Back to Statics Of Rigid Bodies repository

Shear-force and bending-moment diagrams2D

Applied-couple diagram

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

Open the complete lesson

Interactive engineering simulation

Applied-Couple Diagram Explorer

Apply a concentrated couple: moment jumps while shear remains continuous.

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)

.

Load w(x)0.00 kN/m

Shear V(x)-1.80 kN

Moment M(x)9.90 kN·m

Beam length10 m

m

6–18

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

Load magnitude20 kN

kN

2–60

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

Load position4.00 m

m

0.50–9.50

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

Clockwise applied couple18 kN·m

kN·m

-40–40

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

Synchronized cursor x4.5 m

m

0.0–10.0

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

Cursor shear

-1.80 kN

Cursor moment

9.90 kN·m

Left reaction

-1.80 kN

Right reaction

1.80 kN

Maximum moment

10.80 kN·m at 4.00 m

Zero-shear locations

None

Piecewise shear equation

V(x)=-1.800⟨x-0.00⟩⁰ + 1.800⟨x-10.00⟩⁰

Piecewise moment equation

M(x)=-1.800⟨x-0.00⟩¹ + 1.800⟨x-10.00⟩¹ + 18.000⟨x-4.00⟩⁰

\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 Bending-moment diagram Synchronized load-shear-moment cursor Distributed-load diagrams