Beam and Load Inputs
Model: simply supported beam with point loads and up to two uniform load segments. Use meters for length, kN for forces, and kN/m for distributed loads.
Formula Used
For a simply supported beam, reactions follow static equilibrium:
- ΣFy = 0: R₁ + R₂ = ΣP + Σ(w Δx)
- ΣMleft = 0: R₂ L = Σ(P x) + Σ\big(W x̄\big)
Each uniform segment with intensity w over [a,b] has total load W = w(b-a) acting at the centroid x̄ = (a+b)/2.
The internal shear at position x (right-limit) is computed by cutting the beam at x:
V(x) = R₁ − Σ Pi(xi ≤ x) − Σ wj \max\big(0, \min(x,bj) - aj\big)
Point loads create jumps in V(x). Uniform loads produce linear slopes.
How to Use
- Enter the beam length L in meters.
- Add point loads with magnitude P and location x.
- Add uniform load segments with intensity w, start a, and end b.
- Press Calculate Shear Diagram to view results.
- Check the plot for overall behavior and the station table for jumps.
- Use Download CSV or Download PDF for documentation.
If a load lies outside the span or a segment has a≥b, it is ignored and flagged.
Example Data Table
| L (m) | P1 (kN) | x1 (m) | w1 (kN/m) | a1 (m) | b1 (m) | R1 (kN) | R2 (kN) |
|---|---|---|---|---|---|---|---|
| 6 | 12 | 2.5 | 3 | 1 | 5 | 10 | 14 |
The reactions shown are for this example only. Your values update after calculation.