Simply Supported Beam

Reactions, shear, and bending moment for UDL, point loads, and multiple point loads.

Span L (m)

UDL w (kN/m)

Reaction at A (R_A)15.000 kN

Reaction at B (R_B)15.000 kN

Max Bending Moment M_max22.500 kN·m

Max Shear Force V_max15.000 kN

Total Load30.000 kN

Floor / Roof Load Takedown

Factored load on beam or column from tributary area, dead load, and live load.

Tributary Area (m²)

Dead Load D (kPa)

Live Load L (kPa)

Load Combination

Combination: 1.2D + 1.6L (LRFD)8.040 kPa

Total Factored Reaction160.80 kN

What This Calculator Does

The structural load calculator analyses simply supported beams under uniform distributed loads (UDL), single point loads, and up to three simultaneous point loads. It computes support reactions, maximum bending moment (and its location), and maximum shear force — and plots the bending moment diagram (BMD) and shear force diagram (SFD). A floor/roof load takedown section applies LRFD (1.2D + 1.6L) or ASD (D + L) load combinations.

It combines Uniform Load (kN/m), Span Length (m) to estimate Max Bending Moment M_max, Reaction at A (R_A), Reaction at B (R_B).

Formula & Method

UDL beam:

R_A = R_B = \frac{wL}{2}, \quad M_{max} = \frac{wL^2}{8}

Point load at position

a

from A:

R_A = \frac{P(L-a)}{L}, \quad R_B = \frac{Pa}{L}, \quad M_{max} = R_A \cdot a

Bending moment at position

x

M(x) = R_A \cdot x - \Sigma P_i(x - a_i)

for all loads to the left. LRFD:

w_u = 1.2D + 1.6L

Notation used in the formulas: $R$ = Max Bending Moment M\_max; $x_{1}$ = Uniform Load (kN/m); $x_{2}$ = Span Length (m).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Simply supported beam — 5 kN/m UDL, 6 m span

w = 5 kN/m, L = 6 m R_A = R_B = 5 × 6 / 2 = 15 kN M_max = 5 × 6² / 8 = 22.5 kN·m (at midspan) V_max = 15 kN (at supports)

Point load 20 kN at 2 m from A, 6 m span

P = 20 kN, a = 2 m, L = 6 m R_A = 20 × (6 − 2) / 6 = 13.33 kN R_B = 20 × 2 / 6 = 6.67 kN M_max = 13.33 × 2 = 26.67 kN·m (at load point)

Reference Book

Engineering Mechanics: Statics & Dynamics

Russell C. Hibbeler · Pearson

A standard mechanics reference for torque, pulleys, equilibrium, load balance, and rigid-body reasoning.

View Book

Inputs Used

Uniform Load (kN/m): Used directly in the calculation.
Span Length (m): Used directly in the calculation.

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