Iran Nezam Civil Design Exam cheat sheet

Static determinacy of a plane frame: 3m + r = 3j + c, where m = members, r = reactions, j = joints, c = internal releases; equality means determinate.

Virtual work deflection: 1·Δ = Σ∫(M·m/EI)ds + Σ∫(N·n/EA)ds + Σ∫(V·v/GA)ds for combined bending, axial, and shear effects.

Influence line for a simply supported beam reaction at A under unit load at distance x from A: R_A = 1 − x/L; maximum shear at a section occurs with the load just to either side.

Castigliano's second theorem: partial derivative of total strain energy with respect to a force gives displacement at that force, in the force direction.

Moment-distribution stiffness factor for a prismatic member of length L: 4EI/L at the near end, 2EI/L at the far end; carry-over factor = 0.5 for fixed-far-end.

Slope-deflection equation: M_AB = 2EI/L (2θ_A + θ_B − 3Δ/L) + FEM_AB; sign convention must be stated explicitly.

Euler buckling load P_cr = π²EI/(KL)²; effective length factor K = 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2.0 cantilever.

Influence ordinate for bending moment at section C of a simple span L under unit load at x: M_C = x(L − a)/L for x ≤ a, and a(L − x)/L for x > a.

Balanced steel ratio ρ_b = 0.85·β₁·(f'c/f_y)·(0.003/(0.003 + ε_y)); for Grade 60 steel ε_y ≈ 0.00207 and β₁ = 0.85 for f'c ≤ 28 MPa.

Nominal flexural strength: M_n = A_s·f_y·(d − a/2) with a = A_s·f_y/(0.85·f'c·b); tension-controlled section requires ε_t ≥ 0.005.

Minimum flexural reinforcement ratio for beams: A_s,min = max(0.25·√f'c/f_y, 1.4/f_y)·b_w·d.

One-way shear capacity V_c = 0.17·λ·√f'c·b_w·d (SI, MPa) for members without axial load; design strength φV_n must be ≥ V_u.

Development length for a deformed bar in tension: l_d = (f_y·ψ_t·ψ_e·ψ_s/(1.1·λ·√f'c))·d_b, subject to a minimum of 300 mm.

Balanced one-way slab strip design: thickness for deflection control is typically L/20 (simply supported) to L/28 (continuous) with normal-weight concrete and Grade 420 steel.

Tied column axial capacity P_n,max = 0.80·[0.85·f'c·(A_g − A_st) + f_y·A_st]; spiral columns use 0.85 instead of 0.80.

Cracked-section effective moment of inertia: I_e = (M_cr/M_a)³·I_g + [1 − (M_cr/M_a)³]·I_cr, with M_cr = f_r·I_g/y_t.

Nominal tensile strength of a member: P_n = min(F_y·A_g, F_u·A_e); shear lag factor U reduces net area, A_e = U·A_n.

Nominal shear strength of a rolled I-shape: V_n = 0.6·F_y·A_w·C_v, with A_w = d·t_w and C_v = 1.0 for h/t_w ≤ 2.24·√(E/F_y).

Nominal flexural strength of a compact laterally supported beam: M_n = F_y·Z_x (plastic modulus), not the elastic section modulus S_x.

Lateral-torsional buckling parameter L_p = 1.76·r_y·√(E/F_y); full plastic moment is available only for L_b ≤ L_p.

Nominal compressive strength P_n = F_cr·A_g; for inelastic buckling F_cr = (0.658^(F_y/F_e))·F_y where F_e = π²E/(KL/r)².

Effective length for a beam-column: P_u/(φP_n) + (8/9)·(M_u/(φM_n)) ≤ 1.0 when P_u/(φP_n) ≥ 0.2; otherwise use P_u/(2φP_n) + M_u/(φM_n) ≤ 1.0.

Bolt shear strength per shear plane R_n = F_nv·A_b; bearing strength R_n = 2.4·d·t·F_u for standard holes with deformation considered.

Fillet weld design strength R_n = 0.6·F_EXX·(0.707·w)·L, where w is the weld leg size and throat = 0.707w.

