Civil Engineering MCQs with Answers and Explanations
Sub Engineer, Assistant Engineer and SDO tests conducted by PPSC, FPSC, WAPDA and NTS draw heavily on core civil engineering theory. These Civil Engineering MCQs with answers cover surveying and levelling, strength of materials, structural analysis, RCC and steel design, building materials and concrete technology, soil mechanics and foundations, fluid mechanics and hydraulics, irrigation and hydrology, highway and railway engineering, environmental engineering and construction planning with PERT and CPM.
Take a scored quiz instead →In surveying, the curvature of the earth is taken into account when the area exceeds:
In surveying, when the survey area is small (less than 250 km^2), earth curvature is negligible and plane surveying is used. When survey area exceeds 250 square kilometers, geodetic surveying must be employed to account for earth curvature.
The whole circle bearing (WCB) of a line is 290 degrees 30 minutes. Its reduced bearing (RB) is:
The line lies in the 4th quadrant (NW) since 270° < 290°30' < 360°. Reduced bearing RB = 360°00' - 290°30' = N 69°30' W.
In levelling, the correction for combined curvature and refraction is given by (where D is distance in km):
Combined correction for curvature (-0.0785 D^2) and atmospheric refraction (+0.0112 D^2) in levelling is given by C = -0.0673 * D^2 meters, where D is horizontal distance in kilometers.
The contour lines of different elevations can intersect each other only in the case of a:
Contour lines of different elevations never cross or intersect each other except in the single special topographical case of an overhanging cliff or cave.
The sensitivity of a level tube increases with:
The sensitivity of a level bubble tube increases with an increase in the internal radius of curvature of the tube, increase in tube diameter/length, and decrease in liquid viscosity/surface tension.
The ratio of linear stress to linear strain within the elastic limit is defined as:
According to Hooke's Law, within the elastic limit of a material, uniaxial stress is directly proportional to strain. The constant of proportionality is Young's Modulus of Elasticity (E = Stress / Strain).
For a simply supported beam of length L carrying a central point load W, the maximum bending moment is:
For a simply supported beam of span L loaded with a concentrated load W at midspan, maximum bending moment occurs directly under the load at center and equals M_max = W * L / 4.
The point of contraflexure in a beam is defined as the point where the:
A point of contraflexure (or point of inflection) occurs along a flexural member where the bending moment diagram changes algebraic sign (passes through zero), causing curvature to switch between sagging and hogging.
The maximum shear stress in a rectangular beam section subjected to shear force V is:
In a rectangular beam section subjected to shear force V, shear stress distribution is parabolic across the depth. Maximum shear stress occurs at the neutral axis and equals 1.5 times average shear stress (τ_max = 1.5 * τ_avg).
Euler’s crippling load formula for a column with both ends hinged (pinned) is given by:
Euler's critical buckling load for an ideal slender column with both ends hinged/pinned (effective length Le = L) is given by P_cr = (π^2 * E * I) / L^2.
In a cantilever beam of length L subjected to a uniform distributed load w over its entire span, maximum deflection occurs at the free end and is equal to:
For a cantilever beam of length L carrying a uniform distributed load w over its entire length, maximum deflection occurs at the unsupported free end and is given by δ_max = (w * L^4) / (8 * E * I).
According to IS 456 / ACI standards, the characteristic compressive strength of concrete is measured after curing for:
Concrete compressive strength testing standardly uses 150mm cubes or 150x300mm cylinders cured for 28 days under water at standard temperature (27±2°C) to reach design characteristic strength.
The slump test for concrete is used to measure its:
The slump cone test measures consistency and workability of fresh concrete before placement, indicating ease of flow, mixing, handling, and placement without segregation.
In reinforced concrete beams, side face reinforcement is provided when the depth of the web exceeds:
In RCC beam design (IS 456 / standard codes), when web depth exceeds 750 mm, side face reinforcement of at least 0.1% of web area must be distributed equally on both vertical faces to prevent lateral buckling and shrinkage cracking.
The modular ratio ‘m’ in working stress design of reinforced concrete is taken as:
In working stress design (WSD) of reinforced concrete, modular ratio accounts for long-term concrete creep under sustained loads and is calculated as m = 280 / (3 * σ_cbc), where σ_cbc is allowable bending compressive stress.
The minimum percentage of shear reinforcement in a beam is provided to prevent sudden failure from:
Minimum shear reinforcement (stirrups) is provided in reinforced concrete beams to prevent sudden brittle failure caused by diagonal tension cracks when principal tensile stresses exceed concrete tensile strength.
The maximum strain in concrete at the outermost compression fiber in flexure at collapse is assumed to be:
In Limit State Method (LSM) design of concrete structures, maximum ultimate compressive strain in concrete at the extreme compression fiber in flexure is assumed to be fixed at 0.0035 (0.35%).
The ratio of volume of voids to the total volume of soil mass is called:
Porosity (n) of a soil mass is defined as the ratio of volume of voids (Vv) to total volume of soil sample (V), expressed as a percentage: n = (Vv / V) * 100%.
When the degree of saturation of a soil sample is 100%, the soil is said to be:
Degree of saturation (S) is the ratio of water volume to void volume. When all soil voids are completely filled with water, S = 100% (S = 1.0), classifying the soil as fully saturated.
