Compute beam maximum bending moment, shear forces, support reactions, and elastic deflection under point and uniform distributed loads with CivilMath.
Formula and method
Uniform loading bending mechanics determine maximum bending moments and shear load profiles. Servicability limits verify if elastic deflection exceeds span L/240 controls.
M_{max} = \frac{w L^2}{8} \quad , \quad \Delta_{max} = \frac{5 w L^4}{384 E I}
Bending moment peaks at midspan: M_max = wL²/8 (UDL) or PL/4 (Point Load).
Reaction Shear Force totals peak at boundaries: wL/2 or P/2.
Structural deflection is evaluated from elastic modulus (E) and inertia (I).
Deflection is validated against statutory safety margins.
Frequently asked questions
What load types are supported?
The calculator supports uniformly distributed loads (UDL) in kN/m or lb/ft and point loads at midspan. Both can be combined for composite loading analysis.
How is deflection calculated?
Maximum elastic deflection is computed using Euler-Bernoulli beam theory: Δ = 5wL⁴/384EI for UDL and Δ = PL³/48EI for point loads. Results are checked against L/240 serviceability limits.
What beam properties are required?
You need the beam span length, elastic modulus (E), and moment of inertia (I). For concrete beams, the calculator provides standard E values based on the concrete grade (f'c).
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Calculations are preliminary estimates for planning and education.
Verify results against project documents and applicable codes with a licensed Professional Engineer.
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