Steel — AISC 360

Member strength to Chapters D to H, LRFD or ASD — compression buckling, lateral-torsional buckling and every C_b option written down.

Design checks 4 min read

The aisc360.member-resistance module verifies member strength to AISC 360-22, Chapters D to H, at every sampled station along the member: compression from Chapter E's flexural and torsional buckling, and lateral-torsional buckling inside Chapter F, where AISC puts it as part of $M_{n}$ . It is Elementarium's second steel module; the first is EN 1993-1-1.

New checks use this module. A check created with the older aisc360.member-strength module keeps it; see The older member-strength module.

What is checked

Check	Chapter	What the module does
Tension	D2	Yielding on the gross section, D2-1
Compression	E3, E4, E7	Flexural buckling about both axes from $L_{c} = k \cdot L$ ; torsional buckling of doubly symmetric members (E4-2); slender elements on the effective area, $P_{n} = F_{cr} A_{e}$
Flexure	F2–F11	$M_{n}$ about both axes, including lateral-torsional buckling
Shear	G2–G6	Both directions, with web shear buckling
Torsion	H3	St. Venant, plus the H3-6 torsion / shear / flexure interaction for HSS
Combined	H1.1	Axial force with biaxial flexure, H1-1a and H1-1b

LRFD or ASD

Design philosophy is a parameter on the check. Both routes use the same nominal strength $R_{n}$ :

Method	Demand is compared against
LRFD	$ϕ R_{n}$
ASD	$R_{n} /Ω$

The moment-gradient factor C_b

LTB capacity depends on the shape of the moment diagram over the unbraced segment. Taking $C_{b} = 1.0$ throws that away: about 14% of the capacity for a simply supported beam under UDL, and over 100% under a reversing end-moment diagram.

Elementarium already samples internal forces at eleven stations along every member for every combination, which is exactly what these formulas consume. So $C_{b}$ is derived, not stored: it depends on the load combination and could never be a property of the member.

The published options do not agree, so the formula is your choice:

Method	Formula
`AISC F1-1`	The quarter-point formula, below
`Serna et al.`	The root-mean-square form of the same four moments. Reproduces the classical values for reversing diagrams, where F1-1 is markedly conservative
`ψ formula`	$1.88 - 1.40 ψ + 0.52 ψ^{2} \leq 2.7$ , for a linear diagram only; a curved one falls back to F1-1 with a disclosure
`Conservative`	$C_{b} = 1.0$ . Always permitted, always safe

AISC F1-1, from the maximum moment in the segment and the moments at its quarter, centre and three-quarter points:

C_{b} = \frac{12.5 M _{ma x}}{2.5 M _{ma x} + 3 M _{A} + 4 M _{B} + 3 M _{C}}

Or set the value yourself, where the practice mandates one.

Axes

The app's frame is $y$ horizontal and $z$ vertical, with $I_{y}$ strong. AISC calls the strong axis $x$ :

App	AISC
$M_{y}$ (strong)	$M_{x}$
$M_{z}$ (weak)	$M_{y}$

The traces are written in AISC symbols ( $M_{r x}$ , $M_{c x}$ and so on) because they are printed into an AISC calc report.

Effective lengths

$L_{c}$ about each axis comes from the same three sources as the Eurocode check: the $k_{y}$ and $k_{z}$ stored on each member, a named buckling analysis, or the end-restraint estimate. A factor set on the check for one member outranks all three. The unbraced length for LTB is $L_{b} = k_{L T} \cdot L$ , from the member. See Where the buckling lengths come from.

Not covered

Each of these is raised as a message on the check itself, never silently ignored:

E5 single angles and E6 built-up members, and the flexural-torsional forms of E4 for singly symmetric and unsymmetric shapes.
Round HSS with $D / t > 0.45 E / F_{y}$ , which Chapter E does not cover. Such a member is refused rather than checked on its gross area.
A box with a slender web, which F7.3 does not reach.
D2-2, tensile rupture on the net section. There is no connection model.
F9 / F10 tees, double angles and single angles, and F2 channels. These fall back to the yield moment with a loud disclosure, never a silent approximation.
Warping torsion. The six-degree-of-freedom beam carries St. Venant torsion only.
Connections, base plates, foundations, fatigue and fire.

Also not implemented in the $C_{b}$ derivation: the general López–Yong–Serna expression with end-restraint factors (only its unrestrained form is), and the ECCS 119 / Galea tables, which additionally yield $C_{2}$ for transverse loads not acting at the shear centre. Both need model data Elementarium does not carry: warping restraint, and the height at which a load is applied.

The older member-strength module

aisc360.member-strength takes compression as gross-section yielding, $F_{y} A_{g}$ , and so divides the H1-1 interaction by a strength no real column has. It stays registered so that checks created with it reproduce the numbers they were issued with. Such a check offers the upgrade to Member resistance; taking it is your decision, because Chapter E raises the utilisation of every compression member. See Module versions.

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