AISC 360-22 Structural Steel Design Guide

1.1 Common Structural Steel Grades — ASTM Designations

Grade	Fy (ksi / MPa)	Fu (ksi / MPa)	Primary use	Notes
ASTM A36	36 / 250	58–80 / 400–550	Plates, angles, channels	Original workhorse grade; rarely used for W-shapes today
ASTM A572 Gr. 50	50 / 345	65 / 450	W-shapes, plates, channels	Most common structural grade; good weldability
ASTM A992	50 / 345	65 / 450	W-shapes only	Fy/Fu ≤ 0.85; max Fy = 65 ksi; preferred for seismic SMF/IMF
ASTM A500 Gr. B (HSS round)	42 / 290	58 / 400	HSS round (tubes)	Standard for circular HSS; Gr. C: Fy = 46 ksi
ASTM A500 Gr. B (HSS rect.)	46 / 317	58 / 400	HSS rectangular / square	Standard for box sections; Gr. C: Fy = 50 ksi
ASTM A53 Gr. B	35 / 240	60 / 415	Pipe sections (standard pipe)	Pipe used for columns/braces; lower Fy than HSS
ASTM A913 Gr. 65	65 / 450	80 / 550	W-shapes (quenched & tempered)	High-strength; Fy/Fu ≤ 0.85 requirement; good notch toughness
ASTM A1085	50 / 345	65 / 450	HSS rectangular/square	Uniform wall thickness; tighter tolerances; preferred for seismic HSS members
ASTM A514	90–100 / 620–690	100–130 / 690–900	Plates (high-strength)	Quenched & tempered; limited weld preheat requirements; t ≤ 2.5 in for Fy = 100 ksi

1.2 Elastic Properties

Property	US	SI
Modulus of elasticity (E)	29,000 ksi	200,000 MPa
Shear modulus (G)	11,200 ksi	77,200 MPa
Poisson's ratio (ν)	0.30
Thermal expansion coefficient (α)	6.5×10⁻⁶ /°F	11.7×10⁻⁶ /°C
Unit weight	490 pcf	77.0 kN/m³

All properties from AISC 360-22 Appendix 2 and AISC Steel Construction Manual (16th Ed.).

1.3 Expected (Probable) Material Properties — Seismic Design

AISC 341-22 §A3.2 — Expected strengths used for capacity design in seismic systems:

Property	Value	Description
Ry · Fy	Expected yield strength	Ry = 1.1 for A992/A572 Gr.50; 1.5 for A36; 1.3 for A500/A1085
Rt · Fu	Expected tensile strength	Rt = 1.1 for A992/A572 Gr.50; 1.2 for A36; 1.3 for A500

Used for connection design, panel zone checks, and capacity-protected elements to ensure yielding occurs in the intended location (link, brace, beam plastic hinge).

Sections are classified as compact, noncompact, or slender based on element width-to-thickness ratios (λ). For seismic design, an additional highly ductile (λ_hd) and moderately ductile (λ_md) classification applies per AISC 341-22 Table D1.1.

2.1 Flexure — Doubly Symmetric I-Shapes (W-shapes) — Table B4.1b

Element	λ (slenderness ratio)	λp (compact limit)	λr (noncompact limit)
Flange (b/t)	bf / (2·tf)	0.38√(E/Fy)	1.0√(E/Fy)
Web (h/tw)	hc / tw	3.76√(E/Fy)	5.70√(E/Fy)

For F_y = 50 ksi (A992): λ_p,flange = 9.15; λ_r,flange = 24.1; λ_p,web = 90.6; λ_r,web = 137.

