Iran Nezam Civil Supervision Exam cheat sheet

Static determinacy for a plane frame: r + 3m = 3j gives a determinate structure, where r is reaction components, m is members, j is joints; r + 3m > 3j means indeterminate to that degree.

For a simply supported beam with uniformly distributed load w over span L: Mmax = wL^2/8 at midspan and Vmax = wL/2 at each support.

For a cantilever with point load P at the free end: Mmax = PL at the fixed end and maximum deflection = PL^3/(3EI).

Point of contraflexure is where bending moment changes sign; in a simply supported beam under UDL it occurs at the supports only, while in fixed-end beams it lies at 0.211L from each support.

Euler buckling load: Pcr = pi^2EI/(K*L)^2; K = 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2.0 fixed-free.

Slenderness ratio lambda = K*L/r; for steel compression members lambda is capped by code limits depending on member type, and capacity drops sharply beyond lambda of about 100.

Influence-line ordinate gives the response (shear, moment, deflection) at a fixed section due to a unit load placed at that point; maximum response is found by placing live load over the positive ordinate region.

Portal frame under lateral load: approximate beam shear is distributed to columns in proportion to their stiffness I/h^3 for columns fixed at base and I/h for pinned bases.

Moment-distribution method: distribution factor at a joint = member stiffness divided by sum of stiffnesses of all members meeting at that joint; carry-over factor is 0.5 for far end fixed and 0 for far end pinned.

Terzaghi bearing capacity for a strip footing: q_ult = cNc + gammaDfNq + 0.5gammaBN_gamma, with Nc, Nq, N_gamma functions of the friction angle phi.

Allowable bearing capacity = q_ult / FS, with FS typically 3 for static loads and 2 to 2.5 where settlement controls or loads are transient.

Standard penetration test N-value correlates with relative density: N < 4 very loose, 4-10 loose, 10-30 medium, 30-50 dense, > 50 very dense (for clean sands at effective overburden near 100 kPa).

Consolidation settlement: S = CcH/(1+e0) * log10((sigma0 + delta_sigma)/sigma0); time factor T = cvt/H^2 with T = 0.197 for 50% and 0.848 for 90% consolidation.

Liquefaction susceptibility rises with saturated loose clean sand, N below about 15, groundwater table within a few metres, and peak ground acceleration above roughly 0.15 g.

Rankine active earth pressure coefficient Ka = (1 - sin phi)/(1 + sin phi) = tan^2(45 - phi/2); passive Kp = 1/Ka.

Pile capacity: Q_ult = Q_tip + Q_skin = q_pA_p + sum(fsperimeterthickness); skin friction in clay fs = alphacu with alpha typically 0.5 to 1.0.

Minimum foundation depth below finished grade is set by frost penetration and by the zone of seasonal moisture change; footings must bear below disturbed or organic topsoil.

Effective stress principle: sigma' = sigma - u; all strength and settlement computations use effective stress, except undrained shear of saturated clays which uses total stress.

Characteristic cube strength fcu is the value exceeded by 95% of test results; design uses fcd = fck/gamma_c with gamma_c typically 1.5 for ultimate limit state.

Water-cement ratio controls strength and durability: w/c of 0.40-0.45 for severe exposure, 0.50-0.55 for moderate; every 0.01 rise in w/c lowers strength by roughly 1 to 1.5 MPa.

Slump test (ASTM C143) measures workability: 25-50 mm for mass concrete, 75-125 mm for normal reinforced sections, above 150 mm only with superplasticizer.

Cube specimens are 150 mm and cured 28 days in water at 20 +/- 2 degrees C; cylinders 150x300 mm give strength about 0.8 of cube strength.

Balanced reinforced concrete section: at the balanced ratio rho_b, concrete crushing and steel yielding occur simultaneously; under-reinforced sections (rho < rho_b) fail ductile and are required by code.

Minimum tensile reinforcement ratio for beams is about 0.25*sqrt(fck)/fyk, and maximum is 0.04 of the cross-section area; clear bar spacing must allow aggregate to pass, at least bar diameter or 25 mm.

Nominal cover depends on exposure: 20 mm for mild indoor, 30-40 mm for moderate, 50 mm or more for severe and coastal; cover is measured to the outer surface of the outermost bar.

