Member stability bracing
The strength and stiffness a brace must have to make a braced point of a column, beam or beam-column, by AISC 360-22 Appendix 6, and a comparison with the brace you have. Use it when a member's design assumes an unbraced length and the thing doing the bracing is not a floor or roof diaphragm: a strut, a kicker, a framing beam, a cross-frame.
The result reads "Calculated", because the calculation does not design the brace member: you give the brace's stiffness elements and its available strength.
Inputs of the stability bracing #
- Braced member and system: column, I-shaped beam or beam-column; lateral point or panel brace; for a beam, torsional point or continuous bracing. A point brace holds one location; a panel brace ties one braced point to the next (Appendix 6.1). A brace on several members takes the sum of their requirements, so enter how many (6.1).
- Required strength: the member's axial force and moment, by load type (each ASCE 7-22 combination is evaluated) or directly. Enter the largest within the unbraced lengths next to the brace.
- Lengths: the member length and the number of braced points in the span (torsional L / n, and the drawing); the unbraced length Lbr next to the brace, the larger Pr / Lbr or Mr / Lbr where the two sides differ. The longest unbraced length the required strength allows is optional: for an intermediate point brace, Lbr need not be taken less than it (6.2.2, 6.3.1b, 6.3.2a). It comes from your member design, for example Manual Table 4-1 or 6-1. It is not used for panel braces, or for beam-columns (6.4(b)), and is required for continuous bracing.
- Your judgment: whether the brace is the one nearest an inflection point in double curvature (Cd = 2.0, Appendix 6.3.1a); Cb for torsional bracing; the Commentary's reduction (2n − 1) / 2n for a finite number of column point braces (Eq. C-A-6-6, off by default).
- Section (beams and beam-columns): an AISC W, S, M or HP shape, or ho, tw, the two flanges' Iy and the distances c and t for a built-up or singly symmetric section. For a torsional point brace, the web stiffener thickness and width if any.
- The brace you have (optional): elements in series, everything between the member and an unyielding support, connections included (6.1): a member in axial A E cos² θ / L, a beam loaded at midspan 48 E I / L³, a cantilever 3 E I / L³, a beam in reverse curvature for torsion 6 E I / L, or a stiffness you enter. Then the braces in parallel, the angle of the brace to the brace force, and the available strength of one brace as you determined it, compression if it can buckle. Without them the calculation reports the required values and says the brace was not checked.
There is no auto-design: the calculation does not design the brace member.
Checks performed #
| Item | Basis |
|---|---|
| Column, panel | Vbr = 0.005 Pr; βbr = (1 / φ or Ω) 2 Pr / Lbr (Eqs. A-6-1, A-6-2), φ = 0.75, Ω = 2.00 |
| Column, point | Pbr = 0.01 Pr; βbr = (1 / φ or Ω) 8 Pr / Lbr (Eqs. A-6-3, A-6-4) |
| Beam, lateral panel | Vbr = 0.01 Mr Cd / ho; βbr = (1 / φ or Ω) 4 Mr Cd / (Lbr ho) (Eqs. A-6-5, A-6-6) |
| Beam, lateral point | Pbr = 0.02 Mr Cd / ho; βbr = (1 / φ or Ω) 10 Mr Cd / (Lbr ho) (Eqs. A-6-7, A-6-8) |
| Beam, torsional point | Mbr of Eq. A-6-9, at least 0.02 Mr; βT of Eq. A-6-11, φ = 0.75, Ω = 3.00; βsec of Eq. A-6-12; βbr of Eq. A-6-10 |
| Beam, continuous torsional | Eq. A-6-9 over the longest unbraced length; Eqs. A-6-10 and A-6-11 with L / n = 1.0; βsec of Eq. A-6-13, no stiffeners |
| Beam-column | The column and beam values summed, with the actual Lbr (6.4(a), (b)); condition (d) stated when both flanges are in compression |
| Web distortional stiffness | βsec above the required system stiffness, or the torsional brace is not effective (User Note to 6.3.2a) |
| Web stiffness and stiffener the brace needs (note) | From the provided brace, Eqs. A-6-10 and A-6-12 |
| Brace stiffness and strength | Your elements and available strength against the required values |
Limitations of the stability bracing #
- The brace member and connections are not designed: their stiffness and strength are your input.
- The alternatives of Appendix 6.1(a) and (b) (second-order analysis, buckling analysis) are not used. They can justify smaller values, which you may then enter as your own comparison.
- Column bracing is against flexural buckling only. Torsional and flexural-torsional buckling (E4) needs its own restraint.
- Beam bracing is for doubly and singly symmetric I-shapes under flexure in a plane of symmetry with no net axial force, as Appendix 6.3 says. For trusses, see the Commentary.
- A beam-column with torsional bracing is refused: Appendix 6.4(c) leaves the combination to the actual brace details. Run the flexure as a beam and the axial force as a column, then combine them for your brace.
- The drawing shows the braced points equally spaced. The calculation works from the Lbr entered.
Verification examples #
Verification status: 38 values compared in 11 examples (11 published, 0 hand calculations from the cited equations): 38 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
From the AISC Design Examples v16.0 Vol. 1, Examples A-6.1 to A-6.6, LRFD and ASD (required strength and stiffness of column and beam point braces, Cd = 2.0, the Commentary's reduction, the longest allowed length, braces at an angle, elements in series, the torsional brace with its web stiffener: 6.30 kips and 46.7 kip/in.; 6.67 kips and 16.7 kip/in.; 11.7 kip-ft, 4,640 and 1,240 kip-in./rad, and a 3.25 in. stiffener): all within tolerance, no deviations.
Hand calculations only, no published example on disk: panel braces for columns and beams, beam-columns, singly symmetric sections and continuous torsional bracing. The Specification states L / n = 1.0 for the stiffness of continuous bracing and does not repeat it for the strength; this calculation reads it into Eq. A-6-9 as well, the reading with consistent units, in line with the Commentary's stiffness per unit length. Check this one yourself if it governs. A torsional brace that bends in single curvature (2 E I / L, Commentary) goes in as an entered stiffness.