6 questions from the UPSC 2024 examination.
6 questions
A 125 mm diameter vertical cylinder rotates concentrically inside a fixed cylinder of diameter 130 mm. Both cylinders are 325 mm long. If a torque of 0·92 Nm is required to maintain a speed of 70 r.p.m., find the dynamic viscosity of the liquid that fills the space between the cylinders. <!--qid:MAINS_2024_Civil_Engineering-I_Q5-->
Design only the flexural reinforcement for a T-beam section to resist a service moment of 200 kNm. The details of the section are given below: Breadth of flange bf = 1400 mm Breadth of web bw = 300 mm Effective depth of the T-beam d = 455 mm Overall depth of the T-beam D = 500 mm Depth of flange Df = 125 mm Use M25 grade concrete and Fe 500 grade steel. Relevant portion of IS 456 : 2000 is enclosed. <!--qid:MAINS_2024_Civil_Engineering-I_Q3-->
A retaining wall 8 m high, with a smooth vertical back is pushed against a soil mass having c = 50 kN/m², φ = 15° and unit weight 18 kN/m³. It carries a surcharge of 40 kN/m² uniformly on its top surface. Draw the passive pressure distribution diagram and find the point of application of the resultant thrust. <!--qid:MAINS_2024_Civil_Engineering-I_Q8-->
A canal is to be excavated through a soil with c = 20 kN/m², φ = 20°, e = 0·80 and G = 2·70. The side slope is 1 in 1. The depth of the canal is to be 8 m. Determine the factor of safety with respect to cohesion when the canal runs full. What will be the factor of safety if the canal is rapidly emptied? For β = 45°, the stability number for various φ values are as given above. <!--qid:MAINS_2024_Civil_Engineering-I_Q7-->
The resistance force F of a ship is a function of its length L, velocity V, acceleration due to gravity g and fluid properties like density ρ and viscosity μ. Write this relationship in a dimensionless form. <!--qid:MAINS_2024_Civil_Engineering-I_Q6-->
A prestressed concrete T-beam having the cross-section of flange 1500 mm wide and 200 mm thick, rib 300 mm wide and 1200 mm deep. The beam carries a live load of 20 kN/m apart from its dead load, over a simply supported span of 20 m. The beam is prestressed with a straight cable having constant eccentricity ‘e’. Assume the losses of prestress as 16 %. Determine the initial prestressing force ‘Pi’ and its eccentricity ‘e’, if the permissible stresses are equal to zero tension and 5 MPa respectively at top and bottom fibres of the beam. The unit weight of concrete is 25 kN/m³. <!--qid:MAINS_2024_Civil_Engineering-I_Q4-->