Design shear resistance of a concrete section without shear reinforcement depends on rho and fck; when applied shear exceeds it, stirrups are provided with maximum spacing of 0.75d or 300 mm, whichever is less.

Development length of a deformed bar in tension is roughly proportional to bar diameter and fy, and inversely to bond strength; hooks and anchorage plates reduce required straight length.

Structural steel designation: St37 (fy = 240 MPa), St52 (fy = 360 MPa); A36 gives fy = 250 MPa and Fu = 400-550 MPa.

Bolted connection capacity: shear per bolt = 0.6FuA_boltn_shear planes / gamma; bearing capacity = 2.5dtFu/gamma for edge distances at least 2d.

High-strength bolts in friction grip transfer load by clamping force; slip-critical design requires pretension and faying surfaces free of paint, oil, and rust scale.

Fillet weld throat = 0.707 * leg size; design strength of fillet weld in shear is about 0.6*Fexx with Fexx the electrode tensile strength (E60 = 420 MPa, E70 = 490 MPa).

Local buckling of plate elements is governed by width-to-thickness ratios b/t; compact sections reach plastic moment, non-compact reach yield only, slender sections buckle elastically.

Plastic section modulus Z exceeds elastic modulus S; shape factor Z/S is about 1.12-1.15 for I-sections and 1.5-1.7 for rectangular solid sections.

Lateral-torsional buckling governs the moment capacity of unbraced beams; bracing spacing Lb compared with Lp (plastic) and Lr (elastic limit) determines which curve applies.

Block shear failure combines a tension rupture plane and a shear rupture plane at a connection; capacity = 0.6FuAnv + UbsFuAnt, checked against yielding plus rupture limits.

Column base plates distribute axial load over the concrete pedestal; plate area must keep bearing stress below 0.85*fck over the supporting area.

Cement types: Type I ordinary, Type II moderate sulfate resistance, Type III high early strength, Type IV low heat, Type V sulfate resisting; initial setting time of ordinary Portland cement is at least 45 minutes and final set within 10 hours.

Aggregate grading is checked by sieve analysis and fineness modulus; well-graded sand has FM around 2.3-3.1, and gap-graded mixes need more paste and bleed.

Concrete acceptance sampling: at least one set of specimens per 50 m3 or per day of placing, whichever is more frequent; three specimens per set, tested at 7 and 28 days.

Compaction factor test and Vebe test suit low-workability mixes; slump is unsuitable above about 50 mm aggregate size or for very dry mixes.

Compressive strength acceptance: mean of any three consecutive results must exceed fck plus a margin, and no individual result may fall below fck minus 4 MPa in common national criteria.

Steel reinforcement quality control includes mill certificates, tensile yield and ultimate strength, elongation (at least 14-16% for deformed bars), and bend/rebend tests.

Bitumen grade is defined by penetration (25 degrees C, 100 g, 5 s) or by viscosity; PG grading adds performance at high and low service temperatures.

Soil compaction control uses Proctor maximum dry density and optimum moisture content; field density by sand replacement or nuclear gauge must reach at least 95-98% of maximum dry density.

Curing must keep concrete moist for at least 7 days for normal cement and 10-14 days for blended cements or hot weather; strength gain stops if moisture is lost early.

Critical path method: total float = LS - ES = LF - EF; activities with zero total float lie on the critical path and any delay there delays the project.

Earned value metrics: CV = EV - AC, SV = EV - PV, CPI = EV/AC, SPI = EV/PV; CPI below 1 means cost overrun, SPI below 1 means schedule slippage.

Supervisor's core duties: verify work conforms to drawings and specifications, record daily progress, control material approval, issue non-conformance reports, and hold site instructions in writing.

Payment certification is based on measured quantities against the bill of quantities; the supervisor must not certify work that fails testing or lacks approved material certificates.

Variation orders require written instruction and priced agreement before execution; verbal instructions must be confirmed in writing within the contract period.

Safety obligations: scaffolding inspected before use, excavation deeper than 1.2 m supported or sloped, edge protection at openings, and personal protective equipment enforced at all times.

Contract types: lump sum shifts quantity risk to contractor, unit price shifts it to the employer, cost-plus transfers cost risk to the employer with a fee.

