Beam Shear Force Calculator

What This Beam Shear Force Calculator Does

This calculator estimates the maximum shear force in straight, prismatic beams under basic loading. It is intended for quick checks and teaching examples in structural analysis and design.

The tool currently supports:

• Beam types: simply supported (pinned–roller) and cantilever (fixed–free)
• Load types: uniform distributed load (UDL) and single point load at the center or free end
• Outputs: maximum shear force along the beam, in kiloNewtons (kN)

Use the results as input to further checks such as shear capacity, bending stress, and deflection.

Units and Sign Conventions

The calculator assumes consistent engineering units:

• Span length, L: metres (m)
• Uniform load, w: kiloNewtons per metre (kN/m)
• Point load, P: kiloNewtons (kN)
• Shear force, V: kiloNewtons (kN)

Internally, the usual structural engineering sign convention is adopted: positive shear tends to cause clockwise rotation of the segment on which it acts. For the simple cases covered here, the calculator reports the absolute value of the governing maximum shear force, |V_max|, which is typically what is needed for design checks.

Formulas Used

The maximum shear force depends on the support conditions and the type of loading. For all formulas below, L is the span and loads are applied over that span.

MathML summary

The core relations can be written compactly as:

Case‑by‑case formulas

Simply supported beam with uniform distributed load (UDL)

A simply supported beam with constant load w (kN/m) over span L (m) has equal reactions at both supports:

Maximum shear force:

V_max = R_A = R_B = (w · L) / 2

Simply supported beam with point load at center

With a single point load P (kN) applied at mid‑span, the reactions are again equal:

Maximum shear force:

V_max = R_A = R_B = P / 2

Cantilever beam with uniform distributed load (UDL)

For a cantilever fixed at the left and free at the right, under constant load w (kN/m) over span L (m):

Maximum shear force at the fixed support:

V_max = w · L

Cantilever beam with point load at free end

For a single point load P (kN) applied at the free end of a cantilever:

Maximum shear force:

V_max = P

Comparison of Shear Formulas

The table below compares the maximum shear expressions for the supported load cases.

Shear Force vs. Shear Stress

The calculator returns the resultant shear force V, not the stress distribution. To estimate average shear stress in a rectangular cross‑section of area A (m²):

τ_avg = V / A

The true maximum shear stress in a rectangular section is about 1.5 times the average and occurs at the neutral axis. For detailed shear stress checks, you will need the full cross‑section properties and, in many cases, code‑specific design rules.

Worked Example

Example 1: Simply supported beam with UDL

Given:

• Beam type: simply supported (pinned–roller)
• Load type: uniform distributed load (UDL)
• Span: L = 6.0 m
• Uniform load: w = 10 kN/m

Step 1 – Select the correct formula

For a simply supported beam under UDL:

V_max = (w · L) / 2

Step 2 – Substitute numbers

V_max = (10 kN/m × 6.0 m) / 2 = (60 kN) / 2 = 30 kN

Step 3 – Interpret the result

The maximum shear force in the beam is 30 kN at each support (one positive, one negative by sign convention). This is the value you would compare with the shear capacity of the section from your design standard.

Example 2: Cantilever with point load at free end

Given:

• Beam type: cantilever (fixed at one end, free at the other)
• Load type: point load at free end
• Span: L = 3.0 m (for shear, the exact length does not change V in this case)
• Point load: P = 25 kN

Formula:

V_max = P = 25 kN

The shear force is constant along the cantilever, with magnitude 25 kN, acting at the fixed end to balance the applied load.

How to Use This Calculator in Design

1. Select the beam type (simply supported or cantilever) that best represents your real support conditions.
2. Choose the load type that matches your situation: a uniform distributed load for evenly spread loads such as self‑weight or flooring, or a point load for concentrated reactions from columns, equipment, or wheels.
3. Enter the span (clear distance between supports or from fixed support to free end).
4. Enter either the uniform load in kN/m or the point load in kN, depending on your selection.
5. Run the calculation and use the reported V_max in subsequent checks.

Typical follow‑up steps include:

• Checking shear capacity of a concrete beam using code formulas (with a tool such as a concrete beam shear capacity calculator).
• Checking bending stress using a beam bending stress calculator.
• Checking deflection limits with a beam deflection calculator to satisfy serviceability criteria.

Limitations and Assumptions

This calculator is intentionally simple and is based on standard statics. The following assumptions and limitations apply:

• Beams are prismatic (constant cross‑section) and straight.
• Materials behave linearly elastically within the range considered.
• Only statically determinate systems are considered (no continuous or indeterminate spans).
• Loads act in a single vertical plane; torsion, lateral loads, and biaxial effects are not included.
• No account is taken of shear deformation or large deflections; small‑deflection theory is assumed.
• The calculator returns maximum shear force only; it does not produce full shear diagrams or bending moment diagrams.
• No code‑specific resistance checks (such as Eurocode, ACI, AISC) are embedded; you must verify capacity separately against your governing standard.

Disclaimer: Results are for educational and preliminary design purposes only. They do not replace the judgement of a qualified structural engineer. Always verify critical structures with detailed calculations, appropriate safety factors, and the applicable design codes and standards for your jurisdiction.

Related Calculators and Next Steps

To build a more complete picture of beam performance, combine this shear force result with other checks:

• Beam Bending Stress Calculator: estimate maximum bending stress from moments and section modulus.
• Beam Deflection Calculator: evaluate mid‑span deflections and confirm serviceability limits.
• Concrete Beam Shear Capacity Calculator: compare V_max from this tool with the shear resistance of reinforced concrete sections.

Together, these tools support quick iterations during preliminary design and help highlight where more detailed analysis is required.