Terzaghi bearing capacity for a strip footing: q_ult = c·N_c + q·N_q + 0.5·γ·B·N_γ; circular footings use 1.3·c·N_c and 0.3·γ·B·N_γ terms.

Effective stress principle: σ' = σ − u; for a soil with water table at depth z_w below surface, unit weight transitions from γ_bulk to γ' = γ_sat − γ_w below that depth.

Consolidation settlement S_c = C_c·H/(1 + e_0)·log₁₀[(σ'_0 + Δσ)/σ'_0] for normally consolidated clay.

Coefficient of consolidation from Casagrande's log-time method: c_v = T_50·H_dr²/t_50, with T_50 = 0.197 for 50% primary consolidation.

Rankine active earth pressure coefficient K_a = (1 − sin φ)/(1 + sin φ); passive coefficient K_p = 1/K_a; total thrust = 0.5·γ·H²·K_a.

Standard penetration test N-value corrections: N_60 = N·(60/ER); overburden correction C_N = √(100/σ'_v) with σ'_v in kPa.

Pile ultimate axial capacity Q_ult = Q_p + Q_s = q_p·A_p + Σ f_s·A_s·ΔL; skin friction in clay f_s = α·c_u.

Slope stability factor of safety F = resisting moment/driving moment; for an infinite slope with seepage parallel to the surface, F = (γ' tan φ)/(γ_sat tan β).

Base shear V = C_s·W; seismic response coefficient C_s = S_DS/(R/I_e) and must not be less than 0.044·S_DS·I_e, nor greater than S_D1/(T·(R/I_e)).

Fundamental period approximation for a moment frame T_a = C_t·h_n^x with C_t = 0.0466 and x = 0.9 (SI); for other systems C_t = 0.0488 and x = 0.75.

Equivalent static lateral force at level i: F_i = (w_i·h_i^k / Σ w_j·h_j^k)·V, with k = 1 for T ≤ 0.5 s and k = 2 for T ≥ 2.5 s.

Design spectrum: S_DS = (2/3)·S_MS; S_D1 = (2/3)·S_M1; site coefficients F_a and F_v depend on site class and mapped S_S and S_1.

Story drift limit for most structures: Δ ≤ 0.02·h_sx for Risk Category I/II (with allowable drift expressed as a fraction of story height).

Response modification factor R, overstrength Ω_0, and deflection amplification C_d are tabulated per seismic force-resisting system; R governs design forces, C_d governs displacements.

Seismic weight W includes full dead load plus applicable portions of other loads; effective seismic weight excludes live load in most cases unless storage exceeds 25% of floor area.

Ductile detailing for special moment frames: strong-column/weak-beam ratio ΣM_nc ≥ (6/5)·ΣM_nb at each joint, and beam longitudinal reinforcement ratio ≤ 0.025.

Abrams' law: f_c = A/B^(w/c), where w/c is water-cement ratio; lower w/c yields higher strength but reduced workability.

Water-cementitious ratio limits: 0.40 for concrete exposed to freezing and thawing or deicing chemicals, 0.50 for normal exterior exposure.

Entrained air content typically 5–8% by volume for 20–25 mm aggregate in freeze-thaw exposure; air voids relieve ice-crystallization pressure.

Slump test measures workability: 25–100 mm for normal structural concrete; a slump of 180 mm or more indicates high-range water reducer or self-consolidating mix.

Concrete compressive strength increases with age; design strength f'c is typically based on 28-day standard-cured cylinders (150 × 300 mm).

Unit weight of normal-weight concrete ≈ 24 kN/m³; modulus of elasticity E_c = 4700·√f'c MPa (normal-weight, λ = 1.0).

Sulfate resistance is achieved with Type V cement; Type I is general purpose, Type II moderate sulfate, Type III high early strength.

Chloride content limits for reinforced concrete: 0.15% by mass of cement for moist environments, 0.30% for dry or protected conditions.

Critical path is the longest path through the activity network; its total float is zero, and any delay on it delays project completion.

Total float TF = LS − ES = LF − EF; free float FF = ES_successor − EF_activity.

