UPSC Civil Engineering 2024 — Paper I

(a) A cantilever beam ABCD, as shown in the above figure, is carrying a uniformly distributed load of 10 kN/m between B & C and a clockwise moment of 50 kN-m at free end D. Draw the free body diagram for A, D and for the member BC only. (10 marks) (b) Cross-section of an axially loaded compression member is shown in the above figure. This compression member was to be loaded at centre 'O' of the Section. Due to mistake this was loaded at point 'P' by a concentrated load of 500 kN. Find out the stresses at points A, B, C and D of the Section. (10 marks) (c) A uniformly distributed load of 20 kN/m intensity and 6 m length moves over a simply supported girder of 30 m span. What will be the maximum bending moment at a section 6 m from the left support A ? (10 marks) (d) Determine the maximum permissible load (P) on the bolt A. Assume the Bolt value as 45·3 kN. (10 marks) (e) What are the functions of transverse reinforcement in a reinforced concrete column ? (10 marks)

(a) A cantilever beam ABC as shown in the above figure is having a total span of 2·0 m. The maximum safe allowable bending stress is 7500 kN/m² for the material. Find the maximum safe uniformly distributed load which this beam can carry. What will be the maximum shear stress at support A for the obtained safe UDL ? (Neglect the self weight of beam) (20 marks) (b) From first principles, derive the expression for determining the depth of neutral axis, for a rectangular reinforced concrete section without compression reinforcement, as per Limit State Method. Use the stress-strain curves for concrete and reinforcing bars shown in the Figs. 1 and 2. (10 marks) (c) Two angles ISA 100×100×12 mm transmit an ultimate tensile force of 540 kN, acting through the C.G. of angle sections as shown in the Figure. The angles are connected to the gusset plate on either side by welding. Design the lengths l₁ and l₂ of the weld if the size of the fillet weld is 6 mm, fᵤ = 410 MPa, partial safety factor for the weld γₘw = 1·25. Relevant portion of the IS 800 : 2007 is enclosed. (20 marks)

(a) A box culvert ABCD is shown in the above figure. By using member fixed end moments given above; calculate the final end moments in the box culvert using "Moment distribution method." Also sketch these moments only. (20 marks) (b) 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 b_f = 1400 mm Breadth of web b_w = 300 mm Effective depth of the T-beam d = 455 mm Overall depth of the T-beam D = 500 mm Depth of flange D_f = 125 mm Use M25 grade concrete and Fe 500 grade steel. Relevant portion of the IS 456 : 2000 is enclosed. (20 marks) (c) A 10 mts long steel pipe is simply supported at both ends. It is having 500 mm external diameter and 20 mm thickness. It is carrying a total uniformly distributed load of 100 kN/m (including the self weight). Calculate the maximum deflection of the pipe. Take E = 200 GPa. (10 marks)

(a) A prestressed concrete T-beam having the cross-section of flange 1500 mm wide and 200 mm thick, rib of 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 18 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 net stresses are equal to zero and 5 MPa respectively at top and bottom fibres of the beam. The unit weight of concrete is 25 kN/m³. (20 marks) (b) A pin jointed, symmetrically loaded, truss 'ABCDE' is shown in the above figure. Cross-sectional area of each member is 500 mm² and E = 200 GPa. Forces in the members meeting at joint C are also shown in the figure. Calculate the vertical deflection of joint C by unit load method. (20 marks) (c) What are the different modes of failure of a structural steel tension member ? Explain with sketches. (10 marks)

(a) A 125 mm diameter vertical cylinder rotates concentrically inside a fixed cylinder of diameter 130 mm. Both cylinders are 325 mm long. Find the dynamic viscosity of the liquid that fills the space between the cylinders, if a torque of 0·92 Nm is required to maintain a speed of 70 r.p.m. (10 marks) (b) Calculate the friction drag on a flat plate 15 cm wide and 45 cm long placed longitudinally in a stream of oil of relative density 0·925 and kinematic viscosity 0·9 stoke, flowing with a free stream velocity of 6 m/s. Also find the thickness of the boundary layer and shear stress at the trailing edge. Take density of water 1000 kg/m³. (10 marks) (c) A large tank as shown in the above figure has a vertical pipe 70 cm long and 2 cm in diameter. The tank contains an oil of density 920 kg/m³ and viscosity 1·5 poise. Find the discharge through the pipe when the height of the oil level of the tank is 0·80 m above the pipe inlet. (10 marks) (d) A field density test was conducted by core-cutter method and the following data was obtained: Weight of empty core-cutter = 23 N Weight of soil and core-cutter = 50 N Dimensions of the core-cutter dia = 90 mm and height = 180 mm Weight of wet sample for moisture determination = 55×10⁻² N Weight of oven dry sample = 52×10⁻² N Specific gravity of soil grains = 2·70 Determine its dry density, void ratio and degree of saturation. (10 marks) (e) Two plate load tests were conducted at a site – one with a 300 mm square plate and other with a 600 mm square test plate. For a settlement of 25 mm the loads were found to be 21·6 kN and 64·8 kN respectively in the two tests. Determine the allowable bearing pressure of the sand and the load which a square footing 1·5 m×1·5 m can carry with the settlement not exceeding 25 mm. (10 marks)

(a) 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. (15 marks) (b) The stream function for a two-dimensional flow is given by ψ = 2xy. Calculate the velocity and velocity potential at point P(2, 3). (15 marks) (c) A group of nine friction piles is driven through 5 m of clay with unconfined compressive strength of 60 kN/m² followed by 10 m of clay with unconfined compressive strength of 100 kN/m². The piles are in 3 rows and will be 1·00 m centres in a row and the rows will be 750 mm on centres. Each pile has a diameter of 300 mm. If a factor of safety of 2·5 is required, determine the maximum load that can be carried by the group. Take Nc = 9 and unit weight of clay as 16·4 kN/m³. (20 marks)

(a) 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. (15 marks) (b) The soil profile at a building site consists of dense sand up to 3 m depth, normally loaded soft clay from 3 m to 8 m depth and stiff impervious rock below 8 m depth. The ground water table is at 0·60 m depth below ground level. The sand has a density of 18·6 kN/m³ above water table and 19·2 kN/m³ below water table. For the clay, natural water content is 50%, liquid limit is 70% and specific gravity is 2·70. Calculate the probable ultimate settlement resulting from a uniformly distributed surface load of 50 kN/m² applied over an extensive area of the site. (15 marks) (c) The flow of water in a canal varies from 425 l/s to 680 l/s. It is desired to discharge not less than 340 l/s of water and not more than 425 l/s over a 90° V-notch weir into one channel, while the remainder goes over a sharp-crested rectangular weir. Find the length of rectangular weir and maximum head on each weir. Take C_d = 0·58 for both weirs. (20 marks)

(a) 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. (15 marks) (b) A particular soil failed under a major principal stress of 600 kN/m² with a corresponding minor principal stress of 200 kN/m². If for the same soil, the minor principal stress had been 300 kN/m², determine what the major principal stress would have been if (i) φ = 35° and (ii) φ = 0°. (15 marks) (c) An inward flow reaction turbine works under a head of 30 m and discharge of 10 m³/s. The speed of runner is 300 r.p.m. At the inlet tip of runner vane, the peripheral velocity of wheel is 0.9√2gH and the radial velocity of flow is 0.3√2gH, where H is the head on the turbine. If the overall efficiency and the hydraulic efficiency of the turbine are 80% and 90% respectively, determine : (i) the power developed in kw (ii) diameter and width of runner at inlet (iii) guide blade angle at inlet (iv) inlet angle at runner vane Assume that the discharge at outlet is radial. (20 marks)