Delay analysis distinguishes excusable delays (employer risk, force majeure) from non-excusable contractor delay; concurrent delays generally deny extension to either party.

As-built documentation, test records, and non-conformance closeout form the handover package; the defects liability period typically runs 12 months from provisional acceptance.

Building regulation structure addresses safety against fire, structural safety, and health/hygiene; each subject is a separate chapter with mandatory minimum requirements, not recommendations.

Fire safety: required exit width is set per occupant load, travel distance to an exit is limited (commonly 20-45 m depending on occupancy and sprinklers), and stairs must be enclosed in fire-rated shafts above certain heights.

Structural load factors for ultimate limit state combine dead and live loads with factors around 1.25-1.5 dead and 1.5 live, and seismic or wind combinations include a load factor near 1.0 with the lateral action.

Seismic design uses the base shear coefficient V = C*W, where C depends on zone seismicity, soil type, structural system, and importance factor; regular structures may use the equivalent static method.

Stair geometry: riser 150-180 mm, tread 250-300 mm, and the sum 2*riser + tread should stay near 600-640 mm for comfortable ascent.

Natural lighting and ventilation: habitable rooms require window area of at least 1/8 to 1/10 of floor area, and minimum ceiling height in habitable rooms is typically 2.4-2.7 m.

Parking and access: minimum parking stall 2.5 x 5.0 m, drive aisle width 5.5-6.0 m for two-way traffic, and ramps limited to about 15% grade for vehicles.

Site supervision duties under the regulations include verifying that construction matches the approved permit drawings, and notifying the authority before covering structural work.

Closed traverse angular closure error must be distributed before coordinates are computed; the allowable misclosure is commonly a*sqrt(n) with a in seconds and n the number of angles.

Latitude = distance * cos(bearing), departure = distance * sin(bearing); sum of latitudes and departures in a closed traverse must be zero after adjustment.

Leveling: height difference = backsight - foresight; arithmetic check is sum(BS) - sum(FS) = last reduced level - first reduced level for a closed loop.

Reciprocal leveling cancels refraction and curvature when the instrument cannot be set midway between two points; the two readings still differ by the earth curvature effect.

Total station layout: set up over a known control point, orient to a second control point, then stake by polar coordinates (azimuth and distance); check the backsight before every layout session.

Horizontal curve elements: tangent T = Rtan(delta/2), length L = Rdelta (radians), external E = R*(sec(delta/2) - 1), middle ordinate M = R*(1 - cos(delta/2)).

Vertical curve: elevation at any point = BVC elevation + g1*x + (g2 - g1)*x^2/(2L); the high or low point occurs where the grade equals zero.

Scale: 1:500 means 1 mm on the drawing equals 0.5 m on the ground; area scales as the square of the linear scale factor.

Allowable building setting-out tolerance is typically 10-25 mm for column lines and 5-10 mm for structural steel anchor bolts, checked against control monuments.

Manning equation: V = (1/n)*R^(2/3)*S^(1/2); n is about 0.013 for concrete pipe, 0.025 for earth channels, and 0.015 for corrugated metal.

Rational method peak flow: Q = CiA/360 with Q in m3/s, i in mm/h, A in hectares, and C the runoff coefficient (0.9 roof, 0.7 asphalt, 0.2 open sandy ground).

Storm sewer design uses the time of concentration to select rainfall intensity; minimum pipe diameter is typically 300 mm and minimum velocity 0.6-0.75 m/s to avoid deposition.

Bernoulli energy equation between two sections: z1 + P1/gamma + V1^2/2g = z2 + P2/gamma + V2^2/2g + hL, with hL the head loss from friction and minor losses.

Hazen-Williams head loss: hf = 10.67LQ^1.852/(C^1.852*D^4.87) in SI units, with C about 130-150 for new pipe and 80-100 for old tuberculated pipe.

Road geometric design: stopping sight distance = Vt/3.6 + V^2/(254(f +/- g)), with t reaction time about 2.5 s and f longitudinal friction about 0.35.

Superelevation e + f = V^2/(127*R) with V in km/h and R in metres; maximum superelevation is commonly 6-8% in urban areas and up to 10% on rural highways.