2.2 Compression — Uniformly Compressed Elements — Table B4.1a

Element	Ratio	λr (slender limit)
W-shape flange (outstanding leg)	bf/(2·tf)	0.56√(E/Fy)
W-shape web	h/tw	1.49√(E/Fy)
HSS rectangular wall	b/t	1.40√(E/Fy)
HSS circular (round)	D/t	0.15·E/Fy
Angle leg	b/t	0.45√(E/Fy)

2.3 Seismic Compactness — AISC 341-22 Table D1.1

More stringent limits to ensure ductile behavior under cyclic loading:

Element	Highly Ductile (λhd)	Moderately Ductile (λmd)
W-shape flange	0.30√(E/CaFy)	0.38√(E/CaFy)
W-shape web (axial + flexure)	2.57√(E/Fy)·(1−1.04·Ca)	3.76√(E/Fy)·(1−2.75·Ca)
HSS rectangular flange	0.55√(E/Fy)	0.64√(E/Fy)
HSS rectangular web	1.25√(E/Fy)	1.40√(E/Fy)
HSS circular D/t	0.053·E/Fy	0.076·E/Fy

C_a = P_u/(φ_c·F_y·A_g) ≤ 1.0 for LRFD  |  C_a = P_a·Ω_c/(F_y·A_g) ≤ 1.0 for ASD. Higher axial load → more stringent web limit.

Highly ductile (λ_hd) required for: SMF beams/columns, EBF members outside link, BRBF beams/columns, SPSW vertical boundary elements. Moderately ductile (λ_md) for: IMF, SCBF, brace members in SCBF.

3.1 Dead Loads

Unit weight: structural steel 490 pcf (77.0 kN/m³); concrete (normal weight) 150 pcf (23.6 kN/m³); typical steel deck + concrete topping ≈ 50–75 psf (2.4–3.6 kN/m²); roofing/insulation 5–15 psf (0.24–0.72 kN/m²). Confirm with actual product data.

3.2 Floor Live Loads — ASCE 7-22 Table 4.3-1 (selected)

Occupancy	Lo (psf)	Lo (kN/m²)
Residential — private rooms	40	1.92
Office areas	50	2.40
Lobbies, first floors	100	4.79
Corridors above first floor	80	3.83
Assembly — fixed seats	60	2.87
Assembly — movable seats / standing	100	4.79
Retail — first floor	100	4.79
Retail — upper floors	75	3.59
Storage — light	125	5.99
Storage — heavy	250	11.97
Parking (passenger vehicles)	40	1.92
Mechanical rooms / penthouses	150	7.18

3.3 Live Load Reduction — ASCE 7-22 §4.7

Reduced live load: L = L_o·(0.25 + 15/√(K_LL·A_T)) ≥ 0.50·L_o (for members supporting one floor) or ≥ 0.40·L_o (columns/two or more floors).

K_LL = live load element factor: 4 (interior columns), 4 (interior beams with two-way action), 2 (edge/exterior beams, interior beams), 1 (cantilevered slabs). No reduction permitted for L_o > 100 psf or assembly occupancies.

3.4 Roof Live Loads — ASCE 7-22 §4.8

L_r = 20·R₁·R₂, where 12 psf ≤ L_r ≤ 20 psf (0.58–0.96 kN/m²). R₁ = reduction for tributary area; R₂ = reduction for slope.

3.5 Wind Loads — ASCE 7-22 Ch. 26–31

Design wind pressure (C&C and MWFRS): p = q·G·C_p − q_i·GC_pi. q_z = 0.00256·K_z·K_zt·K_d·K_e·V² (US units, V in mph). Basic wind speed V from ASCE 7-22 Figs. 26.5-1A/B/C.

4.1 LRFD Strength Combinations — ASCE 7-22 §2.3.1

#	Combination
LC1	1.4D
LC2	1.2D + 1.6L + 0.5(Lr or S or R)
LC3	1.2D + 1.6(Lr or S or R) + (L or 0.5W)
LC4	1.2D + 1.0W + L + 0.5(Lr or S or R)
LC5	0.9D + 1.0W
LC6	1.2D + 1.0E + L + 0.2S
LC7	0.9D + 1.0E

D = dead; L = floor live; L_r = roof live; S = snow; R = rain/ice; W = wind (from MWFRS); E = seismic.

For E in seismic combinations: E = ρ·Q_E ± 0.2·S_DS·D (ASCE 7-22 §12.4.3), where ρ = redundancy factor (1.0 or 1.3).

