Bolt Shear Capacity Calculator

Shear Strength of Structural Bolts

Introduction

Bolted connections are fundamental to steel construction. When two or more steel plates are joined, bolts transfer forces in tension, shear, or a combination of both. This page focuses on bolt shear: the action that tends to slide one plate relative to another. In a typical lap joint, the bolt shank (or the threaded portion, depending on detailing) resists shear across one or more shear planes. If the applied shear exceeds the bolt’s capacity, the bolt can fail by shearing across its cross-section.

This calculator estimates both the nominal shear strength (V_n) and the design shear strength (φV_n) using a simplified AISC-style approach. It is intended for quick checks, preliminary sizing, and education. Final design should follow the governing standard (AISC, Eurocode, CSA, AS/NZS, etc.) and include all required limit states.

How to use the calculator

1. Enter bolt diameter d in millimeters (mm).
2. Enter ultimate tensile strength F_u in megapascals (MPa). (1 MPa = 1 N/mm².)
3. Select the number of shear planes (1 for single shear, 2 for double shear; the input allows up to 3).
4. Choose whether threads are in the shear plane. If yes, the calculator reduces the effective area using a 0.78 multiplier.
5. Set the strength reduction factor φ (commonly 0.75 for bolt shear in LRFD, depending on the code and bolt type).
6. Click Compute Shear Strength to see V_n and φV_n in kN. Use Copy Result to copy a short summary.

Formulas, units, and assumptions

The calculator uses consistent metric units: diameter in mm, strength in MPa (N/mm²), and outputs in kN. The core steps are:

• Gross bolt area (circular shank area): $A_b=\frac{\pi }{4}{d}^2$
• Effective shear area: if threads are in the shear plane, the calculator applies an approximate reduction: A_n = 0.78A_b. Otherwise A_n = A_b.
• Nominal shear strength: $V_n=0.6F_u{A}_{n}N$ where N is the number of shear planes.
• Design shear strength (LRFD-style): φV_n.

The factor 0.6 reflects a common approximation that shear strength is about 60% of tensile strength for ductile steels. The 0.78 thread factor is a practical approximation for standard threaded fasteners; exact stress area depends on thread series and standard. In many specifications, the shear strength expression also depends on whether threads are included in the shear plane and on the bolt type; this page keeps the model intentionally simple.

Worked example (step-by-step)

Example inputs (typical structural bolt): d = 20 mm, F_u = 825 MPa, N = 1 shear plane, threads excluded, and φ = 0.75.

First compute the gross area: A_b = (π/4)·d² = (π/4)·(20²) ≈ 314 mm². With threads excluded, A_n = A_b. Then: V_n = 0.6·825·314·1 ≈ 155,418 N = 155.4 kN. Design strength: φV_n = 0.75·155.4 ≈ 116.6 kN.

If the same bolt is in double shear (N = 2), the nominal and design strengths approximately double. If threads are in the shear plane, the effective area becomes about 0.78·314 ≈ 245 mm², reducing capacity accordingly.

How to interpret the results

The calculator reports two values. The nominal shear strength V_n is the theoretical strength before applying a safety factor. The design shear strength φV_n is the value typically compared to a factored demand in LRFD-style design. If you are working in an allowable-stress format, you would normally divide by a safety factor Ω instead of multiplying by φ; this tool does not compute Ω-based allowables.

Remember that the output is per bolt. For a connection with multiple bolts, a first-pass estimate of total shear capacity is often (number of bolts) × (capacity per bolt), but only when load distribution is reasonably uniform. Eccentric loading, unequal stiffness, and prying can cause some bolts to attract more load.

Limitations and what this calculator does not check

This tool intentionally simplifies bolt shear design. It does not evaluate:

• Bearing strength of the connected plates, tear-out, block shear, or net-section rupture.
• Slip-critical behavior (friction-type joints), where capacity depends on pretension and faying surface condition.
• Combined shear and tension interaction (e.g., prying action, eccentric loading).
• Serviceability (slip, deformation, hole type/clearance, oversized holes, long slots).
• Fatigue and cyclic loading requirements.
• Project-specific code provisions, bolt type (bearing vs. slip-critical), and installation requirements.

