OBC Building Structural cheat sheet

Strength (ultimate) design requires factored resistance ≥ factored load effect: φR ≥ ΣγQ; serviceability checks use unfactored loads against deflection, vibration, and crack limits.

Load combinations follow ASCE 7 §2.3/2.4: 1.2D + 1.6L, 1.2D + 1.6W + L, 0.9D + 1.0W, and 1.2D + 1.0E + L, with 0.2S in snow-governed combos.

Strength reduction factors φ: 0.90 flexure (tension-controlled), 0.75 shear, 0.65 compression (tied columns), 0.90 tension-controlled.

LRFD vs ASD: LRFD uses factored loads and resistance factors; ASD uses service loads with a single safety factor Ω (e.g., Ω = 1.67 for bending).

Reliability index β relates to probability of failure; target β ≈ 3.0–3.5 for typical building members, 4.0+ for more critical elements.

Nominal vs design strength: nominal strength is computed from material properties; design strength is φ×nominal (LRFD) or nominal/Ω (ASD).

Deflection limits (typical, L = span): L/360 for floors under live load, L/240 for roof members, L/180 for cantilever tips.

Importance factor I: 1.0 typical, 1.15/1.25 for higher-occupancy categories; increases wind, seismic, and snow design loads.

Equilibrium, compatibility, and constitutive relations are the three pillars of analysis; indeterminate structures require compatibility (stiffness or flexibility method).

Stiffness method (direct stiffness): assemble K·u = F, solve for displacements, then member forces; basis of all matrix structural analysis software.

Moment distribution: fixed-end moments, distribute to joints by stiffness ratio, carry over ½ to far end, iterate until residual moments are small.

Influence lines give the response at a point as a unit load moves across the structure; used for moving-load positioning.

Approximate methods: portal method (inflection at mid-height) and cantilever method (axial force proportional to distance from centroid) for lateral frames.

Second-order effects (P-Δ) must be considered when the stability index θ = (P·Δ)/(V·h) exceeds 0.10 per ASCE 7; magnify moments or use amplified sway.

Plastic analysis: collapse occurs when enough plastic hinges form to create a mechanism; plastic moment Mp = Fy·Z, shape factor Z/S ≈ 1.1–1.5.

Tributary area and influence area: KLL·AT determines live-load reduction; AT is the influence area, not just the member's own tributary.

Dead load: self-weight plus fixed superimposed loads per ASCE 7 Table C3.1; typical concrete 150 lb/ft³, steel 490 lb/ft³, wood ~35 lb/ft³.

Uniform live loads (ASCE 7 Table 4.1): office 50 psf, residential 40 psf, corridors 100 psf, storage 125+ psf, roofs (ordinary) 20 psf.

Live load reduction: L = L0(0.25 + 15/√(KLL·AT)) with KLL = 4 for interior columns, 2 for beams; not permitted for live > 100 psf or for one-way slabs in some cases.

Concentrated live loads (e.g., 2000 lb on 2.5 ft² for office floors) must be checked separately even when uniform load governs.

Ground snow load pg from ASCE 7 Fig. 7.2; flat roof snow pf = 0.7·Ce·Ct·I·pg, with minimum pf = 20·I when pg > 20 psf.

Sloped roof snow ps = Cs·pf; Cs decreases with slope (e.g., ~1.0 for 0–5°, ~0.7–0.5 for 30–45° depending on surface).

Unbalanced snow: leeward drift load on gable roofs, plus rain-on-snow surcharge of 5 psf for roofs with pg ≤ 20 psf and slope < 1/2 in/ft.

Snow drift on lower roofs: drift height hd = 0.43·lu^(1/3)·(pg + 10)^(1/4) − 1.5, capped by space available; drift width w = 4·hd.

ASCE 7 wind: V (basic wind speed) at 3-second gust, 33 ft exposure; qz = 0.00256·Kz·Kzt·Kd·V² (psf, V in mph) with Kd = 0.85 for buildings.

Velocity pressure exposure coefficient Kz increases with height and depends on exposure category B (urban/suburban), C (open), D (flat/unobstructed).

