Cross-Section Properties (A, I, S, r)
Area, moment of inertia (I = b h^3/12 etc.), section modulus S = I/c.
Example
You enter
- Shape rectangle
- Width b (in; rectangle/tube) 1.5
- Height/depth h (in; bending axis) 7.25
You get
- Area A 10.88 in^2
- Moment of inertia I 47.63 in^4
- S (in³) 13.14
- Radius of gyration r 2.093 in
Details, formula, and sources
Area, moment of inertia (I = b h^3/12 etc.), section modulus S = I/c, and radius of gyration r = sqrt(I/A) for a rectangle, solid round, pipe, or hollow tube. I scales with the cube of the depth, so orientation dominates. A design aid, not the engineer of record.
rectangle I = b h^3/12; round I = pi d^4/64; pipe I = pi(d^4 - di^4)/64; tube I = (b h^3 - bi hi^3)/12; S = I/c; r = sqrt(I/A).
The standard cross-section property formulas (mechanics of materials; AISC Manual shapes), by name.
Section-property formulas are published free in any mechanics-of-materials reference and the AISC Manual shape tables. The engineer of record governs the design.
Estimate. AHJ and licensed professional govern.
Field names used by the API: shape, b_in, h_in, A_in2, I_in4, S_in3, r_in
- Shapes rectangle, solid round, pipe (d/di), hollow rectangular tube (b/h, wall t)mechanics of materials
- Elastic properties I, S = I/c, r = sqrt(I/A); not the plastic modulus ZAISC / mechanics
- Actual dimensions uses the entered actual (dressed) dimensions, not nominalscope of this tile