IESL Part II Civil cheat sheet

Concrete mix design (ACI 211.1): target mean strength f'cr = f'c + 1.34·S or f'c + 2.33·S − 500 psi, whichever is greater, where S is the standard deviation of prior test results.

Slump test (ASTM C143) measures workability/consistency only, not strength; typical slumps are 25–100 mm for normal structural work, and the test is invalid if the sample shears or slumps asymmetrically.

Cylinder compressive strength (ASTM C39): 150×300 mm cylinders, moist-cured, tested at 28 days; a single cylinder result below f'c − 500 psi requires investigation, and the average of three consecutive tests must equal or exceed f'c.

Nominal maximum aggregate size must not exceed 1/5 of the narrowest form dimension, 1/3 of slab depth, or 3/4 of the minimum clear spacing between reinforcing bars.

Water–cement ratio governs strength and durability: lower w/c increases strength and reduces permeability; typical structural w/c is 0.40–0.50, and ACI 318 durability exposure classes set maximum w/c and minimum f'c.

Beam flexural design (ACI 318): φMn ≥ Mu with φ = 0.90 for tension-controlled sections; tension-controlled strain εt ≥ 0.005 at nominal strength, and the balanced ratio ρb = 0.85β1(f'c/fy)(0.003/(0.003+fy/Es)).

Minimum flexural reinforcement As,min = max(0.25√f'c/fy, 1.4/fy)·bw·d for beams, preventing brittle failure on cracking.

Shear design: Vc = 0.17λ√f'c·bw·d (SI, MPa, mm) for non-prestressed members without axial load; φ = 0.75, and stirrups are required wherever Vu exceeds φVc/2.

Development length ld for a deformed bar in tension depends on bar diameter, fy, f'c, cover, and confining transverse reinforcement; hooked and headed bars may use reduced lengths per ACI 318 provisions.

Effective span of a simply supported beam is the clear span plus the lesser of the support depth or the bearing width at each end, not the centre-to-centre distance.

Deflection limits (typical serviceability): L/360 for floors under live load, L/240 for roofs, and L/480 where sensitive finishes or machinery are supported.

Shear force diagram slope equals the distributed load intensity; bending moment is the integral of shear, so the maximum moment occurs where shear is zero.

For a simply supported beam with a central point load P over span L: maximum moment PL/4 and maximum deflection PL³/(48EI).

For a uniformly distributed load w over span L: maximum moment wL²/8 and maximum deflection 5wL⁴/(384EI).

Euler buckling load Pcr = π²EI/(KL)²; effective length factor K is 1.0 pinned–pinned, 0.5 fixed–fixed, 0.7 fixed–pinned, and 2.0 fixed–free (cantilever).

A cantilever with a point load P at the tip has maximum moment PL at the fixed end and tip deflection PL³/(3EI).

Section modulus S = I/c; maximum bending stress σ = M/S. For a rectangle of width b and depth h, S = bh²/6.

Statically indeterminate structures require compatibility of displacements in addition to equilibrium; the degree of indeterminacy equals the number of redundant reactions or internal forces.

Terzaghi bearing capacity for a shallow strip footing: qult = c·Nc + q·Nq + 0.5·γ·B·Nγ, with N factors depending on the friction angle φ.

Allowable bearing pressure = qult/FOS, with a typical factor of safety of 3 for shallow foundations; settlement usually governs the design of footings on sand.

Standard penetration test N-values correlate with relative density and friction angle; corrected N1,60 = N·CN·CE·CB·CR·CS, and N > 50 typically indicates very dense soil or rock.

Atterberg limits: the plasticity index PI = LL − PL; a high PI (>30) indicates highly compressible clay, while low PI indicates silts or sandy soils.

Consolidation settlement Sc = Cc·H/(1+e0)·log10((σ'0+Δσ)/σ'0), where Cc is the compression index and σ'0 is the initial effective vertical stress.

Effective stress σ' = σ − u (total stress minus pore pressure); quick conditions occur when the upward seepage gradient reaches the critical gradient ic = (Gs − 1)/(1 + e).

Rankine active earth pressure coefficient Ka = tan²(45° − φ/2); passive Kp = tan²(45° + φ/2); at-rest K0 ≈ 1 − sin φ for normally consolidated sand.

A soil is classified as well-graded when Cu = D60/D10 ≥ 4 for gravels or ≥ 6 for sands, and 1 < Cc = D30²/(D10·D60) < 3.

Slope stability factor of safety = resisting shear strength / mobilised shear stress; the infinite slope condition for a cohesionless soil gives FOS = tan φ / tan β.

Rational method peak flow Q = C·i·A/360 (SI, with i in mm/h and A in hectares), where C is the runoff coefficient and i is the design rainfall intensity.

Manning equation for open-channel velocity: V = (1/n)·R^(2/3)·S^(1/2); hydraulic radius R = A/P, and typical n values are 0.013 for concrete pipe and 0.025–0.035 for natural channels.

The time of concentration is the travel time from the most hydraulically remote point to the outlet; it sets the minimum design storm duration for the rational method.

Froude number Fr = V/√(gD); Fr < 1 is subcritical, Fr = 1 is critical, and Fr > 1 is supercritical flow; hydraulic jumps occur when flow transitions from supercritical to subcritical.

A culvert flows under inlet control when the headwater is governed by the inlet geometry, and under outlet control when barrel friction and outlet depth govern; the higher headwater governs the design.

HEC-RAS standard-step backwater analysis solves the energy equation between cross-sections, with total head losses comprising friction (Manning) and contraction/expansion losses.

A 100-year return-period event has a 1% annual exceedance probability; the probability of at least one such event in n years is 1 − (1 − 0.01)^n.

Rational method runoff coefficient C ranges from about 0.05–0.35 for forest or open ground and 0.70–0.95 for impervious pavement and roofs.

Storm drainage design typically uses a design storm of 1 in 2 to 1 in 10 years for minor systems and 1 in 25 to 1 in 100 years for major systems, checked for surcharge and overland flow paths.

AASHTO LRFD load combination Strength I: 1.75·(LL + IM) + 1.25·DC + 1.50·DW, where DC is dead load of components and DW is wearing surface; the design truck and lane load are applied together.

The HL-93 design live load is the greater of the design truck alone or the design truck plus 25% of the design lane load (3.6 kN/m), with a dynamic load allowance IM = 33% applied to the truck.

The design truck has axle loads of 35 kN, 145 kN, and 145 kN spaced 4.3 m apart, with the rear axle spacing variable from 4.3 m to 9.0 m to produce the maximum effect.

The design tandem consists of two 110 kN axles spaced 1.2 m apart, and the design lane load is 9.3 kN/m distributed over a 3.0 m design width.

Impact factor for bridge design is IM = 33% of the truck or tandem load, applied at the strength and service limit states but not to the lane load.

Load and resistance factor design requires η·Σγi·Qi ≤ φ·Rn, where η is a load modifier (ductility, redundancy, and importance factors) and φ is the resistance factor.

Bearing capacity of a pile: ultimate capacity Qu = Qp + Qs, with end bearing Qp = qp·Ap and skin friction Qs = Σfs·As; the allowable load is Qu/FOS, typically 2.5–3.0.

Concrete bridge deck design typically uses AASHTO LRFD empirical or strip methods; the minimum deck thickness is 175 mm (with a 25 mm wearing surface allowance).

Seismic design category depends on the mapped spectral acceleration and the structure's occupancy/importance category; higher categories impose stricter detailing and analysis requirements.

Horizontal curve geometry: degree of curve D = 5729.58/R (arc definition, R in feet) or D = 5729.58/R (SI conversion to metres gives D = 1746.38/R); tangent length T = R·tan(Δ/2) and curve length L = R·Δ(radians).

Stopping sight distance SSD = 0.278·V·t + V²/(254·(f ± G)), with t the perception–reaction time (typically 2.5 s), f the friction factor, and G the grade.

Superelevation rate e and side friction f are related by V² = 127·R·(e + f) (SI, V in km/h, R in metres); AASHTO limits e to 0.04–0.10 depending on conditions.

Vertical curve length for crest: L = A·S²/(2158) when S < L, or L = 2S − 2158/A when S > L, where A is the algebraic grade change in percent and S the sight distance.

The K value of a vertical curve is K = L/A; a larger K produces a flatter, longer curve, and minimum K values are tabulated by design speed and curve type.

Traffic flow relationships: q = k·v (flow = density × speed); the capacity of a freeway lane is about 2,200–2,400 pc/h/ln under ideal conditions, and level of service is defined by density thresholds.

Pavement design: the AASHTO flexible pavement equation relates ESALs, structural number SN, subgrade resilient modulus, and serviceability loss; SN = a1D1 + a2D2m2 + a3D3m3.

Asphalt mix design (Superpave) uses the gyratory compactor to select binder content at 4% air voids; the VMA (voids in mineral aggregate) minimum ensures adequate durability.

Pavement distress: rutting is primarily a function of high temperature and binder stiffness, while fatigue cracking results from repeated load cycles and inadequate structural thickness.

Critical path method: the critical path is the longest path through the network, has zero total float, and determines the project duration.

Total float = LS − ES = LF − EF; free float is the amount of time an activity can be delayed without delaying the early start of any successor.

Earned value: CPI = EV/AC and SPI = EV/PV; CPI < 1 means over budget, SPI < 1 means behind schedule, and EAC = BAC/CPI is a common forecast.

The critical path can change during execution as actual durations differ from planned; float can be consumed by delays on non-critical activities.

Concrete formwork design: lateral pressure depends on placement rate, temperature, and slump; formwork must be designed for the greater of the hydrostatic pressure or the code-specified minimum.

Curing of concrete: moist curing for at least 7 days (3 days for Type I cement in some specifications) at temperatures above 10 °C; cold-weather concreting requires protection against freezing until the concrete reaches 3.5 MPa.

Compaction of soil: the standard Proctor test (ASTM D698) uses 25 blows per layer in 3 layers; the modified Proctor (D1557) uses 56 blows in 5 layers and yields a higher maximum dry density.

The optimum moisture content corresponds to maximum dry density; compaction on the dry side of optimum increases strength but also increases swell potential.

Quality control for concrete: sampling frequency is typically one set of cylinders per 50 m³ or per day of placement, whichever governs, and slump and air content are measured on each sample.

Dead load calculations use material unit weights: normal-weight concrete 24 kN/m³, steel 77 kN/m³, and asphalt 22–23 kN/m³.

Live load values (ASCE 7 / typical codes): 1.9 kPa for residential floors, 2.4 kPa for office floors, 4.8 kPa for corridors and stairs, and 1.0 kPa for roofs (non-reducible).

Live load reduction: L = L0·(0.25 + 4.57/√KLL·AT) (SI, with AT in m²), subject to a lower limit of 0.4L0 for members supporting one floor.

Wind load pressure qz = 0.613·Kz·Kzt·Kd·V² (SI, qz in Pa, V in m/s); the velocity pressure exposure coefficient Kz increases with height and depends on exposure category.

Seismic base shear V = Cs·W, where Cs is the seismic response coefficient and W is the effective seismic weight; Cs need not exceed Sds/(R/Ie).

Snow load: pf = 0.7·Ce·Ct·Is·pg, where pg is the ground snow load, Ce the exposure factor, Ct the thermal factor, and Is the importance factor.

Load combinations (ASCE 7 LRFD): 1.2D + 1.6L + 0.5(Lr or S or R); 1.2D + 1.0W + L + 0.5(Lr or S or R); and 0.9D + 1.0W for uplift checks.

The tributary area of a member is the area of floor or roof that loads it; it is used for live load reduction and for determining member forces.

A structure is unstable if its support reactions are concurrent or parallel; stability requires that the reaction system not intersect at a single point or be all parallel.

Steel tension member design: φPn = φ·Fy·Ag for yielding (φ = 0.90) and φPn = φ·Fu·Ae for fracture (φ = 0.75), where Ae = U·An and U is the shear lag factor.

Slenderness limit for compression members is KL/r ≤ 200 (recommended), and the column curve uses Fe = π²E/(KL/r)² to determine the critical stress Fcr.

Bolted connection strength considers shear, bearing, and tear-out; the nominal shear strength per bolt is Fnv·Ab, and bearing strength is 2.4·d·t·Fu for standard holes.

Weld design: the nominal strength of a fillet weld is 0.60·FEXX·Awe, where Awe is the effective throat area (0.707 × leg size × length).

The plastic section modulus Z is used for compact sections in plastic design; the shape factor is Z/S, which is 1.5 for a rectangle and about 1.1–1.2 for I-sections.

Lateral-torsional buckling of beams depends on the unbraced length Lb; the limiting unbraced length Lp separates compact, fully braced behaviour from inelastic and elastic buckling.

Combined axial and bending: the interaction equation Pr/Pc + (8/9)(Mrx/Mcx + Mry/Mcy) ≤ 1.0 applies when Pr/Pc ≥ 0.2.

Shear strength of a steel beam: Vn = 0.6·Fy·Aw·Cv, with φ = 1.0 for rolled I-sections and Aw = d·tw.

The effective length factor K for a braced frame is 1.0; for a moment frame it is determined from the alignment chart based on the relative stiffness of columns and beams at each joint.

Water demand forecasting: average daily demand is typically 200–400 L per capita per day for domestic use; peak factors of 1.5–3.0 times the average apply to design flows.

Pipe flow energy equation: hf = f·(L/D)·(V²/2g), the Darcy–Weisbach friction loss, with f obtained from the Moody diagram or Colebrook–White equation based on Reynolds number and relative roughness.

Hazen–Williams head loss: hf = 10.67·L·Q^1.852/(C^1.852·D^4.87) in SI units; C is about 130–140 for new ductile iron and 100–120 for older pipes.

Water hammer pressure rise: Δp = ρ·a·ΔV, where a is the pressure wave speed (about 1,000–1,200 m/s in water-filled steel pipe); surge protection uses air valves, surge tanks, or slow-closing valves.

Wastewater design flow: average dry-weather flow plus infiltration/inflow; peak wet-weather flow is typically 3–5 times the average dry-weather flow for separate systems.

BOD removal in activated sludge: the effluent substrate concentration is modelled by S = Ks·(1 + kd·θc)/(θc·(μm − kd) − 1), where θc is the solids retention time.

Secondary clarifier design uses the solids loading rate (kg/m²·h) and the hydraulic overflow rate (m³/m²·d); typical overflow rates are 16–32 m³/m²·d for activated sludge.

Chlorine disinfection: CT value (concentration × contact time) determines pathogen inactivation; typical requirements are a free chlorine residual of 0.2–0.5 mg/L after a 30-minute contact time.

Sludge production in activated sludge: the observed yield Yobs = Y/(1 + kd·θc), and the mass of solids wasted per day equals the solids inventory divided by the SRT.

Concrete mix proportioning: the absolute volume method sums the volumes of cement, water, air, and aggregate to 1 m³; the cement content is determined from the water demand divided by the w/c ratio.

Admixtures: air-entraining agents improve freeze–thaw resistance (4–8% air for severe exposure); superplasticisers increase slump without additional water; retarders extend setting time in hot weather.

Concrete strength gain: the 7-day strength is typically about 65–75% of the 28-day strength; the 90-day strength may be 10–15% higher than the 28-day value.

The modulus of elasticity of normal-weight concrete is approximately Ec = 4700√f'c (MPa), which is used for deflection and column buckling calculations.

Hot-weather concreting: limit concrete temperature at placement to 35 °C, use chilled water or ice, and avoid placement when evaporation rates exceed 1.0 kg/m²·h without precautions.

Cold-weather concreting: protect concrete from freezing until it reaches 3.5 MPa, and maintain a minimum temperature of 10 °C for 3 days (or as specified) for normal mixes.

Self-consolidating concrete: high slump flow (550–800 mm) and passing ability through congested reinforcement; it requires higher paste volume and viscosity-modifying admixtures.

Concrete durability: the cover depth and crack width limits depend on the exposure class; for example, ACI 318 Class F2 (freeze–thaw with de-icing salts) requires a maximum w/c of 0.45 and a minimum f'c of 31 MPa.

The slump test is not suitable for very dry or very wet mixes; for high-slump or self-consolidating concrete, use the slump flow test (ASTM C1611) instead.

Governing equation for one-dimensional steady seepage: Laplace's equation ∂²h/∂x² + ∂²h/∂z² = 0, solved by flow nets, in which flow lines and equipotential lines intersect at right angles.

In a flow net, the quantity of seepage per unit width is q = k·H·(Nf/Nd), where Nf is the number of flow channels and Nd the number of equipotential drops.

Consolidation time factor Tv = cv·t/Hdr²; for 50% consolidation Tv = 0.197, and for 90% consolidation Tv = 0.848, with Hdr the drainage path length (half the layer thickness for double drainage).

The coefficient of consolidation cv is obtained from the log-time or square-root-time method applied to the oedometer test; it controls the rate, not the magnitude, of settlement.

Mohr–Coulomb shear strength: τ = c' + σ'·tan φ'; the effective stress parameters c' and φ' govern long-term drained behaviour, while undrained strength su governs short-term behaviour of saturated clays.

The unconfined compression test gives su = qu/2 for saturated cohesive soils; the vane shear test is used in the field for soft clays.

Relative density of sand: Dr = (emax − e)/(emax − emin); Dr > 70% is dense, 35–70% is medium, and < 35% is loose.

Liquefaction susceptibility increases with loose, saturated, uniformly graded sands and silts; the cyclic stress ratio from the simplified procedure is CSR = 0.65·(σv/σ'v)·(amax/g)·(rd).

Pile group efficiency: the capacity of a group is not the sum of individual pile capacities; group efficiency η = Qgroup/(n·Qsingle) is typically less than 1.0 for closely spaced piles in clay.

Detention basin sizing: the required storage volume equals the difference between the inflow and outflow hydrographs integrated over time; the modified rational method uses the critical storm duration that maximises this difference.

Grassed swale design: Manning's equation with a roughness of 0.03–0.05, a maximum velocity of about 1.5 m/s for erosion resistance, and a side slope no steeper than 3:1.

Permeable pavement: the structural design must account for the reduced strength of the base when saturated; the storage layer is sized to detain the design storm volume.

Green infrastructure: bioretention cells remove pollutants through filtration, infiltration, and plant uptake; the typical design storm is 25 mm of rainfall over the contributing area.

Erosion control: the Universal Soil Loss Equation A = R·K·LS·C·P, where R is rainfall erosivity, K soil erodibility, LS slope length/steepness, C cover management, and P support practice.

Sediment basin design: the settling velocity of a particle is given by Stokes' law vs = g(ρs − ρw)d²/(18μ); the basin surface area is sized as Q/vs.

Storm sewer design: the minimum pipe slope is typically 0.5–1.0%, the minimum velocity for self-cleansing is 0.6–0.75 m/s, and the maximum velocity to avoid erosion is about 3–5 m/s.

Culvert design: the inlet control headwater is computed using the inlet control nomographs (based on inlet area, inlet type, and headwater depth), while outlet control uses the energy equation through the barrel.

Rain garden sizing: the surface area is typically 5–10% of the contributing impervious area, with an engineered soil mix of about 50–60% sand, 20–30% topsoil, and 20–30% organic matter.

Geometric design of highways: the minimum horizontal curve radius is R = V²/(127·(e + f)), with e the superelevation rate and f the side friction factor; at high speeds, f decreases as speed increases.

The transition (spiral) curve length is Ls = 0.0214·V³/(R·C) (SI), where C is the rate of change of centripetal acceleration, typically 0.3–0.6 m/s³.

Sight distance on horizontal curves: the middle ordinate M = R·(1 − cos(28.65·S/R)), and the required clearance from the centreline is M plus the offset to the driver's eye.

