Civil Engineering Paper I

(a) A frictionless pulley A as shown in the figure is supported by two bars AB and AC which are hinged at B and C to a vertical wall. A flexible cable, hinged at D, goes over the pulley and supports a load 30 kN at the other end E. The angles between the members are shown in the figure. Neglecting the size of the pulley, determine the forces in the bars AB and AC by drawing the free body diagram : [Figure in source booklet] (10 marks) (b) Draw the bending moment diagram and shear force diagram for the beam ABCD. The beam supports a point load of 12 kN as shown in the figure : [Figure in source booklet] (10 marks) (c) Determine the ‘shape factor’ for the diamond-shaped section shown in the figure : [Figure in source booklet] (10 marks) (d) A pretensioned beam 250 mm wide and 300 mm deep is prestressed by 12 wires (each 6 mm diameter) initially stressed to 1200 MPa with their centroid located at 100 mm from the soffit. Estimate the final percentage loss of stress due to elastic shortening, shrinkage, relaxation of steel and creep effect. Assume that the modulus of elasticity of steel and concrete are 210 kN/mm² and 35 kN/mm² respectively, creep coefficient = 1·6, residual shrinkage strain = 3×10⁻⁴ and relaxation of steel stress = 90 MPa. (10 marks) (e) A steel plate girder is subjected to a maximum factored shear force of 2800 kN. The cross-section of the girder is shown in the figure. Design a suitable fillet weld to connect flange plates to the web. Assume shop welding. E250 grade of steel having fu = 410 MPa is used. Use limit state method of design. Take γmw = 1·25 : [Figure in source booklet] (10 marks)

(a) Using limit state method, design a reinforced concrete circular column (with lateral ties) of height 3·0 m. It is subjected to an unfactored axial load of 1150 kN (dead load + live load). Use M25 grade of concrete and Fe500 grade of steel. Take effective length factor as 1·2. Show the design details in a neat sketch. (15 marks) (b) A straight bar of alloy is mounted in a strut-testing machine with both ends pin jointed and loaded axially till it buckles. Using Euler’s formula, calculate the maximum central deflection before the alloy material attains the yield point at 300 MN/m². Take bar length = 2·0 m, cross-section of the bar as 20 mm × 15 mm and modulus of elasticity E as 90 GN/m². (15 marks) (c) Using moment distribution method, analyse the structure ABCD shown in the figure (joint B is rigid). The loading on the structure, moment of inertia of the members and other dimensions are clearly mentioned in the figure. Give neat sketch of bending moment and shear force diagram, indicating their values in the diagram : [Figure in source booklet] (20 marks)

(a) A vertical member in a truss is subjected to the following member force (factored) : (i) Compressive force = 30 kN (dead and live load) (ii) Tensile force = 150 kN (dead and wind load) The member is composed of two numbers ISA 100 × 100 × 8 connected to both sides of the gusset plate of thickness 10 mm. Find the number of bolts required at the joint. Assume bolt diameter = 16 mm, grade of bolt = 4·6, γmb = 1·25, kb = 0·6, cross-sectional area at the threaded part of the bolt = 0·78 times that of shank. Use limit state method of design. (10 marks) (b) The given figure shows the shear force diagram for a beam ABCDEF. The beam has hinge support at A and at one more point. Draw the load diagram and bending moment diagram (BMD) for this beam, indicating the shape of BMD between two successive points. Also show the point of contraflexure (if any) : [Figure in source booklet] (20 marks) (c) A reinforced concrete passenger shelter is to be constructed as shown in the figure. The thickness of the slab is 150 mm. The ceiling plaster and roof finish load is 1·5 kN/m². The roof is inaccessible. Design and detail the slab only. Use M20 grade concrete and Fe500 grade steel. Use limit state method. Given : Mu/bd² | 0·3 | 0·4 | 0·5 | 0·6 | 0·7 | 0·8 | 0·9 | 1·0 pt (%) | 0·07 | 0·094 | 0·119 | 0·143 | 0·168 | 0·193 | 0·219 | 0·245 Modification Factor vs. Percentage Tension Reinforcement graph is given below : [Figure in source booklet] (20 marks)