4.2 ASD Load Combinations — ASCE 7-22 §2.4.1

#	Combination
A1	D
A2	D + L
A3	D + Lr (or S or R)
A4	D + 0.75L + 0.75(Lr or S or R)
A5	D + 0.6W (or 0.7E)
A6	D + 0.75·0.6W + 0.75L + 0.75(Lr or S or R)
A7	0.6D + 0.6W
A8	0.6D + 0.7E

Note: In AISC 360-22, the safety factor for most member checks is Ω = 1.67 (flexure) or 2.0 (shear/connections) under ASD. The LRFD approach with φ factors is generally preferred for steel design.

4.3 Notation Summary

Term	LRFD	ASD
Design strength / Allowable strength	φ·Rn ≥ Ru	Rn/Ω ≥ Ra
Flexure	φb = 0.90	Ωb = 1.67
Compression	φc = 0.90	Ωc = 1.67
Tension (yielding)	φt = 0.90	Ωt = 1.67
Tension (rupture)	φt = 0.75	Ωt = 2.00
Shear	φv = 0.90 (1.00 for some)	Ωv = 1.67 (1.50 for some)
Connections / welds	φ = 0.75	Ω = 2.00

5.1 Design Tensile Strength

The governing tensile strength is the minimum of the three limit states:

Limit State 1 — Tensile Yielding (§D2a)

Limit State 2 — Tensile Rupture at Net Section (§D2b)

A_e = A_n · U (effective net area). Shear lag factor U from AISC Table D3.1.

Connection type	U	Note
All elements connected (plates, bars)	1.00	No shear lag
W-shape, flanges connected (≥3 bolts per line)	0.90	bf ≥ ⅔d
W-shape, flanges connected (≥3 bolts)	0.85	bf < ⅔d
W-shape, web connected (≥4 bolts per line)	0.70	—
Angle, single row ≥4 bolts	0.80	—
Angle, single row 2–3 bolts	0.60	—
General: all members (alternative)	1 − x̄/L	x̄ = eccentricity; L = connection length

Limit State 3 — Block Shear Rupture (§J4.3)

A_nv = net shear area; A_nt = net tension area; A_gv = gross shear area. U_bs = 1.0 (uniform tension stress) or 0.5 (non-uniform).

φ = 0.75 / Ω = 2.00.

5.2 Slenderness Limit

AISC 360-22 §D1: For tension members (not rods/cables), L/r ≤ 300 preferred (recommendation, not mandatory for tension). For structural integrity, L/r ≤ 240 typical practice for primary members.

5.3 Net Area Calculation

For bolt holes (punched): deduct hole diameter d_h = bolt diameter + ⅛ in (3.2 mm) per AISC §B4.3. For staggered holes, use the s²/4g rule for the critical net section path.

→ Steel Beam Calculator

6.1 Column Curve — Flexural Buckling

The nominal compressive strength is governed by: P_n = F_cr · A_g   (φ_c = 0.90 / Ω_c = 1.67)

Define: λ_c = (KL/r)·√(F_y/(π²E)) = KL/r · √(F_y/E) / π

Inelastic buckling (KL/r ≤ 4.71√(E/F_y), i.e., λ_c ≤ 1.5) — §E3a

Elastic buckling (KL/r > 4.71√(E/F_y)) — §E3b

F_e = π²·E / (KL/r)² — Euler elastic buckling stress.

Slenderness limit: KL/r ≤ 200 (recommended by AISC §E2). For F_y = 50 ksi: threshold KL/r = 113.

6.2 Effective Length Factor K — Table C-A-7.1

Condition	K (ideal)	K (recommended design)
Pin-pin (both ends)	1.0	1.0
Fixed-fixed (no sway)	0.5	0.65
Fixed-pin (no sway)	0.7	0.80
Fixed-free (cantilever)	2.0	2.10
Fixed-fixed (sway permitted)	1.0	1.20
Fixed-pin (sway permitted)	2.0	2.00

For braced frames: K ≤ 1.0. For unbraced (sway) frames: K ≥ 1.0. Use alignment charts (Appendix 7) for continuous frames or the Direct Analysis Method (Appendix 1).

