PE Architectural cheat sheet

Bending stress fb = M/S; required section modulus S = M/Fb. For a rectangular section S = bd²/6, so capacity rises with the square of depth.

Simply supported beam under uniform load: Δmax = 5wL⁴/(384EI) at midspan - deflection varies with the fourth power of span.

Cantilever under uniform load: Δmax = wL⁴/(8EI) at the free end, about 4.8 times the deflection of an equal simple span under the same load.

Tributary area of an interior column equals the product of the two adjacent bay spacings; axial load = tributary area × unit floor load × number of floors carried.

ASCE 7 live load reduction: L = L0(0.25 + 15/√(KLL·AT)); KLL = 4 for interior columns and 2 for beams, with a 50% floor for members supporting one floor.

LRFD gravity combination 1.2D + 1.6L versus ASD D + L; allowable-stress capacities must never be compared with factored demands.

Elastic moduli: steel 29,000 ksi, concrete Ec ≈ 57,000√f'c psi, sawn wood ≈ 1.6 × 10⁶ psi; steel stiffness is roughly ten times that of concrete.

Seismic base shear V = Cs·W; wind pressure p = 0.00256·V² times pressure coefficients, about 20 psf at 90 mph before adjustment factors.

Footing area A = P/q_allow; allowable bearing is typically 2,000–4,000 psf for granular soils and 1,000–2,000 psf for soft clays.

Sensible heat: Qs (Btu/h) = 1.08 × CFM × ΔT(°F) for standard air at sea level.

Latent heat: QL = 0.68 × CFM × Δgr (grains/lb); total heat: Qt = 4.5 × CFM × Δh (Btu/lb).

1 ton of refrigeration = 12,000 Btu/h = 200 Btu/min; a rough office cooling check is 25–35 Btu/h per square foot.

Internal gains dominate commercial loads: a seated adult releases roughly 250 Btu/h sensible plus 200 Btu/h latent under design conditions.

Duct design: 1,000–1,500 fpm in supply mains, 600–900 fpm in branches, friction rate about 0.1 in. w.g. per 100 ft of equivalent length.

Static water pressure rises 0.433 psi per foot of height; a fixture 40 ft below the main sees about 17 psi more than at the main.

Building drain slope: 1/4 in./ft for pipe 3 in. and smaller, 1/8 in./ft for 4 in. and larger; every fixture trap requires a vent.

Fan laws: airflow varies linearly with speed, static pressure with speed squared, and brake horsepower with speed cubed.

ASHRAE 62.1 ventilation = people outdoor-air rate × occupants plus area outdoor-air rate × floor area; CO₂ demand control modulates to occupancy.

Ohm's law V = I·R; power P = V·I for direct current and unity-power-factor loads.

Single-phase P = V·I·PF; three-phase P = √3·V·I·PF, so a balanced three-phase circuit carries about 1.73 times the single-phase power at the same amperage.

Single-phase voltage drop: VD = 2·K·I·L/CM, with K = 12.9 for copper and 21.2 for aluminum; L in feet, CM in circular mils.

Voltage drop targets: 3% maximum on a branch circuit and 5% total from service to the farthest outlet.

Continuous loads are calculated at 125% of ampere rating when sizing overcurrent devices and conductors; a 20A breaker therefore serves 16A continuous.

NEC 110.26 working space in front of panels: 30 in. wide, 36 in. deep (48 in. above 600V), 6 ft 6 in. high, never used for storage.

Conduit fill limits: 53% for one conductor, 31% for two, 40% for three or more of the interior cross-sectional area.

Illuminance in footcandles = lumens ÷ area in square feet; efficacy in lumens per watt and lighting power density in W/ft² drive code compliance.

GFCI protection applies to bathrooms, kitchens, garages, outdoors, and receptacles within 6 ft of a sink; AFCI protects dwelling branch circuits.

Egress capacity (IBC Table 1005.3.2): 0.3 in. per occupant for stairways and 0.2 in. for other components; sprinklered buildings reduce these to 0.2 in. and 0.15 in.

Occupant load factors: business 150 gross, mercantile 60 gross, classrooms 20 net, unconcentrated assembly 15 net, concentrated assembly 7 net.

Two means of egress are required at an occupant load of 50 or more, or wherever the common path or travel distance limits are exceeded.

Travel distance limits for business occupancies are typically 200 ft unsprinklered and 250 ft sprinklered, measured along the path of egress travel.

Stairs: maximum riser 7 in., minimum tread 11 in.; riser plus tread should total about 17–18 in. for a safe, comfortable gait.

Handrails are required on both sides of stairs with four or more risers, mounted 34–38 in. above the tread nosing.

Doors in a means of egress provide 32 in. minimum clear width and swing in the direction of travel when serving 50 or more occupants.

Accessibility: 36 in. clear route, 60 in. turning space, ramp slope maximum 1:12 with a landing every 30 in. of rise, grab bars at 33–36 in.

Minimum ceiling height is 7 ft 6 in. in habitable rooms and corridors, with 6 ft 8 in. permitted at doors and in bathrooms.

Concrete compressive strength f'c is measured on cylinders at 28 days; Ec = 57,000√f'c psi, and normal exposure uses a water-cement ratio of 0.40–0.50.

Steel: ASTM A36 has Fy = 36 ksi, A992 has Fy = 50 ksi; E = 29,000 ksi and elongation at fracture is roughly 20%.

Coefficients of thermal expansion: steel 6.5 × 10⁻⁶/°F, concrete 5.5 × 10⁻⁶/°F, aluminum 13 × 10⁻⁶/°F - mismatched materials need joints or slip connections.

Gypsum fire ratings: 5/8 in. Type X on steel studs yields about 1 hour; two layers or added insulation raises the rating toward 2 hours.

Wood framing should be dried to 19% moisture content or less before enclosure; shrinkage is greatest in the tangential direction, about 1% of width per 4% moisture change.

Concrete masonry unit nominal size is 8 × 8 × 16 in. with 3/8 in. mortar joints; mortar Types M, S, N, O descend in compressive strength.

Safety glazing (tempered or laminated) is required in doors, in sidelights within 24 in. of a door edge, and in glazing whose bottom edge is within 18 in. of the floor.

Stiff substrates are required for brittle finishes: tile and terrazzo need deflection limited to L/360, while carpet tolerates greater movement.

Thermal mass in concrete or masonry shifts peak cooling load by roughly 4–6 hours rather than reducing steady-state conduction.

The critical path is the longest path through the activity network; its duration establishes the contract completion date and its activities carry zero float.

Total float = LS − ES = LF − EF; free float = early start of the successor minus early finish of the activity.

Contract types: lump sum suits fully defined scope, guaranteed maximum price shares savings, and cost plus fee suits fast-track work with incomplete documents.

AIA documents: B101 owner-architect agreement, A101 owner-contractor agreement, A201 general conditions defining the architect's authority and standard of care.

Retainage is commonly 5–10% withheld from each progress payment, reduced at substantial completion and released at final completion.

Bid bonds guarantee the bidder will execute the contract; performance bonds guarantee completion; payment bonds guarantee subcontractors and suppliers are paid.

A change order is written, priced, and signed by the owner; a construction change directive authorizes work before the price is agreed.

Progress payments use AIA G702/G703 with a conditional lien waiver, certified by the architect after site observation of the work in place.

Design liability statutes of limitation typically run 6–10 years from substantial completion, varying by jurisdiction.