(a) Three bodies of weights 200 N, 800 N and 400 N are connected with inextensible strings, passing over the frictionless pulleys as shown in the figure. Using virtual work method, determine the force F required to make the motion impending to the left. Take coefficient of friction for all the contacting surfaces as 0·30 except for the pulleys which are frictionless : [Figure in source booklet] (10 marks) (b) (i) A simply supported beam ISMB 400 @ 61·6 kg/m has an effective span of 5 m. Find the design bending strength of the beam and the intensity of u.d.l. that the beam can carry under service condition. Assume that the beam is laterally supported. The grade of the steel is E250. The class of section is plastic. For ISMB 400, Izz = 20458 cm⁴, Zez = 1023 cm³, Zpz = 1176 cm³. Assume γm0 = 1·1. Use limit state method of design. (10 marks) (ii) Develop the stiffness matrix for the beam element AB with respect to the coordinates ① and ② as shown in the figure. Take modulus of elasticity and moment of inertia of beam section as E and I respectively : [Figure in source booklet] (10 marks) (c) For an industrial building, a gantry girder (without lateral restraint along its span) is designed to carry an overhead travelling crane for the following data : Centre-to-centre distance between columns (i.e., span of the gantry girder) = 7·5 m Crane capacity = 200 kN Self-weight of the crane girder excluding trolley = 200 kN Self-weight of trolley, electric motor, hook, etc. = 40 kN Minimum hook approach = 1·2 m Distance between wheel centres = 3·5 m Centre-to-centre distance between gantry rails (i.e., span of the crane) = 15 m Self-weight of the rail section = 300 N/m Yield stress of steel = 250 MPa Data analysis provided the following information : Total vertical design bending moment (including the bending moment due to drag), Mz = 685·53 kN-m Horizontal design bending moment (due to surge load), My = 19·84 kN-m Based on the analysis and other governing criteria, for the design of gantry girder, it was decided to use ISMB 600 @ 1230 N/m with a channel ISMC 300 @ 363 N/m at the top as shown in the figure : (All dimensions are given in mm) The properties of the sections are as follows : ISMB 600 @ 1230 N/m: A = 15600 mm², tf = 20·8 mm, tw = 12 mm, Width of flange, B = 210 mm, Izz = 91800×10⁴ mm⁴, Iyy = 2650×10⁴ mm⁴, Radius at root, R = 20 mm ISMC 300 @ 363 N/m: A = 4630 mm², tf = 13·6 mm, tw = 7·8 mm, B = 90 mm, Izz = 6420×10⁴ mm⁴, Iyy = 313×10⁴ mm⁴, Centre of gravity, Cyy = 23·5 mm Check the adequacy of the chosen section for the moment capacity. Assume any other data suitably. [Figure in source booklet] (20 marks)

(a) A free jet of water with constant cross-section area of 0·01 m² is deflected by a hinged plate of length 2·0 m, supported by a spring with spring constant k = 500 N/m and uncompressed length x0 = 1·0 m as shown in the figure. If the density of water is 1000 kg/m³ and the deflection angle is θ = 5°, determine the jet velocity. Assume steady-state condition and neglect the weight of fluid and the weight of the plate within the control volume considered in this case : [Figure in source booklet] (10 marks) (b) The nominal flow rate of water over a weir is 2 m³/s. A 1 : 10 scale model of the weir is tested in a water channel. Answer the following : (i) What is the expected flow rate for the model? (ii) If a force of 12 N is measured on the model, what force would be expected on the prototype? (10 marks) (c) A venturi flume, 3·0 m wide at the entrance and 1·5 m wide at the throat, has a horizontal datum. If the depth of water at the entrance and at the throat is 0·75 m and 0·65 m respectively, calculate the theoretical discharge through the venturi flume. If a 0·2 m high streamlined hump is provided at the base so that a standing wave is formed downstream of the throat, calculate the specific energy and upstream depth for the same discharge. (10 marks) (d) The shrinkage limit test was conducted in a laboratory and the following results were obtained : Initial mass of saturated clay = 45·0 g Final mass of dry clay pat = 31·2 g Initial volume of soil in saturated state = 24·8 cc Final volume of dry clay pat = 16·1 cc Determine the following properties of the soil, if the soil is at water content of 28·5% : (i) Shrinkage limit (ii) Shrinkage ratio (iii) Specific gravity of soil solids (iv) Maximum volumetric shrinkage (v) Linear shrinkage (10 marks) (e) An RCC pile of 15 m overall length is driven into a deep stratum of soft clay with unconfined compressive strength of 40 kPa. The diameter of the pile is 300 mm. Determine the safe load which can be carried by the pile. Assume factor of safety as 2·5 and adhesion factor as 0·85. If the weight of the pile is 27 kN, what will be the ultimate uplift capacity under undrained condition? Assume coefficient k as 0·7. (10 marks)

