Bending-moment diagram

Build discontinuity-aware load, shear, and moment diagrams with synchronized analytical relationships.

Interactive engineering simulation

Bending-Moment Diagram Builder

Locate zero shear and verify where maximum or minimum bending moment occurs.

Tension-positive N · sagging-positive M

Sign convention: positive tension. On the left cut face, positive shear acts downward and positive moment counterclockwise; arrows reverse on the right face. Downward distributed load is positive, so

dV/dx=-w(x)

and

dM/dx=V(x)

Moment M(x)60.40 kN·m

Beam length10 m

6–18

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Load magnitude20 kN

2–60

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Load position4.00 m

0.50–9.50

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Synchronized cursor x4.5 m

0.0–10.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Cursor shear

-4.35 kN

Cursor moment

60.40 kN·m

Left reaction

15.65 kN

Right reaction

20.56 kN

Maximum moment

62.58 kN·m at 4.00 m

Zero-shear locations

None

Piecewise shear equation

V(x)=15.645⟨x-0.00⟩⁰ + 20.555⟨x-10.00⟩⁰ - 20.000⟨x-4.00⟩⁰ - 3.600⟨x-5.50⟩¹ + 3.600⟨x-10.00⟩¹

Piecewise moment equation

M(x)=15.645⟨x-0.00⟩¹ + 20.555⟨x-10.00⟩¹ - 20.000⟨x-4.00⟩¹ - 1.800⟨x-5.50⟩² + 1.800⟨x-10.00⟩²

\frac{dV}{dx}=-w(x)

\frac{dM}{dx}=V(x)

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

Shear-force diagram Synchronized load-shear-moment cursor Applied-couple diagram Distributed-load diagrams

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