GATE Technical: Civil Engineering Set 2 (CE 2) questions with solutions

Q1. For a thin-walled section shown in the figure, points P, Q, and R are located on the major bending axis X - X of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section. Qualitatively, the shear center of the section lies at

1. P
2. Q
3. R
4. S

Answer: S

The shear center is the point where the applied load does not cause any twisting of the section; it is typically located at the intersection of the web and the flange, which in this case is point S.

Q2. Consider the following data for a project of 300 days duration. Budgeted Cost of Work Scheduled (BCWS) = Rs. 200 Budgeted Cost of Work Performed (BCWP) = Rs. 150 Actual Cost of Work Performed (ACWP) = Rs. 190 The ‘schedule variance’ for the project is

1. (−) Rs. 50
2. (−)50 days
3. (+) Rs. 50
4. (+)50 days

Answer: (−) Rs. 50

The schedule variance is calculated by subtracting the Budgeted Cost of Work Scheduled (BCWS) from the Budgeted Cost of Work Performed (BCWP). In this case, BCWP (Rs. 150) minus BCWS (Rs. 200) results in a negative variance of Rs. 50, indicating that the project is behind schedule.

Q3. The structural design method that DOES NOT take into account the safety factors on the design loads is

1. working stress method.
2. load factor method.
3. ultimate load method.
4. limit state method.

Answer: working stress method.

The working stress method is based on the elastic behavior of materials and uses allowable stress limits without incorporating safety factors for design loads, unlike the other methods which account for uncertainties and safety.

Q4. Which one of the following saturated fine-grained soils can attain a negative Skempton’s pore pressure coefficient (A)?

1. Quick clays
2. Normally-consolidated clays
3. Lightly-consolidated clays
4. Over-consolidated clays

Answer: Over-consolidated clays

Over-consolidated clays can exhibit a negative Skempton’s pore pressure coefficient because they have experienced higher pressures in the past, leading to a reduction in pore water pressure during loading, which can result in negative pore pressure responses.

Q5. The following figure shows a plot between shear stress and velocity gradient for materials/fluids P, Q, R, S, and T. Which one of the following options is CORRECT?

1. P → Ideal Fluid; Q → Ideal Bingham plastic R → Non-Newtonian fluid; S → Newtonian fluid
2. P → Real solid; Q → Ideal Bingham plastic S → Newtonian fluid; T → Ideal Fluid
3. P → Ideal Fluid; Q → Ideal Bingham plastic R → Non-Newtonian fluid; T → Real solid
4. P → Real solid; Q → Newtonian fluid R → Ideal Bingham plastic; T → Ideal Fluid

Answer: P → Ideal Fluid; Q → Ideal Bingham plastic R → Non-Newtonian fluid; T → Real solid

The correct option accurately categorizes the materials based on their behavior in response to shear stress and velocity gradient, identifying P as an ideal fluid that exhibits no viscosity, Q as an ideal Bingham plastic which requires a yield stress to flow, R as a non-Newtonian fluid that does not have a constant viscosity, and T as a real solid that does not flow under shear stress.

Q6. Which one of the following products is NOT obtained in anaerobic decomposition of glucose?

1. CO2
2. CH4
3. H2S
4. H2O

Answer: H2O

During anaerobic decomposition of glucose, the primary products are gases like carbon dioxide (CO2), methane (CH4), and sometimes hydrogen sulfide (H2S), but water (H2O) is not produced as a direct result of this process.

Q7. For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of 1:13000 using a camera. If the permissible flying height is assumed as 3000 m above a datum and the average terrain elevation is 1050 m above the datum, the required focal length (in mm) of the camera is

1. 100
2. 150
3. 125
4. 200

Answer: 150

The required focal length can be calculated using the formula that relates scale, flying height, and terrain elevation. With a flying height of 3000 m and an average terrain elevation of 1050 m, the effective flying height becomes 1950 m. Using the scale of 1:13000, the focal length is determined to be 150 mm, which is consistent with the given parameters.

Q8. What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them? Instruments/Parts of instruments | Operations P - Bubble tube | i - Tacheometry Q - Plumb bob | ii - Minor movements R - Tangent screw | iii - Centering S - Stadia cross-wire | iv - Levelling

1. P-ii, Q-iii, R-iv, S-i
2. P-iv, Q-iii, R-ii, S-i
3. P-i, Q-iii, R-ii, S-iv
4. P-iii, Q-iv, R-i, S-ii

Answer: P-iv, Q-iii, R-ii, S-i

The bubble tube is used for levelling (P-iv) to ensure the instrument is horizontal, the plumb bob aids in centering (Q-iii) by providing a vertical reference, the tangent screw allows for minor movements (R-ii) to make precise adjustments, and the stadia cross-wire is utilized in tacheometry (S-i) for distance measurement.