6.3 Local Buckling Reduction (§E7)

For sections with slender elements (λ > λ_r): P_n is reduced using Q factor. Q = Q_s·Q_a, where Q_s accounts for slender unstiffened elements (flanges, legs) and Q_a for slender stiffened elements (web, HSS). For non-slender sections: Q = 1.0.

6.4 Torsional and Flexural-Torsional Buckling (§E4)

Doubly symmetric open sections (W-shapes): flexural-torsional buckling occurs when KL_z > KL_y is not the case — instead, check torsional buckling. For singly symmetric (Tees, channels, angles) or asymmetric shapes, always check flexural-torsional buckling in addition to flexural buckling about both axes.

→ Steel Section Properties

Design flexural strength: M_n governed by the most critical limit state (LTB, FLB, WLB). φ_b = 0.90 / Ω_b = 1.67.

7.1 Doubly Symmetric Compact I-Shapes — §F2 (most common case)

M_p = F_y·Z_x (plastic moment capacity)

Yielding (L_b ≤ L_p)

Inelastic LTB (L_p < L_b ≤ L_r) — §F2-2

Elastic LTB (L_b > L_r) — §F2-3

7.2 Limiting Unbraced Lengths

r_ts² = √(I_y·C_w) / S_x; h_o = distance between flange centroids; c = 1.0 for doubly symmetric I-shapes; J = torsional constant.

7.3 C_b Factor — Moment Gradient Modifier

M_max = maximum moment in unbraced segment; M_A, M_B, M_C = moments at quarter, mid, and three-quarter points. C_b = 1.0 for uniform moment (most conservative). C_b > 1.0 gives credit for moment gradient (M_n capped at M_p).

Loading pattern (simply supported)	Cb (approx.)
Uniform moment (equal end moments, reverse curvature)	1.00
Uniform distributed load	1.14
Midspan point load	1.32
Equal end moments (same sign / single curvature)	1.00
Cantilever (free end unbraced)	1.00 (conservative)

7.4 Compact Section Web — Noncompact and Slender (§F3, F4, F5)

§F3: Doubly symmetric I-shapes with compact web but noncompact/slender flanges — M_n reduced for FLB.

§F4–F5: Non-compact or slender web I-shapes (plate girders) — separate compression flange yielding and LTB calculations; tension flange yielding; shear lag in wide flanges.

7.5 Other Cross-Section Types (Summary)

Section	AISC 360 §	Key limit states
Channels (C, MC)	§F6	LTB (Lb–based), FLB
Tees and double angles	§F9	LTB, FLB, local buckling of stem in compression
HSS rectangular	§F7	Yielding, FLB (flanges), WLB (webs); no LTB if loaded about strong axis and closed section
HSS round	§F8	Yielding, local buckling (D/t limits)
Single angles	§F10	LTB (geometric), local buckling (leg)

→ Steel Beam Design Calculator (AISC 360)

8.1 Unstiffened Webs — §G2.1

A_w = d·t_w (overall depth × web thickness).

For most rolled W-shapes with h/t_w ≤ 2.24√(E/F_y) (= 53.9 for A992): C_v1 = 1.0 and φ_v = 1.00 / Ω_v = 1.50. All AISC W-shapes in Gr. 50 qualify for this simplified provision.

For h/t_w > 2.24√(E/F_y): φ_v = 0.90, and C_v1 is computed from web slenderness.

8.2 Stiffened Webs with Tension-Field Action — §G3

a = clear distance between stiffeners. C_v2 based on h/t_w and a/h ratio.

Tension field action is not permitted for: end panels, panels with large openings, or when 2·A_w/(A_fc + A_ft) > 2.5.

8.3 Transverse Stiffener Design — §G2.2 / G3.3

Required when h/t_w > 2.46√(E/F_y). Stiffener moment of inertia: I_st ≥ I_st1 (min for shear) and I_st2 (for tension-field action). Area requirement for intermediate stiffeners when tension field is used.

8.4 Shear in HSS and Box Sections

§G4: V_n = 0.6·F_y·A_w·C_v2. A_w = 2·h·t for rectangular HSS (two webs). φ_v = 0.90. Use b/t limit for slenderness check.

