Beam Shear Force Calculator

Beam Shear Force Formulas Used

These beam shear formulas follow equilibrium of the selected support and loading condition. In every expression, L is the span; a uniform load w acts across that full span.

Beam shear formula summary

The calculator applies the following maximum-shear relations:

Beam shear case-by-case formulas

Simply supported beam shear under a uniform distributed load

For a simply supported beam, a constant load w (kN/m) across span L (m) produces equal vertical reactions at the two supports:

Maximum shear force:

V_max = R_A = R_B = (w · L) / 2

Simply supported beam shear from a centre point load

For a single point load P (kN) at the centre of a simply supported span, each support takes half of the load:

Maximum shear force:

V_max = R_A = R_B = P / 2

Cantilever beam shear under a uniform distributed load

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

Maximum shear force at the fixed support:

V_max = w · L

Cantilever beam shear from a free-end point load

For a point load P (kN) at the free end of a cantilever, the fixed-end reaction has the same shear magnitude:

Maximum shear force:

V_max = P

Comparison of Beam Shear Formulas

This beam shear comparison shows how support condition changes the governing shear for each load pattern available in the calculator.

Worked Beam Shear Force Examples

Simply supported beam shear with a uniform load

This beam shear example uses a simply supported span carrying a UDL over its full length.

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 beam shear formula

For a simply supported beam under UDL:

V_max = (w · L) / 2

Step 2 – Substitute the beam loading

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

Step 3 – Read the support shear

The maximum shear-force magnitude is 30 kN at either support. Its algebraic sign depends on the shear convention used for the beam diagram; the calculator reports the magnitude for comparison with a separate section shear-capacity check.

Cantilever beam shear with a free-end point load

This cantilever beam shear example considers a concentrated load applied at the 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 (span does not change shear magnitude for this load case)
• Point load: P = 25 kN

Formula:

V_max = P = 25 kN

The shear-force magnitude remains 25 kN along the cantilever, with the fixed support supplying the balancing vertical reaction.

How to Use This Beam Shear Calculator in Design

Use this beam shear calculator only after idealizing the real member as one of its available support and loading cases.

1. Select the beam type that represents the actual restraint: simply supported or cantilever.
2. Choose the load type: a uniform distributed load for load spread along the full beam, or a point load for the centre/free-end case represented here.
3. Enter the span as the support-to-support distance for a simply supported beam or the fixed-to-free distance for a cantilever.
4. Enter the uniform load in kN/m or the point load in kN, as appropriate.
5. Run the calculation and carry the reported V_max into the relevant structural checks.

Typical beam-design follow-up checks include:

• Checking shear capacity using the governing material and design standard.
• Checking bending stress or moment resistance for the same load case.
• Checking deflection limits for serviceability.

Beam Shear Force Limitations and Assumptions

This beam shear calculator uses elementary static equilibrium for idealized determinate members, so the following limits apply to its results:

• Beams are prismatic (constant cross-section) and straight.
• Only the specified support arrangements and load positions are represented.
• Only statically determinate systems are considered; continuous and indeterminate spans are excluded.
• Loads act in one vertical plane; torsion, lateral loads, and biaxial effects are not included.
• No account is taken of shear deformation or large deflections; small-deflection behaviour is assumed.
• The calculator returns maximum shear force only; it does not produce a full shear-force diagram or bending-moment diagram.
• No code-specific resistance checks are embedded; capacity must be verified separately to the applicable standard.

Disclaimer: These beam shear results are intended for educational and preliminary design use. They do not replace the judgement of a qualified structural engineer or detailed calculations using appropriate load combinations, safety factors, and applicable design requirements.

Beam Shear Units and Sign Conventions

This beam shear calculation expects the following 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)

The calculator displays the absolute maximum shear magnitude, |V_max|. A shear-force diagram may show positive or negative values depending on the sign convention adopted, but the magnitude shown here is the value commonly taken forward to a shear-resistance check.

Beam Shear Force Versus Shear Stress

This tool returns the beam’s resultant internal shear force V, rather than the stress distribution across its cross-section. For a rectangular cross-section of area A (m²), the average shear stress is:

τ_avg = V / A

In a rectangular section, maximum elastic shear stress occurs at the neutral axis and is about 1.5 times the average. A detailed shear-stress or code-resistance check therefore needs the section dimensions, material information, and applicable design provisions.

Related Beam Analysis Calculators and Next Steps

After finding maximum beam shear, assess the same member for the other structural actions that may govern its design:

• Beam Bending Stress Calculator: estimate bending stress from moment and section modulus.
• Beam Deflection Calculator: evaluate displacement and serviceability limits.
• Concrete Beam Shear Capacity Calculator: compare V_max with the shear resistance of a reinforced-concrete section.

Using consistent support conditions and load assumptions across these checks helps identify whether shear, bending, or deflection requires more detailed analysis.