Structural
Beam Load Calculator
Reactions, maximum bending moment and shear for a simply supported beam under common loads.
UDL: M = wL²/8
Also called simply supported beam · beam reaction calculator
Engineering · 10 calculators
Structural Calculators
Simply supported beams: reactions, deflection, bending moment and shear; column buckling, dead and live loads.
Structural
Beam Deflection Calculator
Maximum deflection of a simply supported or cantilever beam, checked against the span/250 limit.
Simply supported UDL: δ = 5wL⁴ / 384EI
Also called beam sag calculator · deflection formula
Structural
Column Load Calculator
Axial capacity of a column and its Euler buckling load, with the slenderness ratio.
P_cr = π²EI / (KL)²
Also called euler buckling · column capacity
Structural
Dead Load Calculator
Permanent (dead) load of a floor or roof build-up, per square metre and in total.
dead load = Σ (thickness × material densi…
Also called permanent load · self weight calculator
Structural
Live Load Calculator
Imposed (live) load for common occupancies and the factored design load with dead load.
Design load = 1.35 × dead + 1.5 × live (E…
Also called imposed load · occupancy load
Structural
Uniformly Distributed Load Calculator
Convert an area load into a line load on a beam, with reactions and the peak moment.
w = area load × tributary width + self we…
Also called udl calculator · line load calculator
Structural
Point Load Calculator
Reactions, moment and deflection from a concentrated load anywhere on a simply supported beam.
R₁ = Pb/L
Also called concentrated load · single load on beam
Structural
Bending Moment Calculator
Bending moment at any point along a simply supported beam, with the bending stress it produces.
M(x) = Rx − wx²/2
Also called moment calculator beam · bending moment formula
Structural
Shear Force Calculator
Shear force along a simply supported beam and the average shear stress in the web.
V(x) = R − wx
Also called shear diagram · shear force formula
Structural
Material Weight Calculator
Weight of a bar, plate, tube or block from its dimensions and material density.
weight = volume × density
Also called steel weight calculator · metal weight
Key structural formulas
| Beam Load | UDL: M = wL²/8 · Central point: M = PL/4 · Offset: M = Pab/L |
|---|---|
| Beam Deflection | Simply supported UDL: δ = 5wL⁴ / 384EI · Cantilever point: δ = PL³ / 3EI |
| Column Load | P_cr = π²EI / (KL)² · slenderness = KL / r |
| Dead Load | dead load = Σ (thickness × material density) |
| Live Load | Design load = 1.35 × dead + 1.5 × live (Eurocode ULS) |
| Uniformly Distributed Load | w = area load × tributary width + self weight |
| Point Load | R₁ = Pb/L · R₂ = Pa/L · M = Pab/L |
| Bending Moment | M(x) = Rx − wx²/2 · σ = M / Z |
| Shear Force | V(x) = R − wx · V_max = wL/2 + P/2 |
| Material Weight | weight = volume × density |
Structural questions
What is a simply supported beam?
One resting on two supports that can rotate freely — no fixed end moments. It is the standard idealisation for a joist or lintel.