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LecturesModule 18

Serviceability: Deflection, Drift, Vibration

L/360, L/240, drift H/400, floor vibration (AISC Design Guide 11).

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 serviceability: deflection, drift, vibration. 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.

Project case study — Cardinal Square — 4-story braced-frame office

Every chapter's worked example is one step in the design of the same building: Plan: 4 bays N–S × 3 bays E–W, each 30 ft × 30 ft. Stories: 4 @ 13 ft (52 ft roof). Composite floor: 4.5 in NW concrete on 3 VLI20 deck. Roof: 1.5 in B-deck + insulation + membrane. Materials: Wide-flange members A992 (Fy = 50 ksi, Fu = 65 ksi). Plates A572 Gr. 50. HSS bracing A500 Gr. C. Bolts A325-N 7/8 in dia. Welds E70XX. Concrete f'c = 4 ksi. Anchor rods F1554 Gr. 36.

Chapter 18 — Serviceability (deflection)
Same composite filler beam under live load only
Demand carried forward
wL = 0.50 klf. ΔL = 5 wL L⁴ / (384 E Ix-comp).
This chapter contributes
Checks ΔL ≤ L/360 = 30·12/360 = 1.0 in. If not met, re-pick a stiffer section and loop back to Chapter 6.
Δ ≤ L/360 (LL)Δ ≤ L/240 (DL+LL)Drift Δstory ≤ H/400 (wind, typ.)
Serviceability limits: LL Δ ≤ L/360, total Δ ≤ L/240, wind drift Δ ≤ H/400 (AISC Ch. L + DG-11).

Formula Sheet

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

Worked Example

Serviceability: Deflection, Drift, Vibration

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
W18×35: Ix=510 in⁴, L=30 ft, wL=1.2 k/ft (service live).
AISC Reference
AISC §L3
Step-by-step solution
  1. ΔL
    5wL⁴/(384EI) = 5(1.2/12)(360)⁴/(384(29000)(510)) = 1.51 in
  2. Limit
    L/360 = 360/360 = 1.0 in → NG (1.51 > 1.0)
Answer Increase Ix — try W18×46 (I=712 in⁴) → Δ=1.08 still slightly NG; try W21×44 (I=843)→ Δ=0.91 ✓.
ΔLive-load deflection check

Course Materials — Lecture & Worked Examples

Lecture and examples below are extracted from the instructor's 'Deflection of Beams' notes. Service-load deflections (not factored!) are compared to code limits L/360, L/240, L/180.

Lecture highlights (from instructor notes)
  • Why limit deflection: protect finishes (plaster), preserve appearance, prevent psychological discomfort, and avoid ponding/load-sharing problems.
  • Use SERVICE loads (no load factors) in every deflection calc. Convert: w in k/in, L in inches.
  • Simply-supported UDL: δ = 5wL⁴/(384 EI). Concentrated load at midspan: δ = PL³/(48 EI). Combine cases by superposition.
  • Make sure I corresponds to the bending axis — I_xx for major-axis bending, I_yy for minor-axis bending.
  • AISC modified equation (simple span I-shapes & channels): δ = ML²/(C₁·I), where M is in k-ft, L in ft, I in in⁴, and C₁ depends on the loading pattern (Manual Fig. 3-2). For UDL on a simple span C₁ = 161; for point load at midspan C₁ = 201.
  • Dead-load deflection is typically removed by cambering the beam, so only live-load deflection matters in service.
Given
Roof beams supporting plaster ceiling: δLL ≤ L/360. Floor beams: δLL ≤ L/360. Roof not supporting ceiling: δLL ≤ L/180.
AISC Reference
IBC 2018 Table 1604.3; AISC §L3
Step-by-step solution
  1. Use the table
    Read the column matching the load (LL only vs D+L vs S/W) and the row for the member type.
Answer Limits range from L/180 to L/360 depending on member type and load type.
Allowable δ_LL, δ_(D+L), and δ_(snow/wind) limits by member type.
Allowable δ_LL, δ_(D+L), and δ_(snow/wind) limits by member type.

Interactive Calculator

Beam Deflection (Simply Supported, UDL)

AISC Design Guide / serviceability
Δ = 5wL⁴/(384 E I)1.232 in
Allowable = L/3601.000 inNG

Practice Problems

  1. [E] State LL deflection L/360 and total L/240.
  2. [E] State wind drift limit H/400.
  3. [E] Identify AISC DG-11 (floor vibrations).
  4. [E] Define camber and when specified.
  5. [E] Distinguish service from factored loads.
  6. [M] LL deflection of W18x35 (Ix = 510 in⁴) on 30 ft, wL = 1.2 k/ft.
  7. [M] Compare above deflection to L/360 limit.
  8. [M] Floor vibration check: 30 ft composite W21x50, fn ~ 5 Hz per DG-11.
  9. [M] Camber for W24x62, 40 ft, wDL = 1.0 k/ft.
  10. [M] Story drift at H = 12 ft, allowable H/400 — max lateral displacement?
  11. [H] Floor vibration: 36 ft span open-web steel joists, 10 ft o.c., walking excitation — full DG-11.
  12. [H] LL deflection of continuous 2-span W21x50 (35 ft each), wL = 1.2 k/ft using coefficients.
  13. [H] Drift compatibility: 5-story braced frame H = 60 ft, ΔW = 1.2 in. Check H/400 and inter-story h/400.
  14. [H] Composite floor long-term creep + shrinkage deflection of partially composite W21x50.
  15. [H] Camber schedule for a 5-bay typical floor accounting for casting sequence + partial composite.

Quiz

1. Which AISC 360-22 chapter primarily governs serviceability: deflection, drift, vibration?
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 serviceability: deflection, drift, vibration. 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.