Terzaghi’s ultimate bearing capacity equation for a strip footing on c-phi soil is given by:
Terzaghi's ultimate bearing capacity formula for a shallow strip footing resting on c-phi soil under general shear failure is qu = c * Nc + q * Nq + 0.5 * γ * B * Nγ.
Atterberg limit corresponding to the water content at which soil passes from plastic state to liquid state is:
The liquid limit (LL) is the boundary water content at which soil transitions from a plastic state to a liquid state, possessing negligible shear strength (approximately 2.7 kPa).
The active earth pressure coefficient Ka for a soil with internal friction angle phi is given by:
According to Rankine's earth pressure theory for cohesionless backfill with horizontal surface, active earth pressure coefficient is Ka = (1 - sin φ) / (1 + sin φ) = tan^2(45° - φ/2).
Quick sand is a condition that occurs in cohesionless soils when the effective stress becomes:
Quick sand is a hydraulic condition in cohesionless sand when upward seepage velocity creates upward hydrodynamic pressure equal to submerged unit weight, reducing effective stress (σ') to zero and causing loss of shear strength.
Bernoulli’s equation is based on the law of conservation of:
Bernoulli's principle for steady, incompressible, frictionless fluid flow along a streamline expresses conservation of energy, stating that total energy head (elevation + pressure + velocity head) remains constant.
The major head loss in a pipeline flowing full under pressure is primarily caused by:
Major head loss in long pressure conduits flowing full is caused by fluid friction along internal pipe walls and is calculated using Darcy-Weisbach equation: hf = (f * L * v^2) / (2 * g * D).
Froude number in open channel flow is defined as the ratio of inertia force to:
Froude number (Fr = v / √(g * D)) in open channel hydraulics represents the ratio of inertial force to gravitational force, governing subcritical (Fr 1) flow regimes.
A hydraulic jump occurs in an open channel flow when the flow transitions from:
A hydraulic jump is a rapid, turbulent open-channel phenomenon that occurs when flow abruptly transitions from high-velocity supercritical flow (Fr > 1) to low-velocity subcritical flow (Fr < 1), dissipating energy.
The discharge Q through a rectangular notch/weir is proportional to:
Discharge Q over a sharp-crested rectangular weir or notch is given by Q = (2/3) * Cd * b * √(2g) * H^(3/2), establishing that discharge is directly proportional to H^(3/2).
Laminar flow through a circular pipe occurs when the Reynolds number is less than:
In circular pipe flow, flow regime depends on Reynolds number (Re = ρ v D / μ): flow is laminar for Re < 2000, transient for 2000 < Re 4000.
The stopping sight distance (SSD) on a highway depends primarily on:
Stopping Sight Distance (SSD) is the minimum distance required for a driver traveling at design speed to safely stop before hitting a stationary object. It depends on design speed, driver perception-reaction time (typically 2.5s), braking efficiency, and road friction coefficient.
The maximum superelevation recommended by IRC for plain and rolling terrain is:
Indian Roads Congress (IRC) recommends a maximum superelevation (e_max) of 7% (0.07) for plain and rolling terrain, 10% for hilly terrain, and 4% for urban roads with frequent intersections.
California Bearing Ratio (CBR) test is performed to determine the strength and thickness design of:
The California Bearing Ratio (CBR) test is an empirical penetration test used to evaluate subgrade soil strength and determine structural thickness requirements for flexible highway pavements.
The aggregate impact value test is conducted to evaluate which property of road aggregates?
The aggregate impact value test measures resistance of road aggregates to sudden shock or impact loading, evaluating aggregate toughness for highway pavement construction.
Biochemical Oxygen Demand (BOD5) test is standardly measured after incubation at:
Standard Biochemical Oxygen Demand (BOD5) test measures dissolved oxygen consumed by microorganisms to decompose organic matter in wastewater incubated at 20°C for 5 days.
The main objective of adding alum during water treatment process is to act as a:
Alum (aluminum sulfate) is added during primary water treatment as a chemical coagulant. It neutralizes negative charges on fine suspended colloidal particles, forming heavy gelatinous flocs that easily settle out.
Self-cleansing velocity in a sanitary sewer pipe is maintained to prevent:
Self-cleansing velocity (typically 0.6 to 0.9 m/s) is the minimum flow velocity maintained in sanitary sewers to ensure suspended organic and inorganic solids remain in suspension and do not deposit or clog pipes.
The maximum permissible limit of fluoride in drinking water as per WHO guidelines is:
According to World Health Organization (WHO) drinking water guidelines, maximum desirable fluoride concentration is 1.0 mg/L and maximum permissible upper limit is 1.5 mg/L to prevent dental and skeletal fluorosis.
Initial setting time of ordinary Portland cement (OPC) should not be less than:
As per standard cement specifications, initial setting time of Ordinary Portland Cement (OPC) must not be less than 30 minutes to allow mixing and placing, while final setting time must not exceed 600 minutes (10 hours).
The soundess of cement is tested to detect excess presence of:
Soundness testing of cement (via Le Chatelier apparatus or Autoclave) measures unburned free lime (CaO) and magnesia (MgO) to ensure cement does not undergo excessive volume expansion after setting.
