Flexure Formula (Bending Stress) Calculator
Calculates the normal stress at a specific point in a beam cross-section resulting from a bending moment.
Formula first
Overview
This formula assumes the beam material is linear-elastic, isotropic, and homogeneous, with a cross-section symmetric about the plane of bending. It relates the internal moment to the stress distribution across the depth of the member, showing that stress varies linearly with the distance from the neutral axis. The negative sign is a convention indicating that a positive moment causes compression on the top fibers of a simply supported beam.
Symbols
Variables
sigma = Bending Stress, M = Bending Moment, y = Distance from Neutral Axis, I = Moment of Inertia
Apply it well
When To Use
When to use: Use this to determine the internal normal stress in a beam subjected to pure bending or bending combined with other loads.
Why it matters: It is fundamental for structural safety, ensuring that the induced bending stress does not exceed the yield strength or allowable stress of the material.
Avoid these traps
Common Mistakes
- Using the wrong Moment of Inertia (I) for the specific axis of bending.
- Confusing the distance from the outer surface with the distance from the neutral axis.
One free problem
Practice Problem
A beam has a moment of inertia I = 5000 cm^4 and is subjected to a bending moment M = 10 kN-m. Calculate the bending stress at a point 10 cm from the neutral axis.
Solve for: sigma
Hint: Convert all units to Newtons and millimeters to maintain consistency (N/mm^2 = MPa).
The full worked solution stays in the interactive walkthrough.
References
Sources
- Hibbeler, R. C. (2017). Mechanics of Materials.
- Beer, F. P., Johnston, E. R., DeWolf, J. T., & Mazurek, D. F. (2014). Mechanics of Materials.
- Beer, F. P., Johnston, E. R., DeWolf, J. T., & Mazurek, D. F. (2015). Mechanics of Materials.