Finite Element Methods B.Tech Question Paper : vardhaman.org
College : Vardhaman College Of Engineering
Degree : B.Tech
Department :Mechanical Engineering
Semester : VI
Subject : Finite Element Methods
Document type : Question Paper
Website : vardhaman.org
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May- 2014 :https://www.pdfquestion.in/uploads/vardhaman.org/6385-BT6RMAY14.pdf
Finite Element Methods Question Paper :
Four Year B. Tech VI Semester Regular Examinations June – 2014
(Regulations: VCE-R11)
(Mechanical Engineering)
Date: 5 June, 2014
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
Related : Vardhaman College Of Engineering Heat Transfer B.Tech Question Paper : www.pdfquestion.in/6384.html
All parts of the question must be answered in one place only
Unit – I :
1. Consider the bar element as shown in the Fig.1. An axial load P = 200x103N is applied as shown. Using the penalty approach for handling boundary conditions do the following: 15M
i. Determine the nodal displacements
ii. Determine the stress in each material
A1 = 2400mm , 2 2 A = 600mm , 9 2 1 E = 70?10 N / m , 9 2 2 E = 200?10 N / m 15M
2. a) Compare FEM with other methods in terms of efficiency and performance. 7M
b) Enumerate the applications of FEM in various facets of the industry. 8M
Unit – II :
3. a) Write difference between the plane trusses and space trusses. 3M
b) For two bar truss shown in Fig.2, Determine displacement at node and stresses in both elements. Take E = 2×105 N/mm2.
4. a) Derive Hermit shape function for linear bar element. 7M
b) A cantilever beam subjected to point load of 250KN as shown in Fig. 3. Determine the slope and deflection at the load application point. Take E = 200 GPa and I = 4×104 mm4.
Unit – III :
5. a) Explain convergence criterion. 8M
b) What are iso parametric, sub parametric and super parametric elements? 7M
6. a) Integrate I= 1 = 1 11 (1 ?? 2? )d?d? by using Gaussian two point method and compare the solution with convention method. 8M
b) Explain the shape functions for CST element. 7M
Unit – IV :
7. A long bar of rectangular cross section having thermal conductivity of 1.5 W/m0C is subjected to the boundary conditions as shown in Fig.4. Two opposite sides are maintained at a uniform temperature of 1800C, one side is insulated and the remaining side is subjected to a convection process with T8 = 250C an h = 50W/m2. 0C. Determine the temperature distribution in the bar.15M
8. Consider the shaft with rectangular cross section as shown in Fig.5. Determine in terms of M and G, the angle of twist per unit length. 15M
Unit – V :
9. Determine the eigen values and eigen vectors for the stepped bar as shown in Fig.6. E = 30?106 psi Specific weight f = 0.283
10. Derive the following equation KU = ?2 MU for a solid body with distributed mass. 15M
Design Of Machine Members-II :
(Mechanical Engineering)
Date: 31 May, 2014
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only :
Unit – I :
1. a) State any five desirable properties of a good bearing materials. 5M
b) A lightly loaded journal bearing has a load of 1 kN. The oil used is SAE 60 and mean effective temperature of operation is 40° C. The journal has a diameter of 50 mm and the bearing has a diameter of 50.5 mm. The speed of the journal is 15000 rpm. The L/d ratio s limited to 1.2. Determine the coefficient of friction and power loss. 10M
2. a) Define equivalent dynamic load in rolling contact bearing and explain briefly. 5M
b) A ball bearing is operating on a work cycle consisting of three parts, i) A radial load of 3000 N at 1440 rpm for ONE quarter cycle, ii) A radial load of 5000 N at 720 rpm for ONE half cycle, and iii) A radial load of 2500 N at 1440 rpm for the remaining cycle. The expected life of bearing is 10,000 hrs. Calculate the dynamic load carrying capacity of the bearing. 10M
Unit – II :
3. Design a connecting rod for a high-speed IC engine using the following data: Cylinder bore = 125mm, Length of connecting rod = 300mm, Max gas pressure = 3.5MPa, length of stroke = 125mm, Mass of reciprocating parts = 1.6kg, Engine speed = 2200 rpm. Assume suitable data and state the assumptions made. 15M
4. The bore of a cylinder of the four stroke diesel engine is 150mm. The max gas pressure inside the cylinder is limited to 3.5MPa. The cylinder head is made of grey cast iron FG200(Sut = 200N/mm2) and the factor of safety is 5. Determine the thickness of the cylinder head. Studs are used to fix the cylinder head to the cylinder and obtain a leak proof joint. They are made of steel FeE250(Syt = 250N/mm2) and the factor of safety is 5.
Calculate:
i. Number of studs
ii. Nominal Diameter of studs
iii. Pitch of studs. 15M
Unit – III :
5. a) Explain why conjugate curves must be used for tooth profiles rather than just any curved surfaces which might be arbitrarily selected. 5M
b) A spur gear reducer is to transmit 4 kW at 1500 rpm of the pinion of cast steel (so = 138 MN/mm2). The gear is made from phosphor bronze (so = 83 MN/mm2). The velocity ratio is 3.5 to 1.0. Assume a pressure angle of 20°. Design the gears for strength only. Assume number of teeth on pinion to be 16. 10M
6. a) What are the limits on helix angle of helical gears? 5M
b) A helical gear pair has to reduce speed from 500 rpm to 100 rpm for 12 hours running time per day continuously. The pinion is of 40 Ni 14 steel and 40 teeth and the wheel is of 40C8 steel normalised and has 200 teeth. The gears are of 6 mm module, 100 mm face width, 30° helix angle and 20° pressure angle. Determine power rating based on strength and wear. 10M