Calculate or reverse-solve elastic first-yield and ideal plastic steel section moments, or evaluate a conditional singly reinforced rectangular-concrete model. These section calculations do not establish structural adequacy.

Use the elastic modulus S for first yield, or the plastic modulus Z for the ideal plastic section moment.

Section estimates only. Steel stability and local buckling are excluded. The concrete model assumes yielding tension steel; yielding, strain limits and the selected strength factor must be verified separately before design use.

Related Calculators

Moment Capacity (Elastic Yield Moment) Formula

The following formula is used to calculate the elastic yield moment of a cross section:

M = Fy ร— S

Unit note: If Fy is in psi (lb/inยฒ) and S is in inยณ, then M comes out in lb-in. To convert to lb-ft, divide by 12: M (lb-ft) = Fy ยท S / 12.

Variables:

  • M is the elastic yield moment (lb-in, or lb-ft after dividing by 12)
  • Fy is the yield strength of the material (psi)
  • S is the elastic section modulus (in^3)

To calculate the elastic yield moment, multiply the yield strength of the material by the elastic section modulus, then convert to your desired moment units if needed.

What is Moment Capacity?

The steel modes evaluate the elastic first-yield section moment using Fy ร— S, or the ideal plastic section moment using Fy ร— Z. S and Z are different section properties. Buckling, stability, bracing, connections, interaction and code resistance factors require separate checks. The concrete mode uses a = As ร— fy / (0.85 ร— fโ€ฒc ร— b) and Mn = As ร— fy ร— (d โˆ’ a/2), assuming a singly reinforced rectangular section without axial load and yielding tension steel. Its entered factor ฯ† scales Mn; the editable default 0.9 is an assumption. This tool does not verify strain compatibility, yielding, appropriate ฯ† or design-code compliance. The demand ratio is numerical comparison only.

How to Calculate Moment Capacity?

The following steps outline how to calculate the Moment Capacity:

  1. First, determine the yield strength of the material (Fy) in psi.
  2. Next, determine the elastic section modulus (S) in cubic inches (inยณ).
  3. Next, use the formula from above: M = Fy ยท S (this gives M in lb-in when Fy is in psi and S is in inยณ).
  4. Finally, if you want M in pound-feet, convert lb-in to lb-ft by dividing by 12.
  5. In the widget, choose the elastic basis and matching units; for this psi example, enter 36 ksi with 10 inยณ and select kipยทft to obtain 30 kipยทft (30,000 lb-ft). Verify all model assumptions and independent design checks.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Yield strength of the material (Fy) = 36,000 psi

Section modulus (S) = 10 in^3

Elastic yield moment: M = 36,000 ร— 10 = 360,000 lb-in = 30,000 lb-ft