Bending Stress Calculator

Calculate flexural stress, section properties, allowable stress, and moment capacity for a solid rectangular beam.

Rectangular beam stress analysis

Enter the applied moment, cross-section dimensions, material, and safety factor.

Bending Moment (N·m)

Beam Width (mm)

Beam Height (mm)

Material

Safety Factor

About bending stress

Bending stress, also called flexural stress, develops when an applied moment curves a beam. Fibers on one side of the neutral axis shorten in compression while fibers on the other side lengthen in tension. For a symmetric, homogeneous rectangular section, the neutral axis passes through the centroid and the greatest stress occurs at the top and bottom surfaces, farthest from that axis. The elastic flexure relationship states that stress equals bending moment times distance from the neutral axis divided by the second moment of area. At the extreme fiber this is conveniently written as moment divided by section modulus. For a solid rectangle, the second moment of area is width times height cubed divided by twelve, and the section modulus is width times height squared divided by six. The calculator converts the entered moment from newton metres to newton millimetres so that dimensions in millimetres produce stress directly in megapascals. Material selection supplies a representative nominal strength: 250 MPa for steel, 30 MPa for concrete, 40 MPa for wood, or 150 MPa for aluminum. The allowable stress is that strength divided by the entered safety factor. Maximum allowable moment is allowable stress multiplied by section modulus. The safety margin shown is allowable stress divided by calculated stress, so a value above one passes this simplified comparison and a value below one exceeds it. These calculations assume linear elastic behavior, a prismatic solid rectangle, small deflection, and bending about the strong centroidal axis. Real members may also be governed by shear, buckling, lateral-torsional instability, fatigue, holes, notches, connections, fire exposure, or serviceability limits. Concrete and timber are especially dependent on grade, reinforcement, duration, moisture, and orientation, so a single nominal strength cannot represent a code design. Use the results to learn the relationship between geometry and stress or to make an early comparison. Final structural sizing requires verified material properties, governing load combinations, applicable codes, and review by a qualified professional.

Bending stress examples

Moment and section	Calculated stress	Observation
5,000 N·m; 200 × 400 mm steel rectangle	0.938 MPa	The deep section provides a section modulus of 5,333,333.333 mm³.
2,000 N·m; 150 × 300 mm wood rectangle	0.889 MPa	With a safety factor of 2, representative allowable stress is 20 MPa.
8,000 N·m; 300 × 500 mm concrete rectangle	0.64 MPa	This is an ideal elastic-section calculation, not reinforced concrete design.

How to calculate bending stress

Enter the maximum bending moment obtained from a suitable beam analysis.
Measure the solid rectangular section width and overall height in millimetres.
Choose the representative material and enter the required safety factor.
Select Calculate Stress and compare calculated stress with the displayed allowable value.

Bending stress calculator FAQ

Why is beam height more influential than width?

The rectangular section modulus increases with height squared but only linearly with width. Increasing depth therefore reduces bending stress much more efficiently than adding the same proportion of width.

What bending moment should I enter?

Enter the largest design moment from structural analysis of the beam and its loads. The calculator does not determine support reactions or load combinations.

Is bending stress the same throughout the section?

No. Under elastic bending it varies linearly from zero at the neutral axis to a maximum magnitude at the extreme fibers.

Can I use this for an I-beam or circular section?

Not with the width and height fields alone, because those fields use solid rectangular formulas. Other shapes require their own section modulus and moment of inertia.

Does a safety margin above one guarantee safety?

No. It passes only this simplified flexural stress comparison. A complete design must also evaluate shear, buckling, connections, deflection, material standards, and code requirements.