GATE Technical: Civil Engineering questions with solutions

Q1. For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity (E), Poisson’s ratio (ν), and shear modulus (G) is

1. G = E / 2(1+ν)
2. G = E / (1+2ν)
3. E = G / 2(1+ν)
4. E = G / (1+2ν)

Answer: G = E / 2(1+ν)

The relationship G = E / 2(1+ν) is derived from the definitions of Young's modulus, shear modulus, and Poisson's ratio for isotropic materials, showing how these properties interrelate under linear elastic behavior.

Q2. Match Column X with Column Y: Column X (P) Horton equation (Q) Penman method (R) Chezy’s formula (S) Lacey’s theory (T) Dicken’s formula Column Y (I) Design of alluvial channel (II) Maximum flood discharge (III) Evapotranspiration (IV) Infiltration (V) Flow velocity Which one of the following combinations is correct?

1. (P)-(IV), (Q)-(III), (R)-(V), (S)-(I), (T)-(II)
2. (P)-(III), (Q)-(IV), (R)-(V), (S)-(I), (T)-(II)
3. (P)-(IV), (Q)-(III), (R)-(II), (S)-(I), (T)-(V)
4. (P)-(III), (Q)-(IV), (R)-(I), (S)-(V), (T)-(II)

Answer: (P)-(IV), (Q)-(III), (R)-(V), (S)-(I), (T)-(II)

The correct option accurately matches each method or formula with its respective application: the Horton equation relates to infiltration, the Penman method is used for calculating evapotranspiration, Chezy’s formula determines flow velocity, Lacey’s theory is applied in the design of alluvial channels, and Dicken’s formula is used for calculating maximum flood discharge.

Q3. A process equipment emits 5 kg/h of volatile organic compounds (VOCs). If a hood placed over the process equipment captures 95% of the VOCs, then the fugitive emission in kg/h is

1. 0.25
2. 4.75
3. 2.50
4. 0.48

Answer: 0.25

The hood captures 95% of the 5 kg/h of VOCs, which means it allows 5% to escape. Calculating 5% of 5 kg/h gives 0.25 kg/h as the fugitive emission.

Q4. In a solid waste handling facility, the moisture contents (MC) of food waste, paper waste, and glass waste were found to be MCf, MCp, and MCg, respectively. Similarly, the energy contents (EC) of plastic waste, food waste, and glass waste were found to be ECpp, ECf, and ECg, respectively. Which of the following statement(s) is/are correct?

1. MCf > MCp > MCg
2. ECpp > ECf > ECg
3. MCf < MCp < MCg
4. ECpp < ECf < ECg

Answer: MCf > MCp > MCg

Food waste typically has a higher moisture content compared to paper and glass waste due to its organic nature, which retains more water. Therefore, the statement that the moisture content of food waste is greater than that of paper waste, which in turn is greater than that of glass waste, is accurate.

Q5. To design an optimum municipal solid waste collection route, which of the following is/are NOT desired:

1. Collection vehicle should not travel twice down the same street in a day.
2. Waste collection on congested roads should not occur during rush hours in morning or evening.
3. Collection should occur in the uphill direction.
4. The last collection point on a route should be as close as possible to the waste disposal facility.

Answer: Collection should occur in the uphill direction.

Collecting waste in the uphill direction is inefficient as it can increase travel time and fuel consumption, making the route less optimal compared to routes that allow for downhill travel.

Q6. Which of the following statement(s) is/are correct?

1. If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that point.
2. If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the load at any point is equal to the deflection at that point.
3. If a structure is acted upon by two force system Pₐ and P_b, in equilibrium separately, the external virtual work done by a system of forces P_b during the deformations caused by another system of forces Pₐ is equal to the external virtual work done by the Pₐ system during the deformation caused by the P_b system.
4. The shear force in a conjugate beam loaded by the M/EI diagram of the real beam is equal to the corresponding deflection of the real beam.

Answer: If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the load at any point is equal to the deflection at that point.

This statement is correct because it reflects the principle of virtual work in linear elasticity, where the change in strain energy with respect to an applied load gives the corresponding deflection at that point, demonstrating the relationship between load and displacement in elastic structures.

Q7. A tracer takes 100 days to travel from W well-1 to W well-2 which are 100 m apart. The elevation of water surface in W ell-2 is 3 m below that in W ell-1. Assuming porosity equal to 15%, the coefficient of permeability (expressed in m/day) is ________

1. (A) 0.30
2. (B) 0.45
3. (C) 1.00
4. (D) 5.00

Answer: (D) 5.00

Seepage velocity = 100 m / 100 days = 1 m/day; Darcy velocity = 1 * 0.15 = 0.15 m/day; hydraulic gradient = 3/100 = 0.03; permeability k = 0.15/0.03 = 5 m/day. The answer is 5.00, option 3, not 0.45.

Q8. The critical flow ratios for a three-phase signal are found to be 0.30, 0.25, and 0.25. The total time lost in the cycle is 10 s. Pedestrian crossings at this junction are not significant. The respective green times (expressed in seconds and rounded off to nearest integer) for the three phases are

1. (A) 34, 28, and 28
2. (B) 40, 25, and 25
3. (C) 40, 30, and 30
4. (D) 50, 25, and 25

Answer: (A) 34, 28, and 28

The correct option is right because the green times are calculated based on the critical flow ratios and the total cycle time, ensuring that the proportions of green time allocated to each phase correspond to their respective flow ratios while accounting for the total time lost.