Calculator · Structural Mechanics
Bending Stress Calculator
Flexural stress from the bending moment the beam itself produces. The moment comes from the same engine as the bending-moment diagram, so the stress you read here belongs to the beam you drew rather than to a number typed in by hand.
Beam
Scroll the schematic sideways to see the whole beam; every result is also listed in the tables below.
Beam and loads
The beam runs from x = 0 to x = L.
Supports
Point loads
Point moments
Uniform distributed loads
Downward loads are negative (q < 0, Fy < 0); an applied couple is positive counter-clockwise. Internally, M > 0 is sagging, v > 0 is upward and θ > 0 is counter-clockwise.
Section and material (optional)
Leave a field empty to leave it unspecified: reactions, shear and bending moment are reported without any section data. A value that is zero or negative is not unspecified — it is reported as an invalid entry. Bending stress additionally needs I and an extreme-fibre distance c; slope and deflection need both E and I.
Evaluation station
Measured from the left end of the beam.
Results
| Bending moment at x | 15 kN·m (sagging) |
|---|---|
| Top-fibre stress σ(+c_top) | -187.5 MPa (compression) |
| Bottom-fibre stress σ(−c_bottom) | 187.5 MPa (tension) |
| Largest tensile bending stress on the beam | 187.5 MPa at 3 m |
| Largest compressive bending stress on the beam | -187.5 MPa at 3 m |
Assumptions
- · Statically determinate planar beam; reactions come from the shared equilibrium solver.
- · Small displacements, linear elasticity, plane sections remain plane (Euler-Bernoulli); shear deformation is neglected.
- · Uniform E and I along the beam when slope and deflection are reported.
Open in the Lab
The Lab plots the extreme-fibre stress along the whole beam.
Technical reference
σx(y) = −M y / I
σ_max = M c / I at the extreme fibre
S = I / c, σ_max = M / S
- M
- internal bending moment, sagging positive[N·m]
- y
- distance from the neutral axis, positive upward[m]
- I
- second moment of area about the bending axis[m⁴]
- c
- extreme-fibre distance from the neutral axis[m]
- σ
- normal stress; positive is tension[Pa]
The minus sign follows from the sagging convention: a positive (sagging) moment compresses the top fibre (y > 0) and puts the bottom fibre into tension.
Validity: linear-elastic material, initially straight prismatic beam, plane sections remaining plane, bending about a principal centroidal axis, no axial force and no local effects near supports or concentrated loads.
The neutral axis passes through the centroid of the section only while the response stays elastic and no axial force acts.