Design wind pressure p = q·G·Cp − qh·(GCpi) for enclosed buildings; internal pressure coefficient GCpi = ±0.18 enclosed, ±0.55 partially enclosed.

Seismic base shear V = Cs·W; Cs = SDS/(R/Ie) for short-period buildings, with upper limit Cs ≤ SD1/(T·(R/Ie)) when T ≤ TL.

ASCE 7 seismic: SDS and SD1 from site class and mapped Ss, S1; site coefficients Fa and Fv amplify for soft soils (Site E/F amplify long-period motion most).

Response modification factor R: ordinary moment frames ~3.5, intermediate ~4.5, special steel moment frames 8, special concrete shear walls 6, base isolation ~2.

Seismic detailing requirements (AISC 341, ACI 318 Ch. 18) apply when SDC C or higher; SDC D–F requires special systems with capacity design.

Equivalent lateral force applies only when T ≤ 3.5·Ts and structure is regular; otherwise modal response spectrum analysis is required.

Bearing capacity: Terzaghi/Meyerhof qult = c·Nc + q·Nq + 0.5·γ·B·Nγ; allowable qa = qult/FS with FS = 2.5–3.0 for bearing.

Settlement governs design more often than bearing for spread footings on granular soil; allowable settlement typically 1 in total, 0.5 in differential.

Consolidation settlement: Sc = Cc·H/(1+e0)·log10((σ'0+Δσ)/σ'0); overconsolidated clays use Cr instead of Cc below preconsolidation pressure.

Lateral earth pressure: at-rest K0 = 1 − sin φ; active Ka = tan²(45° − φ/2); passive Kp = tan²(45° + φ/2).

Pile capacity: Qu = Qp + Qs; driven piles in sand gain capacity from setup; end bearing in rock limited by socket roughness and unconfined strength.

Group efficiency: pile group capacity may be less than sum of single piles due to overlapping stress zones; check block failure and settlement.

Liquefaction potential: loose saturated sands below water table with N60 < 15 and seismic demand; mitigate with densification, drains, or deep foundations.

Slope stability: factor of safety = resisting/shearing; FS ≥ 1.5 for static, ≥ 1.1 for seismic; Bishop simplified method for circular slip surfaces.

ACI 318 strength: Mu ≤ φMn with φ = 0.90 (tension-controlled); φ decreases to 0.65 as strain at tension steel drops below εty.

Flexural design: Mn = As·fy·(d − a/2), a = As·fy/(0.85·f'c·b); reinforcement ratio ρ = As/(b·d).

Minimum flexural steel: As,min = max(3√f'c/fy, 200/fy)·b·d (psi units); temperature/shrinkage steel ratio 0.0018 for Grade 60.

Shear: Vc = 2√f'c·b·d (psi); Vs = Av·fy·d/s; φ(Vc + Vs) ≥ Vu; minimum shear reinforcement required when Vu > 0.5φVc.

Development length ld = (fy·ψt·ψe·ψs)/(25·√f'c)·db for deformed bars (simplified); hooks reduce ld by roughly 0.7.

Concrete cover (cast-in-place, not exposed to weather): 1.5 in beams/columns, 0.75 in slabs; increases for exposed or earth-contact surfaces.

Column ties: spacing ≤ 16db, 48dt, and least column dimension; spiral reinforcement ratio ρs ≥ 0.45(Ag/Ac − 1)·f'c/fy.

Concrete placement and curing: consolidation by internal vibration, curing 7 days (moist) for Type I cement, 3 days for Type III; test cylinders 6×12 in.

TMS 402/602 governs; masonry compressive strength f'm from prism tests or unit strength method (Table in TMS 602).

Allowable stress design: Fa = 0.25·f'm for axial compression on unreinforced masonry, with slenderness reduction for h/r > 99.

Flexural tension in unreinforced masonry is very low; design relies on compression or reinforced masonry with steel in grouted cells.

Reinforcement: Grade 60 bars in grouted cells; development length depends on bar size and whether bar is in tension or compression; lap splices typically 40db.

Masonry modulus Em = 900·f'm (TMS 402); modulus of rigidity Gm = 0.4·Em.

Mortar types: Type M (highest strength, 2500 psi), S (1800 psi), N (750 psi), O (350 psi); Type S most common for structural walls.

