GATE CE format:nat PYQs & Answers — Page 8

Questions 71–80 of 495. Imported answers require independent review unless marked reviewed.

Topic practice 495 questionsPage 8 of 50

A steel beam supported by three parallel pin-jointed steel rods is shown in the figure. The moment of inertia of the beam is

. Take modulus of elasticity of steel as 210 GPa. The beam is subjected to uniform distributed load of 6.25 kN/m, including its self-weight. The axial force (in kN) in the centre rod CD is _____ (round off to one decimal place).

Diagram for Civil Engineering question 52

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Consider the beam section shown in the figure, with

indicating the depth of neutral axis (NA). The section is only subjected to an increasing bending moment. It is given that

mm, when the section has not yielded at the top and bottom fibres. Further,

decreases to 5 mm, when the entire section has yielded. The shape factor of the section is ____________ (rounded off to 2 decimal places).

Diagram for Civil Engineering question 53

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The figure shows a network diagram for a construction project. The activities A, B, C, D, E, and F are represented by arrows and their durations are in the figure.

The total float available for the activity E in day(s) is equal to _____ (round off to the nearest integer).

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Consider the built-up column made of two I-sections as shown in the figure, with each batten plate bolted to a component I-section of the column through 6 black bolts. Each connection of the batten plate with the component section is to be designed for a longitudinal shear of 70 kN and moment of 10 kN.m. The minimum bolt value required (in kN) is ____________ (rounded off to the nearest integer).

Diagram for Civil Engineering question 54

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A reinforced concrete beam has a support section with width of 300 mm and effective depth of 500 mm. The support section is reinforced with 3 bars of 20 mm diameter at the tension side. Two-legged vertical stirrups of 10 mm diameter and Fe415 steel at a spacing of 100 mm are provided as shear reinforcement. Assume that there is no possibility of diagonal compression failure at the section.

As per IS 456:2000, the maximum shear resisted by the vertical stirrups (in kN), as per limit state design, is __________ (round off to one decimal place).

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A cut slope is made in a silty clay soil for a new road project, as shown in the figure. The locations of ground water table (GWT) and potential failure surface are shown in the figure. After the cut is made, the excess pore water pressure is fully dissipated, and the shear stress at the point A is 60 kN/m². The factor of safety at the point A for long-term stability is __________________ (rounded off to 2 decimal places).

Note:

Shear strength properties of silty clay: c′ = 15 kN/m², ϕ′ = 15°, and cᵤ = 75 kN/m²

Unit weight of soil above the GWT (γ) = 19 kN/m³

Unit weight of soil below the GWT (γₛₐₜ) = 20 kN/m³

Unit weight of water (γw) = 9.81 kN/m³

Diagram for Civil Engineering question 55

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The bank of a canal has the profile shown in the figure. The material is a homogeneous clay with a bulk unit weight of 20 kN/m³, undrained cohesion of 30 kPa and it is fully saturated (φᵤ = 0). For the trial slip circle shown, the area ABCDE is 150 m² and the centroid is at P. A tension crack (DE) of 2.5 m deep was also observed. Assume unit weight of water is 9.81 kN/m³ and consider 1 m run of the bank for the analysis.

Considering the canal is empty and tension crack is completely filled with water, the factor of safety against slope failure of the bank is _____ (round off to two decimal places).

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A 6 m × 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi’s bearing capacity theory, the factor of safety of footing against the bearing capacity failure is __________ (rounded off to 2 decimal places).

Note:

Unit weight of concrete = 24 kN/m³

Properties of clay: c = 50 kN/m², ϕ = 0°, and γ = 19 kN/m³

For ϕ = 0°: N꜀ = 5.7, Nq = 1, Nγ = 0

Diagram for Civil Engineering question 56

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A designer used plate load test to obtain the value of the bearing capacity factor Nᵧ. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m³. The plate is loaded to failure at a pressure of 150 kPa.

Considering Terzaghi’s bearing capacity theory, the bearing capacity factor Nᵧ is _____ (round off to the nearest integer).

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A clayey soil has a moisture content of 18%, a specific gravity of soil solids of 2.74, and a degree of saturation of 65%. The soil soaks up water during a rain event, and the degree of saturation increases to 85.2%. The change of the volume during the soaking is negligible. The new moisture content (in %) of the soil will be ____________________ (rounded off to 2 decimal places).

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GATE CE format:nat PYQs

Question 52

Question 53

Question 53

Question 54

Question 54

Question 55

Question 55

Question 56

Question 56

Question 57