ENGINEERING – TRUCTURAL ENGINEERING — BEAM & FRAME CALCULATOR
Beam Bending Moment
A precise tool.
What is the Beam Bending Moment & How does it work?
A simply supported beam is a fundamental structural element that rests on two supports at its ends. When external loads such as a uniform distributed load (w) or a concentrated point load (P) are applied, internal shear forces and bending moments develop to maintain equilibrium. Understanding how these internal forces vary along the span is essential for safe and efficient design.
For a beam of length L carrying a uniform load w (kN/m) and a point load P (kN) located a distance a from the left support, the bending‑moment diagram can be expressed as the superposition of the two load effects. The maximum bending moment occurs at the point of the concentrated load and at mid‑span for the uniform load. The governing expression is:
The shear force V(x) varies linearly between the supports and experiences a discontinuity at the point load. The reactions at the supports are:
RA = (P(L‑a) + wL²/2)/L and RB = (Pa + wL²/2)/L. The maximum shear magnitude is the larger of |RA| and |RB|. Accurate calculation of these values enables engineers to size beam sections and select appropriate reinforcement.
M_{max}=\frac{P,a,(L-a)}{L}+\frac{w,L^{2}}{8}
Mmax = maximum bending moment (kNm)
P = point load magnitude (kN)
a = distance of point load from left support (m)
L = span length (m)
w = uniform distributed load (kN/m)
P = point load magnitude (kN)
a = distance of point load from left support (m)
L = span length (m)
w = uniform distributed load (kN/m)
Parameters
Result
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Frequently Asked Questions
How do I calculate the maximum bending moment in a simply supported beam with a uniform load?
The maximum bending moment (M_max) occurs at the center of the beam and is calculated as M_max = (w * L^2) / 8, where w is the uniform load per unit length and L is the length of the beam.
What is the formula for calculating the bending moment due to a point load on a simply supported beam?
The bending moment (M) at any distance x from the left support due to a point load P located at a distance a from the left support is given by M = P * x if x <= a, and M = P * (L - x) if x > a.
How do I determine the location of maximum bending moment in a beam with both uniform and point loads?
The location of maximum bending moment depends on the relative positions and magnitudes of the uniform load and the point load. It can be found by setting the derivative of the bending moment equation to zero and solving for x.
Can you explain how shear force affects the bending moment in a beam?
Shear force causes changes in the bending moment as it acts along the length of the beam. The rate of change of bending moment is equal to the shear force at that point.
What are the units for bending moment and shear force in this calculator?
The units for bending moment are typically kN-m (kilonewton-meters), and the units for shear force are kN (kilonewtons).
Results are for informational purposes only and do not constitute professional advice.