Pavement layers: subgrade, subbase, base, and surface course; the structural number SN = a1D1 + a2D2 + a3*D3 must meet the required SN from traffic (ESAL) and soil support.

Asphalt compaction must reach at least 92-95% of laboratory density (Marshall or gyratory) and the layer temperature must stay above the cessation temperature during rolling.

Degree of static indeterminacy of a plane frame is r + 3m - 3j; a positive value means redundant reactions or internal forces exist.

Maximum bending moment in a simply supported beam under uniform load w over span L is wL^2/8 at midspan.

Euler buckling load is pi^2*EI/(KL)^2, with effective length factor K of 1.0 pinned-pinned and 0.5 fixed-fixed.

Moment distribution factors equal member stiffness divided by the sum of stiffnesses of all members framing into the joint.

Influence lines give the response at one fixed section as a unit load moves across the structure.

Terzaghi strip footing ultimate capacity is cNc + gammaDfNq + 0.5gammaBN_gamma.

Allowable bearing capacity equals ultimate capacity divided by a factor of safety, commonly 3.

SPT N between 10 and 30 indicates medium dense sand; above 50 indicates very dense sand.

Rankine active coefficient Ka = tan^2(45 - phi/2) and passive Kp = 1/Ka.

Effective stress equals total stress minus pore pressure and governs strength and settlement in drained conditions.

Design concrete strength fcd = fck/gamma_c with gamma_c typically 1.5 at ultimate limit state.

Lower water-cement ratio raises strength and durability; 0.40-0.45 suits severe exposure.

Standard cube specimens are 150 mm and are tested after 28 days of moist curing.

Minimum beam tensile reinforcement ratio is about 0.25*sqrt(fck)/fyk; maximum is 0.04 of section area.

Stirrup spacing in beams is limited to 0.75d or 300 mm, whichever is smaller.

St37 steel has yield strength 240 MPa; St52 has 360 MPa.

Fillet weld throat thickness equals 0.707 times the weld leg size.

Slip-critical bolted connections transfer load through clamping friction, not bolt shear.

Lateral-torsional buckling governs unbraced beam capacity between bracing points Lp and Lr.

Compact sections can develop the plastic moment; slender sections buckle before yielding.

Ordinary Portland cement initial set is at least 45 minutes and final set within 10 hours.

Concrete is sampled at least once per 50 m3 or per day of placing.

Field compaction must reach 95-98% of Proctor maximum dry density.

Curing keeps concrete moist for at least 7 days, or 10-14 days for blended cement.

Bitumen penetration grade is measured at 25 degrees C with a 100 g needle for 5 seconds.

Total float equals late start minus early start; zero float marks the critical path.

CPI = EV/AC below 1 indicates cost overrun; SPI = EV/PV below 1 indicates delay.

Verbal site instructions must be confirmed in writing within the contract period.

Excavations deeper than 1.2 m require shoring or safe sloping.

The defects liability period commonly runs 12 months from provisional acceptance.

Regulation chapters set mandatory minimum requirements for fire safety, structural safety, and hygiene.

Stair risers are 150-180 mm and treads 250-300 mm, with 2*riser + tread near 600-640 mm.

Habitable room window area is at least 1/8 to 1/10 of the floor area.

Seismic base shear is V = C*W, with C depending on zone, soil, system, and importance.

Construction must match approved permit drawings, and structural work is notified before covering.

Latitude = distancecos(bearing) and departure = distancesin(bearing).

Height difference between points equals backsight minus foresight.

Horizontal curve tangent T = Rtan(delta/2) and length L = Rdelta in radians.

Total station layout uses polar coordinates from two known control points, with a backsight check.

Setting-out tolerance is about 10-25 mm for column lines and 5-10 mm for anchor bolts.

Manning velocity is (1/n)*R^(2/3)*S^(1/2), with n near 0.013 for concrete pipe.

Rational method peak flow Q = CiA/360 for Q in m3/s, i in mm/h, and A in hectares.

Minimum storm sewer diameter is typically 300 mm and minimum velocity 0.6-0.75 m/s.

Stopping sight distance = Vt/3.6 + V^2/(254(f +/- g)).

Superelevation and side friction satisfy e + f = V^2/(127*R) with V in km/h.