PE Civil: Structural cheat sheet

Critical path is the longest path through the network; total float = LS - ES = LF - EF, and critical activities have zero total float.

PERT expected duration te = (O + 4M + P)/6; variance = ((P - O)/6)^2.

Crashing shortens critical activities with the lowest cost per unit time saved; recheck the network after each change because the critical path can shift.

Earned value: CV = EV - AC; SV = EV - PV; CPI = EV/AC; SPI = EV/PV.

Contract document precedence is usually agreement, conditions, drawings, specifications; verify the specific order in the contract.

Addenda modify bid documents before bid opening and must be acknowledged by bidders.

Bid responsiveness concerns meeting material bid requirements; responsibility concerns contractor capability and qualifications.

Float ownership, liquidated damages, and retainage are contract terms that must be defined in project planning.

ACI 347 formwork pressure depends on concrete placement rate, temperature, slump, admixtures, and vibration.

Rankine earth pressure: Ka = tan^2(45 - phi/2), Kp = tan^2(45 + phi/2), and K0 = 1 - sin phi for at-rest conditions.

OSHA excavation rules require spoil and equipment at least 2 ft from the edge; trench access/egress is required within 25 ft for trenches 4 ft or deeper.

Dewatering methods: sumps for shallow water, wellpoints for drawdown of about 15 to 20 ft, and deep wells for larger drawdown.

Concrete free fall should not exceed about 5 ft; use a tremie or drop pipe and vibrate to consolidate.

Crane capacity decreases with increasing radius and boom length; deduct rigging weight and use outriggers on stable mats.

Compaction success depends on lift thickness and moisture near optimum; verify with Proctor and field density tests.

OSHA requires scaffolds to support 4 times the intended load, with guardrails, base plates, and proper access.

Static equilibrium requires sum Fx = 0, sum Fy = 0, and sum M = 0.

Simply supported beam with uniform load w: Vmax = wL/2, Mmax = wL^2/8, and delta_max = 5wL^4/(384EI).

Simply supported beam with point load P at midspan: Mmax = PL/4 and delta_max = PL^3/(48EI).

Cantilever with point load P at free end: Mmax = PL and delta_max = PL^3/(3EI).

Relationship: dM/dx = V and dV/dx = -w; the slope of the moment diagram equals shear.

Euler buckling: Pcr = pi^2 EI/(KL)^2; K = 0.5 fixed-fixed, 1.0 pinned-pinned, and 2.0 fixed-free.

Degree of static indeterminacy: plane frame = 3m + r - 3j; plane truss = m + r - 2j.

Circular shaft torsion: tau = Tc/J and angle of twist theta = TL/(JG).

Normal-weight concrete: Ec = 57,000 sqrt(f'c) psi and modulus of rupture fr = 7.5 sqrt(f'c) psi.

Structural steel E = 29,000 ksi; ASTM A992 has Fy = 50 ksi and Fu = 65 ksi; ASTM A36 has Fy = 36 ksi and Fu = 58 ksi.

Concrete reaches peak stress near strain 0.002 and crushing near 0.003; steel yield strain is approximately Fy/E.

Creep and shrinkage are time-dependent; creep increases with sustained load, lower humidity, and higher stress levels.

Poisson's ratio is approximately 0.30 for steel and 0.20 for concrete.

Wood allowable stress design uses adjustment factors including CD, CM, Ct, CF, and Cb.

Fatigue design uses stress range and detail category; welded details generally have lower fatigue resistance.

Thermal expansion is about 6.5e-6 per degree F for steel and about 5.5e-6 per degree F for concrete.

Bolt shear strength Rn = Fnv Ab; bearing strength includes 2.4 d t Fu for AISC checks, and edge distance must be verified.

Standard hole diameter = bolt diameter + 1/16 in; oversized hole = bolt diameter + 1/8 in; short-slotted hole = bolt diameter + 1/16 in.

Fillet weld effective throat = 0.707 times leg size; weld strength Rn = 0.60 FEXX times throat times length.

Block shear combines shear rupture on one plane with tensile rupture on a perpendicular plane along the failure path.

Slip-critical connections use pretensioned high-strength bolts; design is based on slip resistance at service loads.

Composite beams use shear studs to transfer horizontal shear; effective slab width limits are specified by AISC.

Eccentric connections add moment equal to load times eccentricity to the bolt group or weld group.

Prestressing counteracts tensile stress; pretensioned members are stressed before casting, post-tensioned members after concrete hardening.

LRFD basic gravity combination is 1.2D + 1.6L; ASD uses service loads with allowable stresses.

Wind velocity pressure qz = 0.00256 Kz Kzt Kd V^2 in psf when V is in mph.

Seismic base shear V = Cs W; Cs is limited by Sds/R and other ASCE 7 provisions.

Retaining wall stability commonly requires FS >= 1.5 against sliding and FS >= 2.0 against overturning.

Lateral systems must be checked for drift limits and P-Delta effects.

Diaphragms collect and distribute lateral loads; collectors tie the diaphragm to vertical lateral-force-resisting elements.

Moment frames resist lateral loads primarily through flexure; braced frames resist through axial action.

Foundation design considers bearing capacity, settlement, and overturning stability.