In PERT, the duration of an individual activity is assumed to follow which probability distribution?
PERT assumes that each activity's duration follows a Beta distribution, described by an optimistic (a), most likely (m) and pessimistic (b) estimate, with expected time te = (a + 4m + b) / 6.
The total project (event) completion time, being the sum of many activity times, is then treated as approximately Normal by the central limit theorem.
The critical path in a CPM network diagram represents the sequence of activities having:
In Critical Path Method (CPM) networks, the critical path is the longest continuous chain of activities from start to finish. Activities along this path have zero total float, meaning any delay directly delays project completion.
The graphical representation of discharge versus time at a specific section of a stream is called a:
A hydrograph is a graphical plot of stream flow discharge (m^3/s) versus time at a specific location along a river or channel following a precipitation event.
Duty of irrigation water is defined as the area of land irrigated per unit of:
Duty of water is defined as the total area of land (in hectares) that can be fully irrigated by a continuous unit discharge of water (1 cumec = 1 m^3/s) flowing throughout the base period of a crop.
Lacey’s regime theory for stable channel design in alluvial soil is applicable when flow is in:
Lacey's regime theory applies to stable alluvial channels carrying silt-laden water where channel cross-section and slope adjust naturally under a true regime condition governed by a silt factor f.
The loss of water from soil surface by evaporation and from plants by transpiration is combinedly termed:
Evapotranspiration represents total water loss to the atmosphere from a cropped area, combining direct evaporation from soil and water surfaces with transpiration through plant stomata.
The effective length of a column of actual length L fixed at one end and hinged at the other end is:
For a column of length L fixed at one end and hinged at the other, theoretical effective length is Le = L / √2 ≈ 0.707 L (standard design codes recommend 0.80 L for practical considerations).
In steel structure design, slenderness ratio of a compression member is defined as the ratio of effective length to:
Slenderness ratio (λ) of a structural compression member is defined as the ratio of its effective length (Le) to its least radius of gyration (r_min), governing buckling capacity.
Plastic modulus of section Zp for a rectangular section of width b and depth d is given by:
Plastic section modulus Zp measures ultimate bending capacity of a cross section in plastic design. For a rectangular section of width b and depth d, Zp = (b * d^2) / 4 (compared to elastic section modulus Ze = b * d^2 / 6).
The shape factor for a solid circular cross-section in plastic design is:
Shape factor (S = Zp / Ze) represents reserve plastic strength after yield. For a solid circular cross-section, plastic section modulus Zp = d^3 / 6 and elastic modulus Ze = π * d^3 / 32, giving Shape Factor S ≈ 1.70.
The principal stress plane in a stressed element is defined as the plane on which:
Principal planes are mutually perpendicular planes within a loaded body on which normal stresses reach maximum and minimum values, and shear stress is exactly zero.
In concrete mix design, what is the nominal mix ratio for M20 grade concrete as per standard engineering specifications?
Nominal mix ratios for concrete grades are M5 (1:5:10), M7.5 (1:4:8), M10 (1:3:6), M15 (1:2:4), M20 (1:1.5:3), and M25 (1:1:2). Thus, M20 has a nominal proportion of 1 part cement, 1.5 parts fine aggregate, and 3 parts coarse aggregate.
The aggregate crushing value test measures which physical property of coarse aggregates used in road construction?
The Aggregate Crushing Value (ACV) gives a relative measure of resistance of an aggregate to crushing under a gradually applied compressive load (40 tonnes over 10 minutes). Aggregate Impact Value measures toughness, and Los Angeles Abrasion measures wear resistance.
According to IS 456, what is the minimum grade of reinforced cement concrete (RCC) permissible for structural members in moderate exposure conditions?
Under IS 456:2000 (Table 5), the minimum grade of reinforced concrete is M20 for mild exposure, M25 for moderate, M30 for severe, M35 for very severe and M40 for extreme exposure. So for moderate exposure the minimum grade is M25.
What is the standard size of a modular clay building brick including mortar joint thickness?
The standard size of a modular brick without mortar is 19 cm x 9 cm x 9 cm. With nominal mortar joint thickness (10 mm), the modular dimensions become 20 cm x 10 cm x 10 cm.
In plastic analysis of steel structures, what is the shape factor for a rectangular cross-section?
Shape factor (S) is the ratio of plastic section modulus (Zp) to elastic section modulus (Ze). For a rectangular section, Zp = bd^2/4 and Ze = bd^2/6, giving S = 1.50. For an I-section S ≈ 1.12 to 1.15, for a solid circular section S = 1.70, and for a diamond section S = 2.0.
Which soil fraction has particle sizes smaller than 0.002 mm according to the MIT / IS soil classification system?
In soil mechanics, particle size classification defines Gravel (> 4.75 mm), Sand (0.075 mm to 4.75 mm), Silt (0.002 mm to 0.075 mm), and Clay (< 0.002 mm or 2 microns).
In surveying, what is the allowable error in chaining for rough terrain or ordinary measurement with a chain?
In chaining operations, acceptable precision limits are 1 in 1000 for steel tape, 1 in 500 for precise chaining with a tested chain, and 1 in 250 for ordinary chaining in rough terrain.
