Shear-force and bending-moment diagrams2D
Synchronized load-shear-moment cursor
Build discontinuity-aware load, shear, and moment diagrams with synchronized analytical relationships.
Open the complete lessonInteractive engineering simulation
Load–Shear–Moment Synchronized Cursor
Use one cursor across w(x), V(x), and M(x) and verify the differential relationships.
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)0.00 kN/m
Shear V(x)-0.34 kN
Moment M(x)54.46 kN·m
Cursor shear
-0.34 kN
Cursor moment
54.46 kN·m
Left reaction
19.66 kN
Right reaction
30.04 kN
Maximum moment
57.15 kN·m at 7.21 m
Zero-shear locations
None
Piecewise shear equation
V(x)=19.658⟨x-0.00⟩⁰ + 30.042⟨x-10.00⟩⁰ - 20.000⟨x-2.80⟩⁰ - 3.200⟨x-4.50⟩¹ - 0.400⟨x-4.50⟩² + 7.600⟨x-10.00⟩¹ + 0.400⟨x-10.00⟩²
Piecewise moment equation
M(x)=19.658⟨x-0.00⟩¹ + 30.042⟨x-10.00⟩¹ - 20.000⟨x-2.80⟩¹ - 1.600⟨x-4.50⟩² - 0.133⟨x-4.50⟩³ + 3.800⟨x-10.00⟩² + 0.133⟨x-10.00⟩³ + 18.000⟨x-7.20⟩⁰
Model scope and verification
Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.