Intersection design: the required stopping sight distance is measured from the driver's eye height (1.08 m) to an object height of 0.60 m, and the intersection sight distance depends on the approach speed.

Traffic signal timing: the cycle length for a two-phase signal is C = (1.5·L + 5)/(1 − Y), where L is the total lost time and Y the sum of critical flow ratios (Webster's equation).

Level of service for two-lane highways is based on percent time-spent-following and average travel speed; for freeways it is based on density (pc/km/ln).

Pavement structural number: SN = a1·D1 + a2·D2·m2 + a3·D3·m3, where a is the layer coefficient and m the drainage coefficient; the required SN is obtained from the AASHTO design equation.

The ESAL (equivalent single axle load) for a given axle load is computed as (axle load/standard axle load)^4 for flexible pavements, with the standard axle being 80 kN (18,000 lb).

Drainage: the pavement cross slope is typically 2% for asphalt and 1.5–2% for concrete, and the shoulder slope is 2–6% to facilitate runoff.

Construction cost estimating: unit cost = material + labour + equipment + overhead + profit; labour productivity is expressed in work-hours per unit of output and is adjusted for site conditions.

Earthwork volume by the average end area method: V = L·(A1 + A2)/2; the prismoidal method uses V = L·(A1 + 4Am + A2)/6 for greater accuracy.

The mass haul diagram plots cumulative earthwork volume against distance; the balance point is where cut equals fill, and the free-haul distance is the distance beyond which haul is paid separately.

Concrete formwork pressure: the lateral pressure is computed from the ACI 347 equations, which depend on the placement rate, temperature, and concrete unit weight; the pressure is capped at the hydrostatic value.

Construction scheduling: the critical path has zero float, and crashing the critical path reduces the project duration at an additional cost; the cost slope is the additional cost per unit of time saved.

Safety: the Occupational Safety and Health Administration (OSHA) requires fall protection at heights of 1.8 m (6 ft) in construction, and excavations 1.5 m (5 ft) or deeper require a protective system unless the soil is stable rock.

Excavation: the angle of repose of the soil determines the safe slope; typical slopes are 1:1 for compacted fill and 1.5:1 for loose sand, with benching or shoring for deeper cuts.

Concrete pumping: the line pressure depends on the pump rate, pipe diameter, and mix pumpability; a lubricating grout slug is used at the start, and the line should be cleaned immediately after use.

Quality assurance: the acceptance of compacted fill is based on the field dry density compared with the maximum dry density from the laboratory Proctor test, with a typical required relative compaction of 95%.

Permissible stress in reinforcing steel: for mild steel, the allowable tensile stress in direct tension is typically 140 N/mm², and in bending it is 230 N/mm² for mild steel and 275 N/mm² for cold-worked steel (working stress method).

Working stress method modular ratio m = 280/(3·σcbc), where σcbc is the permissible compressive stress in concrete in bending; the neutral axis depth factor k = m·σcbc/(m·σcbc + σst).

Limit state of collapse in flexure: the design moment Mu = 0.36·fck·b·xu·(d − 0.42·xu), with the limiting neutral axis depth xu,max/d = 0.53 for Fe 250 and 0.48 for Fe 415.

Minimum area of tension reinforcement in a beam is 0.85·b·d/fy (SI, with fy in MPa), and the maximum is 0.04·b·D for beams.

Shear design: the nominal shear stress τv = Vu/(b·d); the design shear strength of concrete τc depends on the percentage of tension reinforcement and the grade of concrete.

Development length in tension: Ld = (0.87·fy·φ)/(4·τbd), where τbd is the design bond stress, increased by 60% for deformed bars in compression.

One-way slab design: the minimum thickness for a simply supported slab is L/20 (mild steel) or L/26 (Fe 415) for a span up to 3.5 m; the main reinforcement is provided in the short direction.

Column design: the minimum eccentricity is emin = L/500 + D/30, subject to a minimum of 20 mm; the column is designed for the axial load plus the moment due to this eccentricity.

Footing design: the critical section for one-way shear is at a distance d from the face of the column, and for two-way (punching) shear it is at a distance d/2 from the column face.