9.1 Doubly and Singly Symmetric Members — §H1-1

For members subject to combined axial force and biaxial bending:

When P_r / P_c ≥ 0.2 (high axial):

When P_r / P_c < 0.2 (low axial):

P_r = required axial strength (LRFD: P_u; ASD: P_a). P_c = available axial strength (LRFD: φ_c·P_n; ASD: P_n/Ω_c).

M_rx, M_ry = required moment about x and y axes. M_cx, M_cy = available moment strength about each axis.

9.2 Unsymmetric or General Cross-Sections — §H2

f_ra = required axial stress; F_ca = available axial stress. Bending stresses computed at critical point including combined biaxial bending.

9.3 Combined Shear and Torsion — §H3

For HSS members subject to shear and torsion combined:

T_c = φ·F_cr·C based on torsional buckling stress F_cr and section torsional constant C.

9.4 Second-Order Effects

AISC 360-22 Appendix 8 / Chapter C — Direct Analysis Method (DAM) is the primary method. Alternatively, the Effective Length Method (ELM) per Appendix 7 or the First-Order Method per Appendix 8 may be used.

DAM: apply notional loads N_i = 0.002·Y_i at each floor; use reduced stiffness E* = 0.8τ_bE, EI* = 0.8τ_bEI (τ_b = 1.0 when α·P_r/P_y ≤ 0.5; otherwise reduced). K = 1.0 may then be used for compression member design.

10.1 Bolt Types and Strengths

Bolt Type	Fnt (ksi/MPa)	Fnv (ksi/MPa)	Use
ASTM A307 (Grade A)	45 / 310	27 / 186	Non-structural, light connections only
ASTM F3125 Gr. A325 / F1852	90 / 620	54 / 372 (threads excl.)	Standard high-strength; most structural connections
ASTM F3125 Gr. A490 / F2280	113 / 780	68 / 469 (threads excl.)	High-strength; not permitted in tension with A36 material
ASTM F3125 Gr. F3043 (A325 equiv.)	90 / 620	54 / 372	Metric equivalent

When threads are included in shear plane: F_nv = 0.80× tabulated values. AISC 360-22 Table J3.2.

10.2 Bolt Bearing Connections — §J3.6 / J3.7 / J3.8

Bolt Shear

Bearing on Connected Material — §J3.10

φ = 0.75 / Ω = 2.00 for both. Applies per bolt. l_c = clear distance from edge of bolt hole to next hole edge (or member edge).

10.3 Slip-Critical Connections — §J3.8

μ = 0.35 (Class A — unpainted clean mill scale, hot-dip galvanized) / 0.50 (Class B — blast-cleaned, untreated / zinc-rich paint) / 0.70 (Class C — blast-cleaned + special coating).

D_u = 1.13 (ratio of mean pretension to minimum). h_sc = hole factor (1.0 standard, 0.85 oversized/short slot, 0.70 long slot). T_b = minimum pretension from AISC Table J3.1 (e.g., ¾" A325: 28 kips; ¾" A490: 35 kips). n_s = number of slip planes.

φ = 1.00 (serviceability) or 0.85 (strength limit state) / Ω = 1.50 or 1.76.

10.4 Bolt Spacing and Edge Distance — §J3.3 / J3.4 / J3.5

Requirement	Minimum	Preferred / Maximum
Bolt spacing (c-to-c)	2⅔db (absolute min)	3db preferred
Edge distance (center of hole to edge)	Table J3.4 (varies by db & hole type)	≥ 1.5db for db ≤ ¾ in
Maximum spacing (environmental)	—	12t or 6 in, whichever less (painted/exposed)

10.5 Weld Design — §J2

Fillet Welds

φ = 0.75 / Ω = 2.00. w = weld size (leg); A_we = effective throat × length = 0.707·w·L. F_EXX = electrode strength (E70xx: 70 ksi / 482 MPa; E80xx: 80 ksi). θ = angle of loading to weld axis (0° = longitudinal, 90° = transverse — 50% stronger).

