Shear Force Calculator
Estimate shear force for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Reviewed by Abdullah, Technical Content Specialist
Formula
Simply Supported UDL: Vmax = wL/2, Mmax = wL^2/8 | Point Load: Ra = Pb/L, Rb = Pa/L
For a simply supported beam with uniform distributed load w over span L, the maximum shear force equals wL/2 at each support and the maximum bending moment is wL squared over 8 at midspan. For a point load P at distance a from the left support, the reactions are Pa/L and Pb/L where b is the distance from the right support.
Worked Examples
Example 1: Simply Supported Beam with UDL
Problem:Find the maximum shear force for a 6m simply supported beam carrying 20 kN/m uniformly distributed load.
Solution:Total load = 20 * 6 = 120 kN\nRa = Rb = wL/2 = 20*6/2 = 60 kN\nVmax = 60 kN (at supports)\nMmax = wL^2/8 = 20*36/8 = 90 kN-m
Result:Maximum shear force = 60 kN at both supports
Example 2: Point Load at Third Point
Problem:Find reactions and shear for a 9m beam with a 45 kN point load at 3m from the left support.
Solution:Ra = P*b/L = 45*6/9 = 30 kN\nRb = P*a/L = 45*3/9 = 15 kN\nVmax = 30 kN\nMmax = P*a*b/L = 45*3*6/9 = 90 kN-m
Result:Ra = 30 kN, Rb = 15 kN, Vmax = 30 kN
Frequently Asked Questions
What is shear force in a beam?
Shear force at any cross-section of a beam is the algebraic sum of all transverse forces acting on either side of that section. It represents the internal force that resists sliding of one part of the beam relative to the other. Shear force is typically maximum at the supports for simply supported beams and at the fixed end for cantilevers. It is measured in kilonewtons (kN) or pounds (lbs).
How do shear force and bending moment relate to each other?
The shear force at any point along a beam equals the rate of change of bending moment at that point, expressed mathematically as V = dM/dx. This means that where the shear force is zero, the bending moment reaches a maximum or minimum value. Engineers use shear force diagrams and bending moment diagrams together to understand the complete internal force distribution along a beam.
What is the difference between positive and negative shear force?
By the standard beam sign convention, positive shear force causes a clockwise rotation of the beam element, meaning the left face moves upward relative to the right face. Negative shear causes counterclockwise rotation. In a simply supported beam with a downward uniform load, the shear force is positive at the left support and transitions to negative at the right support, passing through zero at midspan.
Why is shear force important for structural design?
Shear force determines the required shear reinforcement (stirrups) in concrete beams and governs the web thickness of steel beams. Shear failures in concrete are sudden and brittle, which is why building codes require a minimum level of shear reinforcement even when calculated shear stresses are low. For short, deep beams, shear capacity often controls the design rather than flexural capacity.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy