Shear-force and bending-moment diagrams2D
Distributed-load diagrams
Build discontinuity-aware load, shear, and moment diagrams with synchronized analytical relationships.
Open the complete lessonInteractive engineering simulation
Distributed-Load Diagram Explorer
Compare uniform and triangular loading, including shear slope and moment curvature.
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 and .
Load w(x)13.25 kN/m
Shear V(x)0.19 kN
Moment M(x)157.78 kN·m
Cursor shear
0.19 kN
Cursor moment
157.78 kN·m
Left reaction
75.00 kN
Right reaction
50.00 kN
Maximum moment
157.78 kN·m at 4.50 m
Zero-shear locations
4.51
Piecewise shear equation
V(x)=75.000⟨x-0.00⟩⁰ + 50.000⟨x-10.00⟩⁰ - 20.000⟨x-0.00⟩¹ + 0.750⟨x-0.00⟩² + 5.000⟨x-10.00⟩¹ - 0.750⟨x-10.00⟩²
Piecewise moment equation
M(x)=75.000⟨x-0.00⟩¹ + 50.000⟨x-10.00⟩¹ - 10.000⟨x-0.00⟩² + 0.250⟨x-0.00⟩³ + 2.500⟨x-10.00⟩² - 0.250⟨x-10.00⟩³
Model scope and verification
Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.