Q9. To finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors observed the bearing to a tower located at station Q with the same instrument without shifting it. The bearings observed by the surveyors are 30° 30′ 00″, 30° 29′ 40″, 30° 30′ 20″ and 30° 31′ 20″. Assuming that each measurement is taken with equal precision, the most probable value of the bearing is

1. 30° 29′ 40″
2. 30° 30′ 20″
3. 30° 30′ 00″
4. 30° 31′ 20″

Answer: 30° 30′ 20″

The most probable value of equally precise observations is their mean. Relative to 30deg30'00'', the seconds are 0, -20, +20, +80, summing to +80, mean +20'', i.e., 30deg30'20''. That is option index 1. The stored answer 30deg30'00'' (index 2) is wrong; correct is 30deg30'20''.

Q10. A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam as shown in the figure. The natural frequency of this system is

1. √((kl³ + 6EI)/(ml³))
2. √((kl³ + 48EI)/(ml³))
3. √((6EIk)/(k l³ + 6EI)m)
4. √((48EIk)/(k l³ + 48EI)m)

Answer: √((48EIk)/(k l³ + 48EI)m)

The correct option reflects the relationship between the stiffness of the spring and the beam's flexural rigidity, incorporating the effects of both components on the system's natural frequency. The factor of 48 arises from the specific boundary conditions and mode shapes associated with the beam's deflection under the applied load, leading to a more accurate representation of the dynamic behavior.

Q11. Consider the statements P and Q related to the analysis/design of retaining walls. P: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobilizes in upward direction along the wall. Q: Most of the earth pressure theories calculate the earth pressure due to surcharge by neglecting the actual distribution of stresses due to surcharge. Which one of the following options is CORRECT?

1. Both P and Q are TRUE
2. P is TRUE and Q is FALSE
3. Both P and Q are FALSE
4. P is FALSE and Q is TRUE

Answer: Both P and Q are TRUE

Both statements are accurate; P correctly describes the behavior of wall friction in response to movement, while Q highlights a common simplification in earth pressure theories regarding surcharge effects.

Q12. A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: 1.50), silica sand (specific gravity: 2.60), and ilmenite sand (specific gravity: 4.20), is to be designed for treating wastewater. After back washing, the particles should settle forming three layers: coarse anthracite particles at the top of the bed, silica sand in the middle, and small ilmenite sand particles at the bottom of the bed. Assume (i) Slow discrete settling (Stoke's law is applicable) (ii) All particles are spherical (iii) Diameter of silica sand particles is 0.20 mm The CORRECT option fulfilling the diameter requirements for this filter media is

1. diameter of anthracite particles is slightly less than 0.35 mm and diameter of ilmenite particles is slightly greater than 0.41 mm.
2. diameter of anthracite particles is slightly greater than 0.35 mm and diameter of ilmenite particles is slightly less than 0.41 mm.
3. diameter of anthracite particles is slightly less than 0.64 mm and diameter of ilmenite particles is slightly less than 0.10 mm.
4. diameter of anthracite particles is slightly greater than 0.64 mm and diameter of ilmenite particles is slightly less than 0.10 mm.

Answer: diameter of anthracite particles is slightly greater than 0.35 mm and diameter of ilmenite particles is slightly less than 0.41 mm.

The correct option indicates that the anthracite particles must be larger than the silica sand to ensure they settle on top, while the ilmenite particles need to be smaller than the silica sand to settle below it, aligning with the principles of particle settling based on specific gravity.

Q13. In the context of pavement material characterization, the CORRECT statement(s) is/are

1. The load penetration curve of CBR test may need origin correction due to the non-vertical penetrating plunger of the loading machine.
2. The toughness and hardness of road aggregates are determined by Los Angeles abrasion test and aggregate impact test, respectively.
3. Grading of normal (unmodified) bitumen binders is done based on viscosity test results.
4. In compacted bituminous mix, Voids in the Mineral Aggregate (VMA) is equal to the sum of total volume of air voids (Vv) and total volume of bitumen (Vb).

Answer: The load penetration curve of CBR test may need origin correction due to the non-vertical penetrating plunger of the loading machine.

The load penetration curve of the California Bearing Ratio (CBR) test may require origin correction because the angle of the plunger affects the accuracy of the load measurements, leading to potential misinterpretation of the material's strength characteristics.