15.2 Structural and Cold-Formed Steel Properties

Steel is not defined by one strength number. Elastic stiffness, yielding, ultimate resistance, ductility, residual stress, geometry, and manufacturing route affect different responses. For July 2026, use the April 2024 PE Civil: Structural specification, current PE Civil Reference Handbook, and the AISC Steel Construction Manual 15th edition. Do not substitute the April 2027 standard set.

Read the Stress-Strain Curve by Region

In the initial linear-elastic range,

σ = Eε

and common structural steels use approximately the same elastic modulus, about E = 29,000 ksi, even when their specified yield strengths differ. Raising F_y therefore increases an elastic load threshold but does not make a same-sized beam meaningfully stiffer before yield. Deflection and elastic buckling depend strongly on E and section properties, not simply F_y.

Yield strength F_y marks the onset or specified measure of significant permanent deformation. Ultimate tensile strength F_u is the maximum engineering tensile stress in a coupon test. They enter different limit states: gross-section yielding, net-section rupture, connection bearing, and weld or bolt checks do not all use the same property. Yield ratio and elongation provide additional behavior information, but neither alone is a complete ductility or toughness measure.

Nominal specified values are design inputs; mill certificates and coupon results are measured properties for particular material. A higher test value does not authorize an unreviewed substitution or a change to the specified design basis.

Hot-Rolled and Built-Up Structural Products

Wide-flange shapes, channels, angles, tees, bars, plates, and hollow structural sections place material differently around their centroid. Area governs uniform axial stress; I and section modulus govern elastic stiffness and stress; radius of gyration helps describe slenderness; torsion constant and warping properties govern twist. Always select the axis and property matching the response.

Rolling and welding leave self-equilibrating residual stresses. Although their net axial force over the section is zero, they cause parts of a compression member to yield earlier and influence buckling behavior. Welding can add a different residual-stress and distortion pattern. AISC member equations incorporate calibrated effects; do not add a guessed residual stress as an independent service load.

Built-up sections require transfer among components through welds, bolts, or other connectors. Two plates touching are not automatically one composite steel section. Holes reduce net area; shear lag can reduce effective net area; local load introduction can create yielding, crippling, or buckling not predicted by average P/A.

Worked Elastic Property Check

A 10 ft steel tension bar has area A = 2.00 in^2, carries service axial load P = 72 kips, and has E = 29,000 ksi, specified F_y = 50 ksi, and F_u = 65 ksi. Find nominal axial stress, elastic strain, and elongation.

σ = P/A = 72/2.00 = 36.0 ksi

Because 36.0 < 50 ksi, the stated load remains below specified yield for this simple material check.

ε = σ/E = 36/29,000 = 0.001241

δ = εL = (0.001241)(120 in) = 0.149 in

This does not establish member adequacy: net area, connections, block shear, slenderness, load combinations, and design factors remain. If load increased to 110 kips, nominal stress would be 55 ksi—above F_y but below F_u. The elastic elongation formula would no longer describe the full response, and “below ultimate” would not make yielding acceptable.

Cold-Formed Steel Must Not Disappear

Cold-formed steel members are made by bending relatively thin sheet or strip at ambient temperature into studs, joists, tracks, deck, panels, lipped channels, and other shapes. Their high strength-to-weight ratio comes with slender plates and open-section behavior. Corners may gain strength from cold work, but property variation and reduced ductility can accompany that increase. Forming also creates residual stress.

Three instability scales are important:

• Local buckling: a web, flange, or lip plate element buckles while fold lines remain substantially straight.
• Distortional buckling: the cross-section changes shape, often involving flange-lip rotation and movement of fold lines.
• Global buckling: the member bends or twists over its unbraced length.

Thin elements can carry post-buckling stress nonuniformly, leading to effective-width or effective-section concepts. Gross area and gross I may therefore differ from properties used for a particular strength calculation. Screw holes, web openings, concentrated bearing, web crippling, connection eccentricity, sheathing restraint, and corrosion loss can be proportionally significant.

The listed 2026 references support the exam's controlled workflow; do not import a future standard or apply a hot-rolled AISC capacity equation blindly to a cold-formed stud. When a problem supplies cold-formed section properties or an equation, use the supplied basis consistently. Concept questions often ask which mode or property changes, not a full specification design.

Property Workflow

1. Identify product and manufacturing route: rolled shape, plate, HSS, welded built-up member, or cold-formed sheet shape.
2. Separate E, F_y, F_u, ductility, and residual stress roles.
3. Use the correct gross, net, effective, or transformed section property.
4. Identify local, distortional, member, and connection limit states.
5. Match LRFD or ASD demand with its compatible resistance.

A final reasonableness check asks whether a changed variable affects stiffness, strength, or stability. Higher F_y changes strength; greater I changes stiffness and elastic buckling; shorter unbraced length changes global stability. They are not interchangeable improvements.