bearing stress between a bolt and connected plate. | Bolt Bearing Stress Calculator |
| τplate = F / 2ct | Plate edge shear stress in a bolted connection. | Bolt Plate Shear Calculator |
| σ = Ft / A | Bolt tensile stress from axial tensile load. | Bolt Tensile Stress Calculator |
| σvm = √(σ2 + 3τ2) | Von Mises equivalent stress for combined tensile and shear stress. | Bolt Combined Stress Calculator |
| T = KFd | Approximate torque-preload relationship, where K is the nut factor. | Bolt Preload Calculator and Bolt Tightening Torque Calculator |
| As = π(d - 0.9382p)2 / 4 | ISO metric thread tensile stress area approximation. | Thread Tensile Stress Area Calculator |
| Fproof = SpAs | Bolt proof load from proof stress and tensile stress area. | Bolt Proof Load Calculator |
| dm = d - 0.6495p | Approximate mean thread diameter for thread engagement and stripping checks. | Thread Engagement Length Calculator and Thread Stripping Calculator |
| As,thread = πdmLe | Approximate thread shear area for engagement and stripping checks. | Thread Engagement Length Calculator and Thread Stripping Calculator |
| A = π(Do2 - Di2) / 4 | Annular washer bearing area. | Washer Bearing Pressure Calculator |
| Cd = D - d | Diametral clearance between a bolt and hole. | Bolt Hole Clearance Calculator |
| Application | Typical Use |
| Bolt shear checks | Checking whether a bolt is suitable for a given transverse shear load. |
| Bolt tensile checks | Checking axial tensile stress in bolts, threaded sections and preloaded fasteners. |
| Plate bearing checks | Estimating local compressive bearing stress around a bolt hole. |
| Plate edge shear checks | Checking whether a plate may fail by shear-out near the bolt hole or plate edge. |
| Bracket and base plate checks | Analysing bolt groups subject to eccentric loads and torsional moments. |
| Combined stress checks | Checking bolts subject to both axial tension and shear loading. |
| Preloaded bolted joints | Estimating clamp force, tightening torque and torque-related bolt loading. |
| Threaded joint checks | Checking thread tensile stress area, engagement length, proof load and thread stripping capacity. |
| Fastener layout checks | Checking bolt length, hole clearance, spacing, edge distance, washer bearing pressure and tool access. |
The calculators above should be used alongside the RoyMech fastener reference material:
These bolted joint and fastener calculators are intended for preliminary engineering calculations and educational use. Final bolted joint design should be checked against the relevant design standard, bolt grade, material properties, thread engagement, preload method, fatigue requirements, loading conditions and safety factors.
Bolted joints can fail in several ways, including bolt shear, tensile failure, bearing failure, plate tear-out, thread stripping, fatigue, loosening, local washer bearing, hole deformation and joint slip. A complete design check may need to consider more than one failure mode.
Bolt shear stress is calculated by dividing the applied shear load by the bolt shear area. For a circular bolt in single shear:
τ = 4F / πd2
where F is the applied shear force and d is the bolt diameter.
In single shear there is one shear plane through the bolt. In double shear there are two shear planes, so the same applied load is shared over twice the shear area. For the same bolt diameter and applied force, double shear gives approximately half the shear stress of single shear.
Bearing stress is calculated from:
σc = F / dt
where F is the applied force, d is the bolt diameter and t is the plate thickness.
Bolt preload is the tensile force introduced into a bolt during tightening. Preload clamps the connected parts together and can significantly affect joint stiffness, fatigue behaviour, slip resistance and service stress.
Thread tensile stress area is the effective tensile area of the threaded section of a bolt or screw. It is normally smaller than the nominal shank area because the thread root reduces the effective cross-section.
Thread stripping is a failure mode where the engaged internal or external threads shear off under load. It is especially important for tapped holes in softer materials, short nuts and threaded inserts.
Use the calculator that matches the likely failure mode or design question. For example, use the shear stress calculator for transverse bolt loading, the bearing stress calculator for plate contact stress, the preload calculator for torque-to-clamp-force estimates and the thread calculators for threaded-section checks.
These calculators are intended for preliminary engineering calculations and educational use. Final bolted joint design should be checked against the relevant design standard, bolt grade, material properties, loading conditions, fatigue requirements and safety factors.