Connected part thickness t	Minimum fillet weld size	Maximum fillet weld size
t ≤ ¼ in (6 mm)	⅛ in (3 mm)	t (for t < ¼ in)
¼ < t ≤ ½ in (6–12 mm)	3/16 in (5 mm)	t − 1/16 in
½ < t ≤ ¾ in (12–19 mm)	¼ in (6 mm)	t − 1/16 in
t > ¾ in (>19 mm)	5/16 in (8 mm)	t − 1/16 in

Complete Joint Penetration (CJP) Welds — §J2.1a

φ·R_n = φ·F_BM·A_BM — base metal governs; weld itself not the limit state. Pre-qualified joints per AWS D1.1 / AISC.

Partial Joint Penetration (PJP) Welds — §J2.1b

Effective throat = minimum of groove depth or deposited weld; R_n = 0.60·F_EXX·A_we (same as fillet weld). Not permitted for primary tensile members in seismic SMF/IMF connections — CJP required there.

10.6 Base Plate Design (Anchor Rods)

AISC Design Guide 1 (2nd Ed.) — bearing pressure f_p = P_u/(B·N) ≤ φ·f_p,max. Overhang dimensions N and B from required bearing area; plate thickness from cantilever bending at critical sections. ASTM F1554 Gr. 36, 55, or 105 anchor rods.

11.1 System Types and R Factors — ASCE 7-22 Table 12.2-1

System	R	Ωo	Cd	Min SDC permitted	Height limit (SDC D/E)
Moment Frame Systems
Special Moment Frame (SMF)	8	3	5.5	All (A–F)	NL
Intermediate Moment Frame (IMF)	4.5	3	4	B–C (D/E/F with limits)	35 ft (SDC D/E/F)
Ordinary Moment Frame (OMF)	3.5	3	3	A–C only	NP (SDC D/E/F)
Concentrically Braced Frame Systems
Special Concentrically Braced Frame (SCBF)	6	2	5	All (A–F)	NL
Ordinary Concentrically Braced Frame (OCBF)	3.25	2	3.25	A–C (D/E with limits)	35 ft (SDC D/E)
Eccentrically Braced Frame & Special Systems
Eccentrically Braced Frame (EBF)	8	2	4	All (A–F)	NL
Buckling-Restrained Braced Frame (BRBF)	8	2.5	5	All (A–F)	NL
Special Plate Shear Wall (SPSW)	7	2	6	All (A–F)	NL
Dual Systems (Frame + Braced Frame or Wall)
Dual — SMF + SCBF	7	2.5	5.5	All	NL
Dual — SMF + EBF	8	2.5	4	All	NL
Dual — SMF + BRBF	8	2.5	5	All	NL

NL = Not Limited; NP = Not Permitted. Ω_o = overstrength factor; C_d = deflection amplification factor. Verify current ASCE 7-22 Table 12.2-1 for complete height limits by SDC.

11.2 Special Moment Frame (SMF) — AISC 341-22 §E3

• Beam-column connections must be prequalified (AISC 358-22) or qualify by test — §E3.6a
• Protected zone (plastic hinge region): no welded attachments, no holes in protected zone — §E3.5c
• Highly ductile compactness for beams: λ_hd required — §D1.1
• Strong column–weak beam: ΣM^*_pc / ΣM^*_pb > 1.0 — §E3.4a (using expected material strengths)
• Panel zone shear: check separately per §E3.6e; doubler plates as needed
• Continuity plates required per §E3.6f when column flange does not satisfy local force transfer conditions
• Common connections: RBS (dog-bone), BU-E-EP, WUF-W — all prequalified per AISC 358

11.3 Special Concentrically Braced Frame (SCBF) — AISC 341-22 §F2

• Braces: moderately ductile λ_md required; KL/r ≤ 200 — §F2.5b
• V- and inverted-V (chevron) braces: beam must resist unbalanced force assuming one brace buckles at φ_c·P_n, other brace reaches R_y·F_y·A_g in tension — §F2.4b
• Gusset plate: clearance ≥ 2t_gusset for hinge zone; no folded plate connections — §F2.5c
• Columns and beams: designed for amplified seismic load (capacity design) using R_y·F_y·A_g of brace in tension + P_cr of brace in compression — §F2.3