Use the results as a starting point, then confirm the full connection design per your governing standard and project details. In practice, the controlling limit state for a connection is often not bolt shear; plate bearing, tear-out, or block shear can govern.

Typical bolt grades (reference)

Engineers often start with a bolt grade and then verify capacity. The table below lists typical ultimate tensile strengths. Always confirm the exact specification for your project.

Understanding shear planes (quick guide)

A shear plane is a cross-section through the bolt where sliding between connected parts would cut the bolt. In a single-lap joint, there is typically one shear plane. In a double-lap joint (one plate sandwiched between two plates), there are typically two shear planes. More than two planes is uncommon, but the calculator supports any integer input within the form limits.

A practical detailing note: if you can arrange the connection so that the unthreaded shank crosses the shear plane, the effective area is larger and the shear capacity increases. If the threads cross the shear plane, the reduced stress area governs and capacity decreases. This is why connection details often specify bolt length and grip so that threads are excluded.

Design note (checks that typically accompany bolt shear)

In a complete connection design, bolt shear is only one part of the story. Engineers typically also check: edge distance and spacing requirements, plate thickness adequacy, bearing and tear-out, block shear, and whether the joint is bearing-type or slip-critical. For slip-critical joints, the governing resistance is based on friction and pretension rather than bolt shear; the same bolt may have a high shear strength but still be limited by slip.

For design verification, the factored shear demand per bolt V_u should satisfy V_u ≤ φV_n. For multiple bolts sharing load, total connection capacity is often approximated as (number of bolts) × (capacity per bolt), provided load distribution is reasonably uniform. Eccentricity, prying, and connection geometry can significantly change bolt demands.

FAQ (practical questions)

Why does the calculator use MPa and mm?

Using MPa (N/mm²) with area in mm² produces force in newtons (N) directly. The script then converts to kilonewtons (kN) by dividing by 1000. This keeps the arithmetic consistent and avoids hidden unit conversions.

What does “threads in shear plane” mean in practice?

It means the shear plane cuts through the threaded portion of the bolt rather than the smooth shank. Threads reduce the effective resisting area. The calculator approximates this by multiplying the shank area by 0.78. For precise work, use the stress area from the relevant fastener standard.

Is the 0.6 factor always correct?

It is a common simplified relationship between shear and tensile strength for ductile steels and is used in many introductory calculations. Some codes provide different coefficients, different resistance factors, or separate values depending on bolt type and whether threads are included. Treat this tool as a quick estimate unless you have confirmed the coefficient matches your governing standard.

Can I use this for stainless or nonstandard bolts?

You can enter any ultimate tensile strength F_u value, but the assumptions (0.6 factor and 0.78 thread reduction) may not match specialty fasteners. For stainless, high-temperature, or proprietary bolts, consult the manufacturer data and the applicable design standard.

Does increasing the number of shear planes always double capacity?

In the simplified model here, yes: V_n scales linearly with the number of planes N. In real connections, load sharing can be affected by fit-up, plate stiffness, and deformation compatibility. Still, for typical double-shear details, the linear scaling is a good first approximation.

Good practice checklist (before you rely on the number)

Use this checklist to avoid common mistakes when using a bolt shear capacity calculator:

• Confirm the bolt standard and grade and use the correct F_u for that product.
• Confirm the shear plane location (threads included or excluded) based on grip length and bolt length.
• Confirm the joint type: bearing-type versus slip-critical; this calculator is for bearing-type shear transfer.
• Check connected material limit states (bearing, tear-out, block shear) which often govern thin plates.
• Check geometry rules for spacing, edge distance, and hole type (standard, oversized, slotted).
• Consider load path and eccentricity that may increase demand on some bolts.
• Document assumptions (units, φ value, number of planes) so the result can be reviewed later.

Educational note: the same basic mechanics apply to rivets and pins, but design rules differ. If you are designing a pin connection, bearing and bending of the pin can become important, and the shear plane may not be the only controlling limit state.