Tool NotesWhat it does, the formula, and what it assumes

What this tool does

Search the AISC shape database by name or by size and get the full property set back: depth, flange width, web and flange thickness, area, weight per foot, and the moments of inertia and section moduli about both axes.

Compare sections side by side to see what you gain or lose by moving a size up or down before you commit to it on a drawing.

Formula

The tabulated values are geometry. These are the relationships that put them to work.

S = I / celastic section modulus, c to the extreme fiber
f_b = M / Sbending stress; M in kip-in, S in in³, f_b in ksi
Δ = 5wL⁴ / (384·E·I)midspan deflection, simple span, UDL; w in kip/in, L in in, E = 29,000 ksi, I in in⁴, Δ in in; convert kip/ft and ft first

Assumptions

All tabulated values are from the AISC Shapes Database v16.0. They describe the shape as rolled, with no deductions and no allowance for what happens to it on a job. Custom pipe sections in the Pipe tool are computed, not tabulated.

  • Nominal geometry, holes, copes, notches and reinforcement are not reflected; a coped beam end has less net section than the table says.
  • Gross section, properties are gross, not net or effective. Tension members and slender elements need their own reduction.
  • Material independent, geometry does not change with grade. Fy and Fu come from the specification, not from this table.
  • Radii of gyration, the shape table carries I and A but not r, so r_x and r_y on the reference pages are computed as √(I/A). A computed value and a published one are not the same claim.
Technical NotesDerivation, worked example, applications and checks

How the properties relate to each other

Area sets weight and axial capacity. Moment of inertia sets stiffness and therefore deflection. Section modulus (I divided by the distance to the extreme fiber) sets bending stress. Radius of gyration is what slenderness is measured against, so it decides buckling.

A → weight (lb/ft) and axial capacityI → deflection:  Δ ∝ 1 / IZ → plastic bending:  M_p = F_y · Zr → slenderness:  KL / r
  • Z against S, Zx governs strength in a compact section; Sx governs where the section is not compact or where service stress is the check. They are not interchangeable.

Worked example

Reading a W12x30

Given

  • Search: W12x30

Solve

d = 12.3 in,  bf = 6.52 in,  tw = 0.260 in,  tf = 0.440 indimensions
A = 8.79 in²,  Weight = 30 lb/ft
Ix = 238 in⁴,  Sx = 38.6 in³,  Zx = 43.1 in³strong axis
Iy = 20.3 in⁴,  Sy = 6.24 in³,  Zy = 9.56 in³weak axis

Ix is nearly twelve times Iy (238 / 20.3 = 11.7), which is why a wide-flange beam laid flat is not a beam.

Applications

  • Sizing, work back from a required Sx or Zx to the lightest section that carries the moment.
  • Substitution, check that a proposed swap matches or beats the original on every property that governs, not just weight.
  • Detailing, web and flange thickness drive bolt edge distance, weld size limits and connection geometry.
  • Deflection, Ix drives deflection, not strength. Compare Ix across candidates when a span/360 limit rather than moment is what decides the member.

Field notes

  • Nominal depth is not actual depth. A W12x30 measures 12.3 in; a W12x336 measures 16.8 in. Detail to the tabulated d, never to the name.
  • The property table says nothing about availability. A legal size is not a stocked size; check supply before you detail around an unusual member.
  • Two shapes with the same weight per foot can behave very differently. Compare Ix and rx, not lb/ft.

Educational reference only. Verify every result independently and apply the safety factors and load combinations required by the governing code and a qualified engineer.

Quick reference

  • QR03 - Beam Analysis

    PDF · 651 KB — Static Beam Analysis - Shear, Moment, Deflection, Equations, Worked Example, Field Notes, Reference Table, + More

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Related reference

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