Beam Shear Force Calculator

Understanding Shear Force

Shear force is the internal force that attempts to slide one layer of a beam over another. Imagine a deck of cards: if you slide the top half one way and the bottom half the other, that sliding action is shear. In beams, high shear forces usually occur near supports (columns or walls) and can cause sudden, catastrophic failure if not properly reinforced (e.g., with stirrups in concrete or web stiffeners in steel).

Formulas Used

The maximum shear force ($V_{\max }$) depends on the beam support and load type:

1. Simply Supported Beam

• Uniform Distributed Load ($w$): The load is shared equally by both supports. $$V_{\max }=\frac{wL}{2}$$
• Point Load at Center ($P$): The load is split evenly. $$V_{\max }=\frac{P}{2}$$

2. Cantilever Beam

• Uniform Distributed Load ($w$): The fixed support carries the entire load. $$V_{\max }=wL$$
• Point Load at Free End ($P$): The shear is constant throughout the beam. $$V_{\max }=P$$

Shear Stress vs. Shear Force

While this calculator gives you the total Shear Force ($V$) in kiloNewtons (kN), engineers also check the Shear Stress ($\tau$). For a rectangular beam, the average shear stress is:

where $A$ is the cross-sectional area. Note that the maximum shear stress in a rectangular section is actually $1.5$ times the average stress and occurs at the neutral axis.

Design Considerations

When designing a beam, you must ensure the calculated shear does not exceed the material's capacity:

• Concrete: Weak in tension/shear, so steel stirrups (vertical bars) are added to "stitch" the crack.
• Steel: The web of the I-beam resists most of the shear. If the web is too thin, it might buckle.
• Wood: Shear often governs short, heavily loaded beams, causing them to split horizontally along the grain.

To round out your analysis, combine this tool with the Beam Bending Stress Calculator, Beam Deflection Calculator, and Concrete Beam Shear Capacity Calculator.