Advanced Load Case
Triangular Load Beam Deflection Calculator
Estimate deflection, reactions, shear, and bending moment for a simply supported beam under a full-span triangular load.
Use meters for geometry, kN/m for the peak triangular load, GPa for E, and cm^4 for I.
Calculation Inputs
Beam Diagram
Calculation Basis
Assumptions & Limits
- The model represents 2D bending response only and does not include torsion.
- Supports are idealized as analytical boundary conditions.
- Construction stages, nonlinearity, and settlement effects need a more detailed model.
Reference Basis
- Documentation: Advanced beam methodology
- Documentation: Engineering Review
- Matrix stiffness method references
- Elastic beam theory references for validation checks
Shear Force Diagram
Bending Moment Diagram
Response Summary
| Left support | V = 7.00 kN |
| Right support | V = 14.00 kN |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: Left support @ 0.00 m, Right support @ 6.00 m. E = 210.0 GPa, I = 4,800 cm^4.
Result
Euler-Bernoulli beam under linearly varying distributed load
Load setup
General form
F = F_point + F_distributed
Current model
No discrete point loads. w(x): 0.00 to 7.00 kN/m over 0.00-6.00 m.
Result
Max deflection = 5.87 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 16.18 kN*m, max |V| = 13.14 kN.
Result
Reactions solved at 2 support locations
Model Assumptions
- The beam is simply supported at both ends.
- The triangular load ramps from zero at the left end to the peak value at the right end.
- The model is linear elastic with constant member stiffness.
Related Tools
- This page captures a common load pattern that generic uniform-load calculators miss: one-way ramps such as pressure buildup, fill, or tapered tributary loading.
- The solver resolves reactions and diagrams directly from the triangular load rather than replacing it with an equivalent uniform shortcut in the UI.
- If the real triangular load is partial, reversed, or combined with multiple other load patterns, it should be modeled separately or through a more general beam analysis tool.