If the whole circle bearing (WCB) of a line is 135 degrees 30 minutes, its reduced bearing (RB) is:
A bearing of 135°30' lies in the second quadrant (SE) between 90° and 180°. Reduced Bearing RB = 180° - 135°30' = S 44° 30' E.
Which index parameter in soil mechanics is defined as the difference between Liquid Limit (LL) and Plastic Limit (PL)?
Plasticity Index (IP) is the numerical difference between the Liquid Limit (LL) and Plastic Limit (PL): IP = LL - PL. It represents the range of moisture content over which soil behaves plastically.
According to Terzaghi’s bearing capacity theory, the failure surface for a shallow strip footing undergoing general shear failure consists of how many distinct zones?
Terzaghi's ultimate bearing capacity model identifies 3 distinct failure zones under a shallow strip foundation: Zone I (elastic triangular wedge directly under the footing), Zone II (radial shear zone), and Zone III (Rankine passive zone).
Darcy’s Law for fluid flow through porous saturated soil media is valid only when flow condition is:
Darcy's law (v = k i) assumes that discharge velocity is directly proportional to hydraulic gradient. This holds only for laminar flow, where the Reynolds number is below about 1 (up to about 10 in some soils).
In coarse gravels the flow can become turbulent, and the law no longer applies.
The Darcy-Weisbach friction factor ‘f’ for laminar flow in a smooth circular pipe depends only on Reynolds number (Re) and is given by:
For laminar flow in circular pipes (Re < 2000), friction factor f is determined analytically as f = 64 / Re. Head loss due to friction is hf = (f * L * v^2) / (2 * g * D).
What parameter is used to classify open channel flow as subcritical, critical, or supercritical?
Froude number Fr = v / sqrt(g * D) represents the ratio of inertial forces to gravity forces. If Fr 1 the flow is supercritical (rapid).
In highway design, stopping sight distance (SSD) consists of two main distance components:
Stopping Sight Distance (SSD) = Perception-reaction distance (Lag distance = v * t) + Braking distance (v^2 / (2 * g * f)). Total SSD is the minimum distance required for a vehicle moving at design speed to stop safely.
The California Bearing Ratio (CBR) test on subgrade soil is used to evaluate:
The CBR test measures force per unit area required to penetrate a soil mass with a standard circular piston at 1.25 mm/min. CBR values directly correlate with subgrade shear strength and determine pavement thickness in empirical flexible pavement design.
In water treatment plants, the addition of alum as a coagulant works primarily by:
Alum (aluminum sulfate) acts as a coagulant by neutralizing negative surface charges on microscopic colloidal particles in raw water. This allows particles to agglomerate into larger, settleable flocs during flocculation.
In CPM network analysis, total float of an activity is defined as:
Total Float = Latest Start - Earliest Start = Latest Finish - Earliest Finish. It represents the maximum allowable delay in an activity without impacting the final project completion date. Activities on the critical path have zero total float.
A Unit Hydrograph is a direct runoff hydrograph resulting from how many units of effective rainfall falling uniformly over a watershed?
A Unit Hydrograph (UH) is defined as a direct runoff hydrograph resulting from 1 unit (1 cm or 1 inch) of excess rainfall (direct runoff) occurring uniformly over a catchment area at a constant rate for a specified duration.
Which apparatus is standardly used to test the soundness of Ordinary Portland Cement caused by free lime?
Le Chatelier apparatus measures volumetric expansion (unsoundness) in cement due to unburned free lime (CaO). Autoclave testing is used when unsoundness is caused by both free lime and magnesia (MgO).
The shear strength of a soil mass under two-dimensional stress condition is governed by which empirical failure envelope?
The shear strength (tau) of soil is defined by the Mohr-Coulomb equation: tau = c + sigma * tan(phi), where c is cohesion, sigma is normal stress on the failure plane, and phi is the angle of internal friction.
In surveying, plane table surveying works on which fundamental governing principle?
The basic governing principle of plane table surveying is parallelism, meaning all lines plotted on the drawing sheet remain parallel to the corresponding lines on the ground during orientation at all survey stations.
The horizontal distance measured between two consecutive contour lines on a topographic map is termed:
Contour interval is the constant vertical distance between two adjacent contour lines. Horizontal equivalent is the horizontal distance between two consecutive contour lines on the map, which varies depending on steepness of slope.
The phenomenon of creep in reinforced concrete structures is defined as:
Creep in concrete is the slow, time-dependent, irreversible deformation occurring under sustained dead or structural loads over extended periods of time, increasing long-term deflection in structural members.
In flexible pavement structural layers, the layer placed directly above the natural compacted subgrade soil is:
Typical flexible pavement layers from bottom to top are: (1) Natural Subgrade, (2) Sub-Base Course (granular materials), (3) Base Course (crushed stone), (4) Binder Course, and (5) Surface/Wearing Course.
In water supply distribution networks, which piping layout system is most suitable for well-planned modern cities with gridiron street layouts?
The Gridiron (or Reticulated/Loop) system interconnects main, sub-main, and branch pipes, eliminating dead ends. Water can reach any point from multiple directions, making it ideal for planned gridiron road networks.
