Beam Shear Input Form
Example Data Table
| Case | Support | Load | Beam Length (m) | Key Value | Typical Maximum Shear |
|---|---|---|---|---|---|
| 1 | Simply Supported | 20 kN point load at 3 m | 6 | RA = RB = 10 kN | 10 kN |
| 2 | Simply Supported | 8 kN/m full-span UDL | 6 | Total load = 48 kN | 24 kN |
| 3 | Cantilever | 6 kN/m from 1 m to 4 m | 5 | Fixed moment = 45 kN·m | 18 kN |
| 4 | Cantilever | Triangular load to 12 kN/m | 4 | Total load = 24 kN | 24 kN |
Formula Used
Support reactions: For simply supported beams, equilibrium gives ΣV = 0 and ΣM = 0. For cantilevers, the fixed end resists total shear and fixed-end moment.
Point load: For a simply supported beam with point load P at distance a from the left support, reactions are RA = P(L − a)/L and RB = Pa/L.
Full-span uniform load: Total load is W = wL. For simply supported beams, reactions are equal, so RA = RB = wL/2. Shear along the beam is V(x) = RA − wx.
Partial uniform load: Total load is W = w(b − a). The resultant acts at the midpoint of the loaded region, c = (a + b)/2.
Triangular load: Total load is W = 0.5wmaxL. Its resultant acts at 2L/3 from the zero-intensity end. For the simply supported case here, RA = W/3 and RB = 2W/3.
Shear stress: Average shear stress is τavg = V/A. For rectangular sections, τmax = 1.5V/A. For circular sections, τmax = 4V/(3A).
How to Use This Calculator
- Enter the beam length and choose the support type.
- Select the loading pattern that matches your beam case.
- Fill only the fields relevant to the chosen load type.
- Enter the section location x where shear is required.
- Choose a section shape if you want shear stress results.
- Click the calculate button to show reactions, shear, moment, and the shear-force diagram above the form.
- Use the CSV and PDF buttons to export the generated values and sampled shear table.
FAQs
1. What does this calculator compute?
It computes support reactions, internal shear at a chosen section, bending moment at that section, maximum absolute shear, optional shear stress, and a plotted shear-force diagram.
2. Which support conditions are included?
This version includes simply supported and cantilever beams. The cantilever assumes the fixed support is on the left side and positions are measured from that fixed end.
3. Which loads can I analyze?
You can analyze a point load, a full-span uniform load, a partial uniform load, and a triangular load increasing from zero to a maximum value.
4. How is the section shear value treated at a point load?
At the exact position of a concentrated load, the displayed shear is taken immediately to the right of the load. This avoids ambiguity in the shear jump.
5. Are the stress results design-code checks?
No. They are mechanics-based estimates using common section formulas. Final design should still be checked against the relevant steel, concrete, timber, or machine design code.
6. What units should I use?
Use meters for beam geometry, kilonewtons for loads, kilonewtons per meter for distributed loads, and millimeters for section dimensions. Stress results are reported in MPa.
7. Why is the shear diagram curved for triangular loading?
A triangular load varies linearly with position. Because shear is the integral of load intensity, the resulting shear-force diagram becomes a curved, second-order profile.
8. Can I use this for multiple simultaneous loads?
This page handles one load case at a time for clarity. You can extend it by superposition if you want to combine several loads in one custom version.