11.4 Eccentrically Braced Frame (EBF) — AISC 341-22 §F3

• Energy dissipation in link beam (between brace attachment points)
• Shear link: e ≤ 1.6·M_p/V_p — governed by shear yielding (most ductile)
• Moment link: e ≥ 2.6·M_p/V_p — governed by flexural yielding
• Link rotation angle: γ_p ≤ 0.08 rad (shear link) or 0.02 rad (moment link) — §F3.4b
• Link stiffeners required at both ends and at intermediate points — §F3.5b
• Lateral bracing at both ends of link — §F3.4d
• Members outside link: capacity designed for 1.25·R_y·V_link forces — §F3.3

11.5 Buckling-Restrained Braced Frame (BRBF) — AISC 341-22 §F4

• BRB elements must be qualified by testing per §K3 or prequalified
• Adjusted brace strength for capacity design: ω·β·R_y·F_y·A_sc (compression) and ω·R_y·F_y·A_sc (tension), where ω = strain hardening factor, β = compression overstrength factor (typically ω ≈ 1.5, β ≈ 1.1)
• Beams and columns: highly ductile λ_hd compactness required — §D1.1

11.6 Capacity Design Principle

In all seismic systems, capacity design ensures the intended yield mechanism forms before non-ductile failure modes (fracture, connection failure). Forces for capacity-protected elements use expected (probable) strengths — R_y·F_y (yield) and R_t·F_u (ultimate) — rather than nominal values.

12.1 Deflection Limits

AISC 360-22 §L3 — deflection limits are not prescribed in the specification; they are left to engineering judgment and project requirements. The following are widely used industry benchmarks:

Condition	Typical limit	Notes
Floor beams — live load only	L/360	Prevents cracking of brittle finishes
Floor beams — total load (L+D post-SDL)	L/240	General serviceability; adjust for camber
Roof beams — live/snow/wind	L/240	Ponding concern for flat roofs (< ¼:12 slope)
Roof beams — total load	L/180	—
Cantilever beams — live load	L/180	L measured as full cantilever length
Spandrel beams (supporting masonry/glass)	L/600 to L/1000	Project-specific; check façade consultant
Interstory drift (wind)	H/400 to H/600	H = story height; varies by cladding type
Interstory drift (seismic) — ASCE 7-22 §12.12	0.010H to 0.025H	Risk Category dependent — see ASCE 7 Table 12.12-1

12.2 Camber

Beams are typically cambered for 75–80% of dead load deflection to offset long-term deflection. Minimum practical camber: L/48" (weld distortion makes less than ~¾ in uneconomical). No camber for spans < 25 ft (7.6 m) typically.

12.3 Floor Vibration — AISC Design Guide 11

Walking-induced vibration governed by frequency and damping:

Occupancy	ap/g limit	Minimum natural frequency fn
Office / residential	0.5%	Typically > 4 Hz for bay length < 40 ft
Open-plan office, large rooms	0.5%	Consider panel modes; fn > 8 Hz preferred
Shopping malls	1.5%	—
Rhythmic activities (aerobics, dance)	1.5–2.5%	fn must not coincide with forcing frequency harmonics
Sensitive labs / operating rooms	0.005–0.1%	Requires specialist vibration analysis (e.g., GMO VC-A)

f_n ≈ π/2·√(g/Δ_total), where Δ_total = total deflection of composite system under sustained loads. Use composite section properties (n = E_s/E_c) for transformed moment of inertia.

12.4 Ponding — AISC 360-22 Appendix 2

Flat roofs must be checked for ponding instability (rain water accumulation that increases deflection → more water → positive feedback). AISC uses the C_p and C_s coefficients; adequacy condition: C_p + 0.9·C_s ≤ 0.25 (simplified check). Alternatively, provide ¼:12 minimum slope or design for full ponding load via Appendix 2 procedure.

12.5 Thermal Expansion

Steel expansion: α = 6.5×10⁻⁶/°F (11.7×10⁻⁶/°C). For long structures (>200 ft / 60 m), expansion joints are typically provided to control thermal movement. Required joint width = α·L·ΔT, where ΔT = design temperature range.