In open channel flow, the critical depth (yc) for a rectangular channel with discharge per unit width ‘q’ is given by:
At critical flow in a rectangular channel, specific energy is minimum and Froude number Fr = 1. The critical depth yc = (q^2 / g)^(1/3), where q is discharge per unit width (q = Q / b).
In steel structure design, the effective length of a column fixed at one end and completely free at the other end is:
Theoretical effective lengths (Le) for standard end conditions: Both ends fixed (0.5 L), One end fixed and other hinged (0.707 L), Both ends hinged (1.0 L), and Fixed at one end & Free at the other end (2.0 L).
In structural analysis, static indeterminacy of a pin-jointed plane truss is calculated using the relation:
For a 2D pin-jointed plane truss, each joint provides 2 equilibrium equations (Sum Fx = 0, Sum Fy = 0). Total degrees of static indeterminacy Ds = Internal indeterminacy + External indeterminacy = (m - 2j + 3) + (r - 3) = m + r - 2j.
Which type of compaction roller equipment is most effective for compacting heavy cohesive clayey soils?
Sheepsfoot rollers exert high pressure combined with kneading action, making them the most effective equipment for compacting cohesive clay soils. Vibratory rollers are best for non-cohesive sands and gravels.
The workability of concrete measured by the slump test for heavy mass concrete construction should ideally range between:
For heavy mass concreting (such as dams and massive foundations) compacted by vibrators, low workability with a slump of 25 to 50 mm is preferred to minimize shrinkage and thermal cracking.
According to IS 456, the clear cover to main reinforcement bars in a concrete column should not be less than:
According to standard structural codes (IS 456), clear cover for main longitudinal bars in columns should not be less than 40 mm, or the diameter of the longitudinal bar, whichever is greater.
In brick masonry, a brick laid with its breadth parallel to the face of the wall is called a:
A header is a brick unit laid such that its shorter face (breadth) is visible on the wall surface. A stretcher is laid with its longer face (length) parallel to the wall face.
The ratio of maximum bending stress to maximum shear stress for a rectangular cantilever beam of depth ‘d’ loaded with a point load at free end is:
For a rectangular section beam of width b and depth d under point load P: max bending stress sigma = 6 P L / (b d^2); max shear stress tau_max = 1.5 P / (b d). The ratio sigma / tau_max = (6 P L / b d^2) / (1.5 P / b d) = 4 L / d.
What is the relation between Young’s Modulus (E), Bulk Modulus (K), and Poisson’s Ratio (nu)?
The fundamental elastic constants relate as: E = 3K(1 - 2*nu) and E = 2G(1 + nu). Combining them gives E = 9KG / (3K + G).
The maximum shear stress in a solid circular shaft of diameter ‘d’ subjected to a twisting moment ‘T’ is given by:
Torsion formula: T / J = tau / r. For a solid circular shaft, polar moment of inertia J = pi*d^4 / 32 and radius r = d / 2. Therefore, tau_max = 16 T / (pi * d^3).
A beam of uniform strength has a cross-section designed such that maximum bending stress developed is:
A beam of uniform strength is configured (by varying cross-sectional width or depth along its length) so that extreme fiber bending stress remains constant across all sections along the span under design load.
In surveying, the true bearing of a line is 180° 00′ and magnetic declination is 4° 30′ West. What is the magnetic bearing of the line?
True Bearing (TB) = Magnetic Bearing (MB) - Declination West. Therefore, Magnetic Bearing = True Bearing + West Declination = 180° 00' + 4° 30' = 184° 30'.
The reciprocal levelling method eliminates errors due to which of the following factors?
Reciprocal levelling eliminates line of collimation error, curvature error, and atmospheric refraction error when finding height differences across wide rivers or valleys without intermediate setups.
The ratio of liquid limit minus natural moisture content to plasticity index of a soil is called:
Consistency Index (Ic) = (LL - w) / IP. Liquidity Index (IL) = (w - PL) / IP. Note that Ic + IL = 1.
Unified Soil Classification System (USCS) classifies soil as fine-grained when more than 50% of soil particles pass through which sieve?
In USCS and ASTM classification, soil is coarse-grained if 50% or more is retained on No. 200 sieve (0.075 mm), and fine-grained if more than 50% passes through No. 200 sieve.
Compaction of soil using Proctor test aims at driving out which component from soil voids?
Compaction is a mechanical process that reduces void volume primarily by expelling entrapped air from soil voids.
The continuity equation for incompressible steady fluid flow expresses conservation of:
The continuity equation (A1 * v1 = A2 * v2) is based on the principle of conservation of mass.
The discharge through a Venturimeter installed in a pipe is proportional to:
Venturimeter discharge formula is Q = [Cd * A1 * A2 / sqrt(A1^2 - A2^2)] * sqrt(2gh). Thus, discharge Q is directly proportional to sqrt(h).
What type of turbine is a Pelton wheel turbine?
Pelton wheel is a high-head (usually > 250m), low-discharge tangential flow impulse turbine.
The most economical trapezoidal open channel section has a hydraulic radius (R) equal to:
For the most economical trapezoidal channel section, hydraulic radius R = y / 2, where y is flow depth.
