Steel Section Properties — Zx, Sx, Zy, Sy

Area, moment of inertia, elastic and plastic section modulus (Sx, Sy, Zx, Zy) and radius of gyration for a W-shape, a rectangular/square HSS, or a round HSS, from typed dimensions, with a scaled dimensioned cross-section.

Shape

Dimensions

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bf = 8.00 ind = 17.00 intf = 1.000 intw = 0.250 in
Zx
142.06 in³
Sx
128.90 in³
Zy
32.23 in³
Sy
21.34 in³
Gross area
19.750 in²
rx
7.448 in

All properties

Ag19.750 in²
Ix / Iy1095.6 / 85.4 in⁴
Sx / Sy128.90 / 21.34 in³
Zx / Zy142.06 / 32.23 in³
rx / ry7.448 / 2.079 in
Shape factor Zx/Sx, Zy/Sy1.10 / 1.51

Calculation

  1. 1Clear web height
    h = d - 2t_f
    h = 17.00 - 2(1.000) = 15.00
    h15.00 in
  2. 2Gross area
    A_g
    A_g = 19.750
    A_g19.750 in²
  3. 3Moment of inertia
    I_x, \quad I_y
    I_x = 1095.650 \text{ in}^4, \quad I_y = 85.350 \text{ in}^4
    I_x1095.6 in⁴
  4. 4Elastic section modulus
    S_x = \frac{I_x}{c_x}, \quad S_y = \frac{I_y}{c_y}
    S_x = 128.900 \text{ in}^3, \quad S_y = 21.340 \text{ in}^3
    S_x128.90 in³
  5. 5Plastic section modulus
    Z_x, \quad Z_y
    Z_x = 142.060 \text{ in}^3, \quad Z_y = 32.230 \text{ in}^3
    Z_x142.06 in³
  6. 6Radius of gyration
    r_x = \sqrt{I_x/A_g}, \quad r_y = \sqrt{I_y/A_g}
    r_x = 7.448 \text{ in}, \quad r_y = 2.079 \text{ in}
    r_x7.448 in

Notes

  • Shape factor Zx/Sx = 1.10, Zy/Sy = 1.51 — how much reserve strength lies between first yield and full plastic moment. 1.0 for a thin round tube, 1.5 for a solid rectangle; a typed section outside roughly 1.0–1.7 is worth double-checking.

Assumptions

  • Sharp corners on the box and round sections — no fillet radius. Real HSS has a corner radius; AISC publishes exact properties per cataloged designation that account for it.
  • The I-shape is doubly symmetric: equal flanges, web centered.

What this calculator does not check

  • Does not check any AISC 360 provision — no local slenderness classification, no capacity, no design check of any kind. This is geometry only.
  • Not a substitute for the published dimensions and properties of a specific cataloged shape (a particular W-shape or HSS designation) — for that, use the manufacturer's or AISC's own tables.

Results are for preliminary sizing and educational use. They are not a design and must be reviewed, verified and sealed by a licensed or registered engineer before being used in construction.

steel-section-properties v1.0.0 · — · input c22e39e9e3e133b9