(a) Assuming the law for the velocity distribution in the boundary layer as v/V = 2(y/δ) − (y/δ)², derive an expression for the thickness of boundary layer. Hence calculate the thickness of boundary layer at a point 2·5 m from the leading edge of a plate, if the size of the plate is 3·0 m long and 1·25 m wide, and it is immersed in the water moving at a velocity of 0·3 m/s. Take viscosity of water equal to 0·001 N-s/m². [Notations used in the above expression have their usual meanings] (15 marks) (b) Water flows in a triangular channel having side slope 1 Horizontal : 1 Vertical and longitudinal slope of 0·001. Estimate whether the channel is mild, steep or critical sloped when a discharge of 0·2 m³/s flows through it. Assume Manning’s coefficient n = 0·015. Also, determine for what range of depths, the flow will be on type 1, 2 and 3 curve. (15 marks) (c) (i) A retaining wall 5 m high with a smooth vertical back is pushed against a soil mass. What is the total passive pressure, if the horizontal soil surface carries a uniform load of 60 kN/m²? Also, determine the location of resultant thrust, where it is acting. The properties of the soil are as follows : Effective cohesion = 35 kPa Effective angle of shearing resistance = 20° Bulk density = 19·5 kN/m³ (10 marks) (ii) Discuss the effect of earthquake forces on the stability of earth dams. (10 marks)

(a) The data with respect to a normally consolidated clay are as follows : Thickness of the clay layer = 3·0 m Initial void ratio = 0·75 Liquid limit = 50% Effective overburden pressure on the clay layer = 130 kN/m² Increment of effective pressure on the clay layer = 50 kN/m² Secondary compression index, Cα = 0·02 Time for completion of primary settlement = 2·0 years What will be the consolidation settlement of the clay layer, six years after the completion of primary consolidation settlement? (15 marks) (b) The plan of a foundation is shown in the figure. The uniform load intensity on the soil is 100 kN/m². Determine the vertical stress increment at a depth 4 m below the point O, using Boussinesq’s method : [Figure in source booklet] (15 marks) (c) Oil of specific gravity of 0·8 and kinematic viscosity of 1·5×10⁻⁴ m²/s is pumped at a rate of 0·015 m³/s through a 150 mm diameter, 325 m long pipe. Determine the Reynolds’ number, pressure drop, average shear stress at the pipe wall and power required to maintain flow under the following conditions : (i) If the pipe is horizontal (ii) If the pipe is inclined at 10° with the horizontal and the flow is in the upward direction (20 marks)

(a) Consolidated drained tests on clay specimens were performed and the following results were obtained : Specimen No. | Confining pressure (kPa) | Axial load (N) | Axial deformation (mm) | Volume change (cc) 1 | 200 | 410 | 11·0 | 7·0 2 | 400 | 850 | 12·3 | 8·5 3 | 600 | 1275 | 14·6 | 10·0 The initial diameter and length of saturated clay sample were 38 mm and 76 mm respectively. Determine the shear parameters in terms of total stress and effective stress. Also, comment on the results obtained and its application. (15 marks) (b) What is vibroflotation technique? The results of sieve analysis for the backfill material used in a vibroflotation project are as follows : IS sieve | Mass of the soil retained (g) 4·75 mm | 9·40 2·36 mm | 54·00 1·18 mm | 78·20 600 µm | 83·10 300 µm | 86·20 150 µm | 75·30 75 µm | 13·80 Determine the suitability number. What would be its rating as a backfill? (15 marks) (c) (i) A Francis turbine has a speed of 300 r.p.m. The inlet diameter of the turbine is 1·20 m and its width is 280 mm at the inlet. The vane thickness coefficient can be taken as 0·95. If at the inlet, the guide vane angle is 30° and the blade angle is 90°, determine the power produced by assuming an overall efficiency of 90%. Assume radial discharge at the outlet and take density of water as 1000 kg/m³. (15 marks) (ii) What is the significance of curves of constant stream function (CSF)? Explain why the stream function is useful in fluid mechanics. (5 marks)