The maximum safe design speed on a horizontal highway curve without considering side friction depends on superelevation ‘e’ and curve radius ‘R’ as:
When side friction f = 0, e = v^2 / (g*R), which gives v = sqrt(e * g * R).
In bitumen testing, the penetration test measures which physical property of asphalt bitumen?
The penetration test measures distance in tenths of a millimeter (dmm) that a standard loaded needle penetrates vertically into a bitumen sample in 5 seconds at 25°C.
The minimum radius of curvature for a circular railway curve of 1 degree (1° curve on 30m arc) is approximately:
Degree of curve D (for 30m arc) relates to radius R by R = 1720 / D meters. For a 1° curve, R = 1720 meters.
The presence of excessive iron and manganese in municipal water supply causes:
Iron (> 0.3 mg/L) and Manganese (> 0.05 mg/L) impart reddish-brown and black stains to clothes and plumbing fixtures.
Which wastewater treatment unit process works primarily on an aerobic suspended-growth biological mechanism?
Activated Sludge Process (ASP) is an aerobic suspended-growth process where microorganisms are kept suspended in aeration tanks.
The sound pressure level corresponding to the threshold of human hearing is standardized at:
The threshold of human hearing corresponds to a reference sound pressure of 20 micro-Pascals, defined as 0 decibels (0 dB).
In PERT project management, the activity variance (sigma^2) is calculated using optimistic (a) and pessimistic (b) time estimates as:
Standard deviation in PERT is sigma = (b - a) / 6. Therefore, variance sigma^2 = [(b - a) / 6]^2.
In CPM network diagramming, a dummy activity is used to:
A dummy activity consumes zero time and zero resources. It is introduced purely to maintain logical precedence and unique node numbering.
The silt factor ‘f’ in Lacey’s regime theory for canal design is related to average particle diameter ‘d’ (in mm) by:
Lacey's silt factor formula is f = 1.76 * sqrt(d_mm), where d_mm is the average grain size in millimeters.
The depth of water required by a crop during its entire period of growth in the field is called its:
Delta is the total depth of water supplied to a crop during its base period.
A rainfall hyetograph represents a graphical plot of:
A hyetograph is a plot showing rainfall intensity over successive time intervals.
In steel tension member design, net effective cross-sectional area for a plate with staggered rivet holes is increased compared to chain riveting because:
For staggered hole patterns, net width net_b = b - n*d + Sum[s^2 / (4*g)]. The added term increases net effective area.
Vicat apparatus with plunger of 10 mm diameter is used to determine which property of cement?
Standard consistency of cement paste is determined using Vicat apparatus fitted with a 10 mm diameter plunger.
The development length (Ld) of a deformed reinforcement bar in tension as per limit state design is given by:
Development length equation is Ld = (phi * sigma_s) / (4 * tau_bd).
The maximum shear stress in a triaxial compression test on soil occurs on a plane inclined to the major principal plane at an angle of:
In Mohr circle analysis, maximum shear stress occurs at an angle 2*theta = 90°, which corresponds to a physical plane inclined at theta = 45°.
The optimum moisture content (OMC) of a soil during compaction test corresponds to the point where soil achieves:
Optimum Moisture Content (OMC) is the specific water content at which a given compaction energy produces maximum dry density.
According to Coulomb’s wedge theory of earth pressure, the failure wedge is assumed to be bounded by a plane surface and acts as a:
Coulomb's wedge theory considers the sliding soil wedge as a rigid body.
For a propped cantilever beam of span L with fixed support at A and prop support at B carrying UDL ‘w’, the reaction at prop support B is:
Equating downward deflection due to UDL with upward deflection due to prop reaction yields RB = 3/8 wL.
The Moment Distribution Method developed by Hardy Cross is primarily an iterative method used for analyzing:
Hardy Cross's Moment Distribution Method is an iterative technique used to analyze statically indeterminate beams and frames.
In a parabolic three-hinged arch of span L and central rise h carrying UDL over entire span, horizontal thrust (H) at supports is:
Taking moment about crown hinge C gives H = w * L^2 / (8 * h).
In Total Station surveying, distance measurement is executed using which technology?
A Total Station combines an electronic theodolite with Electronic Distance Measurement (EDM) system.
Sensitivity of a level tube is defined as the angle subtended at the center by an arc of one division of the level tube, expressed in:
Level tube sensitivity alpha is measured in seconds of arc per 2mm division.
In two-point and three-point problems of plane table surveying, orientation is achieved by:
Two-point and three-point problems are methods of resection used to locate instrument position and orient the table.
The phenomenon of bleeding in fresh concrete refers to:
Bleeding is a form of segregation where free water in fresh concrete rises to the top surface.
In rigid pavement slab design, expansion joints are provided primarily to:
Expansion joints allow concrete slabs to expand horizontally during high temperatures without crushing or buckling.
Which type of sewer pipe material is immune to crown corrosion caused by hydrogen sulfide gas (H2S)?
Vitrified Clay Pipes (VCP) and PVC pipes are highly resistant to crown corrosion caused by sulfuric acid.
The design period for municipal water treatment plant units is standardly taken as:
Water treatment plants and pumping structures are standardly designed for a 15 to 30 year horizon.
