Question 1

What is the section modulus and how does it differ from the moment of inertia?

Accepted Answer

The second moment of area I (mm⁴) describes how the area is distributed about the neutral axis, while the section modulus Z = I / c (mm³) divides I by the distance c from the neutral axis to the extreme fibre. Bending stress is σ = M / Z, so Z directly sets how much moment a section can carry for a given allowable stress.

Question 2

How do I calculate the section modulus of a rectangle?

Accepted Answer

For a solid rectangle of width b and height h bending about the horizontal axis, I = b·h³/12 and c = h/2, so Z = I / c = b·h²/6. A 50 mm × 100 mm bar gives I = 4.1667×10⁶ mm⁴ and Z = 83,333 mm³.

Question 3

How do I get the bending stress from the section modulus?

Accepted Answer

Bending stress at the extreme fibre is σ = M / Z. Convert the moment to N·mm and use Z in mm³ to get stress in N/mm² (MPa). For Z = 83,333 mm³ and M = 1000 N·m = 1×10⁶ N·mm, σ = 1×10⁶ / 83,333 = 12.0 MPa.

Question 4

What is the radius of gyration used for?

Accepted Answer

The radius of gyration r = √(I/A) (mm) is the effective distance at which the whole area could be concentrated to give the same moment of inertia. It is used in column buckling through the slenderness ratio L/r — a larger r resists buckling better.

Question 5

Which axis does this calculator use?

Accepted Answer

All results are for bending about the horizontal centroidal (neutral) axis, assuming the cross-section is symmetric and the neutral axis passes through the centroid. For round and square sections the result is the same about any centroidal axis; for a rectangle, swap b and h to bend about the other axis.

Section ModulusCalculator

Section Modulus
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