Section Modulus and Allowable Moment Calculator
The elastic section modulus S is a key cross-sectional property that links an applied bending moment to the resulting bending stress: sigma = M / S. Rearranging, the maximum allowable bending moment a section can carry under allowable stress design (ASD) is M = S x Fb, where Fb is the allowable bending stress for the material and design method. This calculator computes S from the moment of inertia I and extreme-fibre distance c, then multiplies by the allowable stress Fb to give the allowable moment capacity. It also works in reverse: enter a required moment and allowable stress to find the minimum required section modulus.
Section modulus formulas
S = I / c
M = S × Fb
Where I is the second moment of area, c is the distance from the neutral axis to the extreme fibre, and Fb is the allowable bending stress. M is the allowable bending moment capacity in consistent units (e.g. kip-in or kN-mm).
Selecting allowable bending stress
- AISC ASD (9th edition) Chapter F: Fb = 0.66 Fy for compact sections without lateral-torsional buckling.
- For non-compact sections or long unbraced lengths, Fb is reduced per AISC tables or AISC 360 Section F.
- AWC NDS provides reference design values Fb for sawn lumber and glulam, adjusted by applicable factors (CF, CM, Ct, CL).
- ACI 318 does not use allowable stress for flexure; concrete beams are designed using strength (LRFD) methods with phi-factors.
Frequently asked questions
What is section modulus?
The elastic section modulus S equals the moment of inertia I divided by the distance c from the neutral axis to the extreme fibre: S = I / c. It has units of length cubed (in^3 or mm^3) and measures a cross-section's resistance to bending.
How is allowable moment calculated from section modulus?
Allowable moment M = S x Fb, where Fb is the allowable bending stress in the material. For AISC ASD, Fb is typically 0.60 Fy for compact sections in the absence of lateral-torsional buckling.
What is the difference between elastic and plastic section modulus?
The elastic section modulus S assumes linear-elastic material behaviour and locates the neutral axis at the centroid. The plastic section modulus Z accounts for full yielding of the cross-section and is used in LRFD moment capacity calculations (Mn = Z x Fy).
What are typical values of Fb for steel?
For AISC ASD with A36 steel (Fy = 36 ksi), Fb = 0.66 Fy = 23.76 ksi for compact sections bending about the strong axis. For A992 steel (Fy = 50 ksi), Fb = 33 ksi. These values apply when lateral-torsional buckling is not the governing limit state.
Can I use this for timber or concrete?
Yes. For sawn timber, use the reference design value Fb (from AWC NDS tables) adjusted for moisture, temperature, and other factors. For concrete, use transformed section properties and consult ACI 318 for stress limits.
Official sources
- American Institute of Steel Construction: AISC Steel Construction Manual.
- American Wood Council: National Design Specification (NDS) for Wood Construction.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.