Section Modulus Calculator

Your details

Switches all length inputs and the section modulus output units.
Overall width of the cross-section.
mm
Overall height (depth) of the cross-section.
mm
Enter a design bending moment to compute the maximum elastic bending stress. Leave at 0 to skip.
N·mm
Elastic section modulus (Sx)High plastic reserve
666,666.6667

Strong-axis elastic section modulus S = I / c. Relates bending moment to maximum stress.

Plastic section modulus (Zx)1,000,000
Second moment of area (Ix)66,666,666.6667
Elastic section modulus (Sy)333,333.3333
Plastic section modulus (Zy)500,000
Second moment of area (Iy)16,666,666.6667
Shape factor (Zx/Sx)1.5
Cross-sectional area (A)20,000
Distance to extreme fiber (cx)100
_unitLabelmm
_areaUnitmm²
_iUnitmm⁴
_sUnitmm³
_stressUnitMPa
Elastic Sx666,666.6667
Plastic Zx1,000,000
Elastic Sy333,333.3333
Plastic Zy500,000

Solid rectangle section: Sx = 666666.6667 mm³

  • Elastic section modulus Sx = 666666.6667 mm³: the bending moment that causes first yield equals Sx * yield_stress.
  • Second moment of area Ix = 66666666.6667 mm⁴: governs beam deflection and bending stiffness.
  • Shape factor (Zx/Sx) = 1.500: a solid rectangle can develop 50.0% additional moment capacity beyond first yield before full plastic hinge forms.
  • Plastic section modulus Zx = 1000000.0000 mm³: multiply by the material yield strength to get the full plastic moment capacity.

Next stepCompare Sx to the required section modulus (M_design / sigma_allow) to verify beam adequacy. Use the I-beam shape for the most efficient bending sections.

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