The critical velocity ratio (V / Vo) in Kennedy’s silt theory for canal design is defined as:
Critical Velocity Ratio CVR = V / Vo, where V is actual mean velocity and Vo is Kennedy's critical velocity.
In steel beam design, laterally unsupported beams are susceptible to which mode of failure?
When the compression flange of a beam lacks lateral support, it tends to deflect laterally and twist (Lateral Torsional Buckling).
The kinematic indeterminacy (Dk) of a fixed-fixed beam of span L under general loaded 2D plane conditions is:
At a fixed support in 2D, all 3 joint displacements are restrained. Hence for fixed-fixed beam, Dk = 0.
The standard test temperature for the bitumen penetration test is:
The penetration test measures the depth, in units of 0.1 mm, to which a standard needle penetrates bitumen under a 100 g load in 5 seconds at 25°C.
Bitumen grades such as 60/70 and 80/100 are named from the results of this test.
In soil mechanics, quick conditions are prevented by placing a graded inverted filter on the downstream side, which must satisfy:
Terzaghi's filter criteria specify that an inverted filter must be sufficiently permeable to allow free seepage drainage while fine enough to prevent erosion of soil particles.
The compressive strength of standard mortar cubes made with 33-grade Ordinary Portland Cement after 7 days of curing should not be less than:
Under IS 269, 1:3 cement-sand mortar cubes of 33-grade OPC must reach at least 22 N/mm² at 7 days and 33 N/mm² at 28 days.
For 43-grade OPC the 7-day minimum is 33 N/mm², and for 53-grade it is 37 N/mm².
In concrete mix design, the compaction factor test is specifically suitable for concrete mixes having:
The Compaction Factor test is more precise and sensitive than the slump test for concrete mixes with low and medium workability (compaction factor ranging from 0.75 to 0.95).
In stone masonry, a vertical joint that continues continuously through two or more consecutive courses is called a:
Continuous vertical joints in masonry reduce structural load-bearing capacity and wall integrity. Brick and stone masonry bonding rules strictly mandate staggering vertical joints.
The ratio of maximum shear stress to average shear stress for a circular beam cross-section subjected to shear force is:
For a circular cross-section, tau_max = (4/3) * tau_avg = 1.33 * tau_avg. For a rectangular section, tau_max = 1.5 * tau_avg.
For a simply supported beam of span ‘L’ loaded with a point load ‘W’ at midspan, the maximum deflection at midspan is given by:
The maximum midspan deflection for a simply supported beam under central point load W is delta = W L³ / (48 E I).
The section modulus (Z) of a solid circular cross-section of diameter ‘d’ is equal to:
Section Modulus Z = I / y_max. For a solid circle, I = pi*d⁴/64 and y_max = d/2, so Z = (pi*d⁴/64) / (d/2) = pi*d³/32.
In compass surveying, the local attraction at a station is indicated if the difference between fore bearing and back bearing of a line is not equal to:
In the absence of local attraction and observational errors, the difference between fore bearing and back bearing of any survey line must be exactly 180°.
The Plasticity Index (IP) of a soil with a Liquid Limit (LL) of 45% and a Plastic Limit (PL) of 20% is:
Plasticity Index IP = Liquid Limit − Plastic Limit = 45% − 20% = 25%.
It is the range of water content over which the soil behaves plastically; soils with IP above 17% are considered highly plastic.
The active earth pressure coefficient (Ka) for a cohesionless soil with an internal friction angle (phi) of 30° is:
Rankine's active earth pressure coefficient Ka = (1 - sin(phi)) / (1 + sin(phi)). For phi = 30°, Ka = (1 - 0.5) / (1 + 0.5) = 0.5 / 1.5 = 1/3 = 0.333.
According to Terzaghi’s bearing capacity theory, the ultimate bearing capacity of a shallow strip footing on purely cohesive soil (phi = 0) is:
For a strip footing on cohesive soil (phi = 0), Terzaghi's bearing capacity factors are Nc = 5.7, Nq = 1.0, Ngamma = 0. Ultimate bearing capacity qu = c * Nc = 5.7 c.
The loss of head due to sudden enlargement in a pipe flow carrying velocity v1 in smaller pipe and v2 in larger pipe is given by:
Head loss due to sudden expansion is given by he = (v1 - v2)² / (2g), derived using impulse-momentum principle.
Bernoulli’s equation is derived along a streamline under the assumption of:
Bernoulli's energy equation assumes fluid is ideal (frictionless/inviscid), incompressible, flow is steady, and along a streamline.
The specific energy (E) of flow in a rectangular open channel at critical depth (yc) is equal to:
For a rectangular channel, minimum specific energy Emin = yc + vc² / (2g) = yc + 0.5 yc = 1.5 yc (or 3/2 yc).
The Stopping Sight Distance (SSD) on a level highway depends on vehicle speed (v), driver reaction time (t), and coefficient of longitudinal friction (f) as:
SSD consists of lag distance (v*t) plus braking distance [v² / (2*g*f)].
In railway track engineering, creep of rails refers to:
Creep is defined as the unintended longitudinal movement of rails relative to sleepers in the direction of predominant train movement.
