Bending Moment Calculator
Free Bending moment Calculator for structural engineering projects. Enter dimensions to get material lists and cost estimates.
Formula
M_max = wL\u00B2/8 (simply supported, uniform) | M_max = Pab/L (simply supported, point)
The maximum bending moment depends on the load type and support conditions. For a simply supported beam with uniform load w over span L, the maximum moment at midspan is wL-squared divided by 8. For a concentrated load P at distance a from one support, the maximum moment at the load point is P times a times b divided by L, where b equals L minus a.
Worked Examples
Example 1: Simply Supported Beam with Uniform Load
Problem: A 20-foot simply supported beam carries a uniform load of 2 kips per foot. Find the maximum bending moment and shear.
Solution: M_max = wL\u00B2/8 = 2 * 20\u00B2 / 8 = 100 kip-ft\nV_max = wL/2 = 2 * 20 / 2 = 20 kips\nTotal load = 2 * 20 = 40 kips
Result: Maximum moment = 100 kip-ft, Maximum shear = 20 kips
Example 2: Cantilever with Point Load
Problem: A 10-foot cantilever beam has a 5-kip point load at the free end.
Solution: M_max = P * L = 5 * 10 = 50 kip-ft (at fixed support)\nV_max = P = 5 kips
Result: Maximum moment = 50 kip-ft at the fixed end
Frequently Asked Questions
What is a bending moment and why is it important?
A bending moment is the internal moment at any section of a beam caused by external loads and reactions. It represents the tendency of the beam to bend or flex at that point. The magnitude of the bending moment directly determines the bending stresses in the beam, which must remain below the material yield strength. Engineers use bending moment diagrams to identify the critical section where the moment is maximum and design the beam accordingly.
How do support conditions affect the maximum bending moment?
Support conditions have a dramatic effect on bending moments. A simply supported beam with uniform load has a maximum moment of wL-squared over 8 at midspan. A fixed-fixed beam with the same load has a moment of wL-squared over 12 at the supports and wL-squared over 24 at midspan, reducing the peak moment by 33 percent. A cantilever beam has wL-squared over 2 at the fixed end, which is four times larger than the simply supported case. Choosing proper support conditions is a key design decision.
How do I convert bending moment to bending stress?
Bending stress is calculated from the bending moment using the flexure formula: sigma = M * c / I, where M is the bending moment, c is the distance from the neutral axis to the extreme fiber, and I is the moment of inertia of the cross section. For a rectangular section, this simplifies to sigma = 6M / (b * d-squared). The bending stress must be less than the allowable stress for the beam material, which is typically 0.6 times the yield stress for steel per AISC ASD.
What formula does Bending Moment Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Is Bending Moment Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
Can I use Bending Moment Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.