Grout: coarse grout for cells ≥ 2 in wide; fine grout for smaller cells; grout compressive strength ≥ f'm, typically 2000+ psi.

Masonry shear walls: nominal shear strength depends on masonry tensile strength and axial stress; boundary elements required in special reinforced walls.

NDS reference design values are adjusted by factors: CD (load duration), CM (wet service), Ct (temperature), CL (beam stability), CF (size), Cfu (flat use), Ci (incising), Cr (repetitive).

Allowable bending stress Fb' = Fb·CD·CM·Ct·CL·CF·Cfu·Ci·Cr; CD = 1.0 for normal (10-yr) load, 1.15 for snow, 1.6 for wind/seismic.

Beam stability factor CL depends on slenderness and lateral bracing; for d/b > 2 and unbraced length, CL < 1.0 reduces Fb.

Column stability: Cp from NDS equations using FcE = 0.822·E'min/(le/d)²; effective length factor Ke = 1.0 pinned-pinned, 2.1 fixed-free.

Glulam and LVL have higher design values than sawn lumber; glulam layup combinations (e.g., 24F-V4) define Fb and E.

Wood connections: lateral capacity per NDS yield limit equations (Z); group action factor Cg and geometry factor CΔ reduce capacity for multiple fasteners.

Diaphragm and shear wall design: ASD allowable shear from Table 4.3A (e.g., 15/32 in sheathing, 8d at 6/12 = ~255 plf with wood structural panels).

Moisture: green lumber shrinks ~1% per 4% MC change; design MC ≤ 19% for most framing; wet-service factors CM < 1 reduce strength.

AISC 360 LRFD: φMn = φ·Fy·Zx for compact sections (φ = 0.90); lateral-torsional buckling reduces Mn for unbraced lengths.

Plate girder and beam LTB: Mn between Mp and Mr based on Lp, Lr; for Lb > Lr, Mn = Fcr·Sx with Fcr from elastic LTB.

Column strength: Pn = Fcr·Ag; Fcr = 0.658^(Fy/Fe)·Fy when Fy/Fe ≤ 2.25, else Fcr = 0.877·Fe; Fe = π²E/(KL/r)².

Compact vs noncompact sections: λ = b/t compared to λp and λr; compact sections can reach Mp, noncompact reach yield but local buckling limits rotation.

Bolted connections: nominal shear strength per AISC Table J3.2 (e.g., A325N in single shear with threads excluded = 54 ksi × Ab); bearing and tear-out also checked.

Welds: E70 electrodes give FEXX = 70 ksi; fillet weld strength Rn = 0.6·FEXX·(0.707·w)·L, with φ = 0.75.

Block shear: Rn = 0.6Fu·Anv + Ubs·Fu·Ant ≤ 0.6Fy·Agv + Ubs·Fu·Ant, with Ubs = 1.0 uniform tension or 0.5 nonuniform.

Aluminum and cold-formed steel: AISI S100 uses effective width method; cold-formed members buckle locally at low stress, so effective section properties govern.

Connection types: simple shear (pinned, no moment transfer), moment (rigid), and semi-rigid; design intent must match analysis assumptions.

AISC 360 Chapter J: bolts in tension/combined shear-tension use interaction; slip-critical connections required for fatigue or oversized holes.

Weld symbols: fillet (triangle), groove (V, U, J, bevel), with size, length, and all-around indicators on the reference line.

Fire resistance: IBC Table 601/602 assigns hourly ratings (e.g., Type I-A = 3 hr structural frame, Type V-B = 0 hr); achieved by SFRM, intumescent, concrete encasement, or wood char.

Wood char rate ≈ 1.5 in/hr (NDS); heavy timber members sized with an allowance for char to achieve 1-hr rating.

Concrete cover for fire: ACI 318 Table 20.5.1.3 minimum cover increases with fire rating (e.g., 1.5 in for 2-hr beams, 2 in for 3-hr).

Steel fire protection: W/D ratio drives SFRM thickness; heavier sections need less protection because they heat more slowly.

Connection eccentricity and prying action must be checked for bolted tee and angle connections; prying increases bolt tension beyond nominal.