Beam Stress Calculator Formula
Understand the math behind the beam stress calculator. Each variable explained with a worked example.
Formulas Used
Maximum Bending Stress
bending_stress = m_nmm * dist_to_na / i_mm4Variables
| Variable | Description | Default |
|---|---|---|
moment | Bending Moment (M)(kN-m) | 50 |
dist_to_na | Distance to Neutral Axis (c)(mm) | 150 |
inertia | Moment of Inertia (I)(cm^4) | 8356 |
m_nmm | Derived value= moment * 1e6 | calculated |
i_mm4 | Derived value= inertia * 1e4 | calculated |
How It Works
Bending Stress in Beams
The flexure formula relates the internal bending moment to the normal stress at any fibre of the cross-section.
Formula
sigma = M c / I
M is the bending moment, c is the perpendicular distance from the neutral axis to the outermost fibre, and I is the second moment of area about the neutral axis. The result is the peak tensile or compressive stress at the extreme fibre.
Worked Example
A steel beam with I = 8356 cm^4, depth 300 mm (c = 150 mm), under a moment of 50 kN-m.
moment = 50dist_to_na = 150inertia = 8356
- 01Convert moment: 50 kN-m = 50 x 10^6 N-mm
- 02Convert inertia: 8356 cm^4 = 8356 x 10^4 mm^4 = 8.356 x 10^7 mm^4
- 03sigma = (50 x 10^6 x 150) / (8.356 x 10^7)
- 04sigma = 7.5 x 10^9 / 8.356 x 10^7 = 89.76 MPa
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Open Beam Stress Calculator