Expert-Reviewed · AISC 360-22 Compliant

Bending Stress Calculator Pro (USA)

Calculate bending stress using the flexure formula σ = Mc/I with AISC 360-22 allowable stress checks. Designed for US structural engineers using imperial units (ksi, kips, inches, feet).

Reviewed by: Licensed Structural Engineer, P.E. 15+ Years in Steel Design · Member: AISC, ASCE · Specialization: AISC 360 Steel Design

Select Beam Type

Simply Supported

Cantilever

Fixed-Fixed

Overhanging

Select Load Type

Select Cross-Section

Rectangle

Circle

I-Beam

Hollow Rect.

Hollow Circle

T-Section

Select Material (ASTM Standard)

Material Grade

Enter Dimensions

Enter Load & Span

Calculation Results

Utilization Ratio (σ/F_b) 0%

Stress Distribution

Bending Moment Diagram

Design Notes (AISC 360-22):

Bending Stress Formula Reference

Flexure Formula (Fundamental)

σ = M × c / I

σ = bending stress (ksi), M = bending moment (kip-in), c = distance from neutral axis to extreme fiber (in), I = moment of inertia (in&sup4;). Equivalent form: σ = M / S where S = I/c is the section modulus.

AISC 360-22 Allowable Bending Stress (ASD)

F_b = 0.66 × F_y (compact doubly symmetric sections)

Per AISC 360-22 Chapter F, Table F1-1, for compact I-shaped sections and channels bent about their major axis with adequate lateral bracing. F_y is the specified minimum yield stress per ASTM standard.

Max Bending Moment — Simply Supported, Point Load at Center

M_max = P × L / 4

P = concentrated load (kips), L = span (ft). Moment in kip-ft; multiply by 12 for kip-in.

Max Bending Moment — Simply Supported, UDL

M_max = w × L² / 8

w = uniformly distributed load (kips/ft), L = span (ft). Maximum moment at midspan.

Max Bending Moment — Cantilever, Point Load at Free End

M_max = P × L

Maximum moment at the fixed support. P in kips, L in feet.

Max Bending Moment — Cantilever, UDL

M_max = w × L² / 2

Maximum moment at the fixed support. w in kips/ft, L in feet.

Max Bending Moment — Fixed-Fixed, Point Load at Center

M_max = P × L / 8

Maximum moment at supports (negative) and at midspan (positive = PL/8).

Max Bending Moment — Fixed-Fixed, UDL

M_max = w × L² / 12

Maximum moment at supports. Moment at midspan = wL²/24.

Moment of Inertia — Rectangle

I = b × h³ / 12 | S = b × h² / 6

b = width (in), h = height (in). Neutral axis at mid-height for symmetric sections.

Moment of Inertia — Circle

I = π × d&sup4; / 64 | S = π × d³ / 32

d = diameter (in). For hollow circles: I = π(D&sup4; − d&sup4;) / 64.

Frequently Asked Questions

What is the bending stress formula used in this calculator?

This calculator uses the fundamental flexure formula σ = Mc/I, where σ is bending stress (ksi), M is bending moment (kip-in), c is the distance from the neutral axis to the extreme fiber (in), and I is the moment of inertia (in&sup4;). This is the standard formula per AISC 360-22 Chapter F for flexural members. The equivalent form σ = M/S (where S = section modulus) is also used internally for computation.

How does this calculator comply with AISC 360-22 standards?

The calculator determines allowable bending stress as F_b = 0.66F_y per AISC 360-22 Chapter F, Table F1-1, for compact doubly symmetric sections loaded in the plane of symmetry. Material yield strengths follow ASTM standards (A36, A992, A572, A514). The utilization ratio (σ/F_b) must be ≤ 1.0 for an AISC-compliant design under the ASD method. Design notes remind users to verify lateral-torsional buckling and section compactness per AISC B4 and F2.

What units does this bending stress calculator use?

This calculator uses US customary (imperial) units as standard in American structural engineering practice: beam span in feet (ft), cross-section dimensions in inches (in), point loads in kips (1 kip = 1,000 lbs), distributed loads in kips per foot (kips/ft), bending stress in ksi (kips per square inch), moment of inertia in in&sup4;, section modulus in in³, and bending moment in kip-ft (displayed) and kip-in (used internally for stress calculation).

What safety factor is used in AISC bending stress design?

Under the AISC 360-22 ASD (Allowable Strength Design) method, the effective factor of safety for bending is approximately 1.67. This is derived from F_b = 0.66F_y, which means the allowable stress is 66% of yield — providing a safety margin of 1/0.66 ≈ 1.52 on stress, combined with the ASD load combinations (typically DL + LL without load factors) resulting in an overall safety factor near 1.5–1.67. The calculator displays the utilization ratio rather than a standalone safety factor, which is the modern AISC convention.

What is section modulus and why is it important?

Section modulus (S = I/c) is a geometric property that measures a cross-section’s resistance to bending. A larger section modulus means the section can resist more bending moment for the same stress level. It combines the moment of inertia (I) and the distance to the extreme fiber (c) into a single value. Engineers use S to quickly compare different cross-sections — for example, a W12×50 has S_x = 64.7 in³, while a W8×31 has S_x = 27.5 in³. This calculator computes S automatically for any custom dimensions you enter.

Can I use this calculator for concrete or wood beams?

The flexure formula σ = Mc/I applies to any linearly elastic, homogeneous material. However, the built-in material database and allowable stress values are calibrated for structural steel and aluminum per ASTM standards. For concrete beams (ACI 318), select “Custom Fy” and input the appropriate allowable stress. Note that concrete is a cracked, non-homogeneous material, so the working stress method requires an effective moment of inertia and transformed section analysis — this calculator does not perform those checks. For wood beams (NDS), select “Custom Fy” with the appropriate allowable bending stress (F_b) per the NDS supplement.

References & Standards

AISC 360-22 — Specification for Structural Steel Buildings, American Institute of Steel Construction, 2022.
AISC Steel Construction Manual, 16th Edition, AISC, 2023.
ASTM A36/A36M — Standard Specification for Carbon Structural Steel.
ASTM A992/A992M — Standard Specification for Structural Steel Shapes.
ASTM A572/A572M — Standard Specification for High-Strength Low-Alloy Columbium-Vanadium Structural Steel.

ASTM A514/A514M — Standard Specification for High-Yield-Strength, Quenched and Tempered Alloy Steel Plate.
IBC 2021 — International Building Code, Chapter 16 (Structural Design).

Disclaimer: This calculator is intended for educational and preliminary design purposes only. It does not replace professional engineering judgment or a complete structural analysis per AISC 360-22. Always verify results with a licensed Professional Engineer (P.E.) before use in construction. The developer assumes no liability for errors, omissions, or damages arising from the use of this tool. Verify section compactness (AISC Table B4.1b), lateral-torsional buckling (AISC F2), and all applicable load combinations per ASCE 7.