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LecturesModule 17

Stability, Bracing, and Second-Order Effects

Direct Analysis Method, B1/B2, appendix 6 bracing.

AISC Reference Box
  • AISC 360-22 — Specification chapter governing this topic
  • AISC Manual 16th Ed. — Design tables and worked examples

Lecture Notes

This module introduces stability, bracing, and second-order effects. Lecture content here covers the governing physics, LRFD philosophy, and how the relevant AISC 360-22 chapter organizes the limit states.

Instructors can replace this text in Admin Mode. Each section is structured around: (1) behavior, (2) failure modes, (3) AISC limit-state equations, (4) design workflow, (5) detailing requirements.

A short comparison to ASD is included only where the resistance factor / safety factor relationship clarifies the LRFD design check.

P-δ (member)P-Δ (story)HB1 amplifies member moments; B2 amplifies story sway moments
Stability: B1 amplifies member moments (P-δ); B2 amplifies story sway moments (P-Δ); DAM uses τb·EI.

Formula Sheet

NameEquationAISC Ref
Design strengthφ Rn ≥ RuAISC 360-22 B3.1

Worked Example

Stability, Bracing, and Second-Order Effects

Given
Replace with project-specific given data (loads, geometry, material).
Load combination
Controlling LRFD load combination from ASCE 7.
Required strength
Compute required strength Ru from the controlling combination.
Limit states
  • Limit state 1
  • Limit state 2
AISC reference
AISC 360-22 — applicable chapter
Solution steps
  1. 1. Required strength
    Compute Ru.
  2. 2. Trial section
    Pick a trial from AISC shape tables Instructor should verify with official AISC Manual.
  3. 3. Check each limit state
    Apply φ Rn ≥ Ru for every governing limit state.
  4. 4. Iterate
    Resize until the most economical section satisfies all checks.
Final design decision
Select the lightest section that satisfies all LRFD limit states.
Common mistakes in this example
  • Skipping a limit state
  • Using the wrong φ factor
  • Forgetting serviceability checks

FE-Style Worked Examples (6)

Each example mirrors the NCEES FE Civil Reference Handbook style: brief givens, a labeled figure, AISC section reference, step-by-step numeric solution, and a single boxed answer.

Given
Second-order/first-order drift ratio = 1.7.
AISC Reference
AISC §C1
Step-by-step solution
  1. Pick
    DAM mandatory (always allowed) Effective length method only when Δ2/Δ1 ≤ 1.5.
Answer Use the Direct Analysis Method.
Loads (ASCE 7)LRFD CombosRequired RuTrial SectionLimit StatesφRn ≥ Ru?Serviceability

Practice Problems

  1. [E] Name the two AISC stability methods (DAM, ELM).
  2. [E] State the notional load = 0.002·Yi.
  3. [E] Define P-δ vs P-Δ.
  4. [E] List the stiffness reduction τb for DAM.
  5. [E] State AISC chapter for stability (Chapter C) and Appendix 7.
  6. [M] Compute notional loads per story of a 3-story building, Y = 1500 k per story.
  7. [M] DAM: reduce EI to 0.8·τb·EI for a column with αPr/Py = 0.6.
  8. [M] B2 for ΣPstory = 2000 k, ΣHstory = 100 k, ΔH/L = 1/400.
  9. [M] Decide if 2nd-order analysis needed: B2 = 1.18 per §C2.1.
  10. [M] Beam-stability brace force per Appendix 6: 2% of compression-flange force.
  11. [H] B1 and B2 for a 4-story unbraced moment frame, 12 ft stories, ΣPstory = 1800 k, ΣHstory = 100 k.
  12. [H] Brace stiffness vs strength: design third-point bracing on W21x62, Lb = 10 ft.
  13. [H] Alignment chart K for W14x120 column with GA = 2.5, GB = 1.0.
  14. [H] DAM: compare τb-modified strength of a W12x72 column to its full elastic strength.
  15. [H] Prove 0.002·Yi notional load envelops L/500 column out-of-plumbness for a 12 ft story.

Quiz

1. Which AISC 360-22 chapter primarily governs stability, bracing, and second-order effects?
2. In LRFD, the basic design inequality is:

Common Student Mistakes

  • Mixing ASD and LRFD load combinations in the same problem.
  • Using nominal strength Rn instead of design strength φRn.
  • Forgetting to check every limit state listed in the AISC chapter.

"Professor Explains" Script

Today we're talking about stability, bracing, and second-order effects. Think of this topic as one step in the LRFD workflow: identify the demand, identify the limit states from the relevant AISC chapter, then check that φ·Rn is at least equal to Ru. We'll walk through the failure modes, the equations, and a worked example. Pay close attention to where the resistance factor changes — that's where students lose points on exams.