Loading Calculator...
Please wait a moment
Please wait a moment
Calculate shear force in beams with point loads, distributed loads, and multiple beam types. Analyze reactions, shear diagrams, and critical locations for structural design.
Two fixed supports at ends
Calculate shear force at a specific point on the beam
Enter beam span
Let us know if this calculator was useful
1245 people found this calculator helpful
Shear force is the internal force within a beam that acts perpendicular to the beam's axis. It represents the algebraic sum of all vertical forces on one side of a cross-section. Shear force diagrams help engineers identify critical locations where the beam experiences maximum shear stress.
Understanding shear force is essential for:
Positive shear occurs when the left face of the element moves upward relative to the right face. This creates a counterclockwise rotation.
Typically found:
Negative shear occurs when the left face of the element moves downward relative to the right face. This creates a clockwise rotation.
Typically found:
Common shear force formulas for standard loading conditions:
| Beam Type & Load | Left Reaction (RA) | Max Shear |
|---|---|---|
| Simply Supported, Point Load at Center | P/2 | P/2 |
| Simply Supported, Uniform Load w | wL/2 | wL/2 |
| Cantilever, Point Load at End | P | P |
| Cantilever, Uniform Load w | wL | wL |
| Simply Supported, Point Load at a from Left | P(L-a)/L | P(L-a)/L or Pa/L |
Where: P = point load (lbs), w = distributed load (lbs/ft), L = span (ft), a = distance to load (ft)
V(0) = +R_A V(a-) = +R_A V(a+) = +R_A - P V(L) = 0 Note: Sudden drop at point load
Point loads cause sudden changes (discontinuities) in the shear diagram. The change equals the magnitude of the load.
V(0) = +wL/2 V(L/2) = 0 V(L) = -wL/2 Note: Linear variation slope = -w
Distributed loads cause linear changes in shear. The slope equals the intensity of the load.
Key Relationship: The slope of the moment diagram at any point equals the shear force at that point (dM/dx = V). Where shear is zero, the moment reaches its maximum or minimum value.
Shear failure occurs when the internal shear stress exceeds the material's shear strength. In concrete beams, this typically happens near supports where shear forces are highest. Steel beams rarely fail in shear unless overloaded, but wood beams can split along the grain.
At the location of zero shear force, the bending moment reaches its maximum value. This is the critical point for bending stress. For simply supported beams with uniform loads, maximum moment occurs at midspan where shear equals zero.
Point loads cause sudden discontinuities (vertical jumps) in the shear diagram. The magnitude of the jump equals the load magnitude. This is different from distributed loads which cause smooth, linear changes in shear.
The shear diagram's slope equals the negative of the distributed load (dV/dx = -w), and the moment diagram's slope equals the shear force (dM/dx = V). Where shear crosses zero, moment reaches an extremum (maximum or minimum).
For simply supported beams, use equilibrium equations: sum of vertical forces = 0 and sum of moments = 0. Take moments about one support to find the other reaction, then use force balance to find the first. For cantilevers, all force goes to the fixed support.
No, shear must always be checked. For short spans with large loads, shear may be the limiting factor. In concrete design, shear reinforcement (stirrups) is essential near supports. Steel beams rarely fail in shear, but the design must still verify adequacy.
In cantilevers, maximum shear occurs at the fixed support and equals the total load. In simply supported beams, maximum shear occurs at the supports but is divided between both ends. Cantilevers also have maximum moment at the fixed support.
Shear calculations help engineers design safe, efficient structures. They identify critical locations for failure, determine required reinforcement, ensure adequate capacity, and prevent unexpected failures in service.
Check out similar construction calculators