The maximum permissible concentration of nitrates (as NO3-) in drinking water to prevent Methemoglobinemia (Blue Baby Syndrome) in infants is:
To prevent methemoglobinemia (blue baby syndrome) in infants, the permissible limit of nitrate in drinking water is 45 mg/L as NO3, which equals 10 mg/L as nitrate-nitrogen (NO3-N). This is the limit used by IS 10500 and the US EPA.
The WHO guideline value is slightly higher, at 50 mg/L as NO3.
In CPM project network planning, Total Float (TF) of an activity is calculated as:
Total Float TF = LS - ES = LF - EF. It represents total allowable delay without delaying project completion.
According to Kennedy’s silt theory, the critical velocity (Vo) in a canal is proportional to flow depth (D) raised to the power:
Kennedy's formula for the critical (non-silting, non-scouring) velocity is Vo = 0.55 m D^0.64, where D is the depth of flow in metres and m is the critical velocity ratio (CVR = V/Vo), taken as 1 for standard silt. So Vo varies as D^0.64.
The relation between Duty ‘D’ (in hectares/cumec), Delta ‘delta’ (in meters), and Base Period ‘B’ (in days) is:
Derivation: Delta (m) = (1 cumec * B days * 86400 sec) / (D * 104 m²) = 8.64 * B / D.
An Isochrone in catchment hydrology is defined as a line connecting points on the catchment having equal:
An Isochrone is a contour line joining points in a watershed that have equal travel time for surface runoff to reach the basin outlet.
In a unconfined compression test on a cohesive clay soil sample, the unconfined compressive strength (qu) is related to undrained cohesion (cu) by:
In unconfined compression test (sigma3 = 0), major principal stress sigma1 = qu. Cohesion cu = q_u / 2 for saturated clay (phi = 0).
According to Cassagrande’s plasticity chart, the A-line separating clays from silts is given by the equation:
Cassagrande's A-line equation is IP = 0.73 * (LL - 20). Inorganic clays lie above the A-line, while inorganic silts and organic soils lie below it.
The vertical stress increments under a point load on soil surface at depth ‘z’ directly along the load axis as per Boussinesq equation is proportional to:
Boussinesq formula directly under point load Q (r=0) is sigma_z = (3 Q / (2 pi)) * (1 / z²). Thus vertical stress is inversely proportional to z².
The Muller-Breslau Principle for constructing influence lines is applicable to:
Muller-Breslau Principle states that the influence line for any stress resultants or reaction in an elastic structure is given by the deflected shape when a unit displacement is applied. It applies to both determinate and indeterminate elastic structures.
The maximum bending moment in a fixed beam of span ‘L’ carrying a uniformly distributed load ‘w’ over entire span occurs at supports and equals:
For a fixed beam under UDL w: Support fixed moments M_fixed = w * L² / 12 (hogging). Midspan moment M_center = w * L² / 24 (sagging).
In EDM distance measurement, the phase shift method measures distance by analyzing:
Phase shift EDM instruments continuously emit modulated wave signals and determine distance by measuring phase difference between transmitted and reflected waves.
In tachometric surveying, the multiplying constant (K) and additive constant (C) for a standard stadia tachometer with an anallactic lens are:
An anallactic lens (fitted inside telescope) eliminates the additive constant C (making C = 0) and maintains multiplying constant K = f/i = 100.
Contour lines crossing a natural valley or stream curve in the shape of a ‘V’ with their convexity pointing toward:
Contour lines cross a valley or stream in V-shapes with the vertex/convexity pointing upstream towards higher ground.
Laitance on a freshly hardened concrete surface is best defined as:
Laitance is a weak, non-durable layer of cement and fine particles brought to the concrete surface by bleeding water, which must be removed before placing new concrete.
The Self-Cleansing Velocity standardly required in municipal sewers to prevent deposition of solid silt is approximately:
To prevent organic and inorganic solids from settling, gravity sewers are designed for a minimum self-cleansing velocity of 0.60 m/s to 0.90 m/s at peak flow.
In water distribution networks, the Hardy Cross method uses which fundamental principle to balance loop flows?
Hardy Cross method enforces two conditions: (1) Total inflow = total outflow at each node, and (2) Sum of head losses around any closed pipe loop is zero.
The critical tractive force (shear stress) acting on an alluvial canal bed in Lacey’s regime theory is proportional to:
Hydrodynamic boundary shear stress acting on canal bed is tau_0 = gamma_w * R * S.
In welded steel connections, the effective throat thickness (t) of a fillet weld with leg size ‘s’ and fusion angle 90° is given by:
For a standard 90° fillet weld, throat thickness t = K * s = 0.7 * s.
In structural analysis, the Castigliano’s First Theorem states that first partial derivative of total strain energy with respect to displacement gives:
Castigliano's 1st Theorem: dU / d(delta_i) = P_i (Force). Castigliano's 2nd Theorem: dU / d(P_i) = delta_i (Displacement).
The Los Angeles Abrasion test on aggregates measures resistance against:
Los Angeles Abrasion test measures aggregate hardness and resistance to surface wear/abrasion caused by friction between steel balls and aggregate samples.
In geotechnical engineering, the Piping Failure under hydraulic structures like dams occurs when effective stress becomes zero due to:
Piping or quicksand condition occurs when upward seepage force equals buoyant weight of soil, making effective stress sigma' = 0 and washing away fine particles.