Earned value: CV = EV − AC, SV = EV − PV, CPI = EV/AC, SPI = EV/PV; CPI < 1 indicates cost overrun.

Estimate at completion EAC = BAC/CPI (typical variance) or EAC = AC + (BAC − EV) (atypical variance).

PERT expected duration t_e = (a + 4m + b)/6; variance σ² = ((b − a)/6)²; project variance is the sum along the critical path.

Crashed cost slope = (crash cost − normal cost)/(normal duration − crash duration); crash the activity with the lowest slope on the critical path.

Contract types: lump-sum (fixed price) shifts quantity risk to the contractor; unit-price shifts quantity risk to the owner; cost-plus shifts both to the owner.

Retention is typically 5–10% of each progress payment, capped at a stated percentage of contract value; released after substantial completion or the warranty period.

Occupant load factor for offices is 9.3 m² per person (gross); the required egress width is 5 mm per person per exit for level components.

Two exits are required when occupant load exceeds 49 persons in most occupancies; travel distance limits vary by occupancy and sprinkler protection.

Fire resistance ratings for structural members are given in hours (e.g., 1, 2, 3, 4 h) and depend on occupancy, construction type, and sprinkler status.

Risk categories I through IV reflect consequence of failure; essential facilities (hospitals) are Category IV, ordinary buildings Category II.

Importance factor I_e is 1.0 for Risk Category I/II, 1.25 for III, and 1.5 for IV.

Building height and area limits are tabulated by construction type (Type I through Type V) and occupancy group; sprinklers may allow increases.

Accessible route requirements: clear width ≥ 915 mm, maximum running slope 1:20, maximum cross slope 1:48, and level landings at intervals.

Means of egress components: exit access, exit, and exit discharge; each must be continuous and unobstructed to a public way.

Horizontal distance by stadia: D = K·S·cos²α + C·cosα; for a level line with K = 100 and C = 0, D = 100·S.

Differential leveling: ΔElevation = BS − FS; the height of instrument HI = elevation of benchmark + backsight.

Traverse closure: linear error of closure = √(Σdeparture² + Σlatitude²); relative precision = error/perimeter.

Latitude = distance·cos(azimuth), departure = distance·sin(azimuth); closure requires Σlatitude = 0 and Σdeparture = 0 for a closed loop.

Curve elements: tangent T = R·tan(Δ/2), length L = R·Δ_rad, external E = R·(sec(Δ/2) − 1), middle ordinate M = R·(1 − cos(Δ/2)).

Total station coordinates: X = X_0 + D·sin(azimuth), Y = Y_0 + D·cos(azimuth), with azimuth measured clockwise from north.

Vertical curve: elevation at any point y = y_PVC + g₁·x + ((g₂ − g₁)/2L)·x², where x is distance from PVC.

Contour interval selection: smaller intervals (0.5–1 m) for flat terrain and detailed design; larger intervals (2–5 m) for steep terrain and reconnaissance.

Manning's equation for open-channel flow: Q = (1/n)·A·R^(2/3)·S^(1/2), where R = A/P (hydraulic radius) and S is the channel slope.

Hazen-Williams head loss: h_f = 10.67·L·Q^1.852/(C^1.852·d^4.87) in SI units, with C ≈ 130–150 for new pipes.

Darcy-Weisbach: h_f = f·(L/d)·(V²/2g); friction factor f depends on Reynolds number and relative roughness.

Chezy formula: V = C·√(R·S); C relates to Manning's n by C = (1/n)·R^(1/6).

Peak design flow for water distribution: Q_peak = peak factor × Q_average; peak factors of 1.5–3.0 are typical for municipal systems.

Sanitary sewer minimum velocity is 0.6 m/s (self-cleansing); maximum velocity is 3.0 m/s to prevent scour of pipe material.

Storm drainage rational method: Q = C·i·A; C is the runoff coefficient (0.9 for pavement, 0.2 for lawns), i is rainfall intensity, A is area.

Minimum pipe cover for water mains is typically 1.0–1.5 m in cold climates; sanitary sewers require slope ≥ 1/d (d in mm) as a rule of thumb.