Subject Code: 2160609
SEMESTER-VI(NEW) - EXAMINATION - SUMMER 2019
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Subject Name: Computational Mechanics
Time: 10:30 AM TO 01:30 PM
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
- Draw neat sketch /diagram wherever necessary.
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Q.1 (a) Derive member stiffness matrix of the beam member with usual notations. 03
(b) Explain symmetry and anti-symmetry with suitable examples. 04
(c) Analyse continuous beam ABC as shown in Figure-1 using stiffness member approach and draw bending moment and shear force diagram. Assume EI to be constant for all members. 07
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Q.2 (a) Explain the concept of rotation of axes in 2D and derive relation Awm = Rt As, from first principles. 03
(b) Explain material and geometric nonlinearities using suitable examples. 04
(c) Determine the displacement and rotation under the force and moment located at the center of the beam in figure-2 using stiffness member approach. Consider E = 210GPa and I=4x10-4 m4 07
OR
(c) Using stiffness member approach compute reactions continuous beam ABCD as shown in Figure-3 when Support B sinks down by 0.005m and support C sinks down 0.01. Assume E =200 GPa and I = 4x10-4 m4. 07
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Q.3 (a) For the plane truss shown in figure-4, determine the joint displacements and support reactions using stiffness member approach. Take modulus of elasticity E= 200 GPa and area of member AB=1500mm2 and area of BC=CA=1500mm2. 07
(b) Using member stiffness method obtain the member forces in the plane truss shown in figure-5 and determine the support reactions. Take E =200 GPa and A = 2000 mm2. 07
OR
Q.3 (c) Analyze the rigid frame shown in figure-6 by direct stiffness method. Assume E= 200GPa; Izz=1.33x10-4 m4 and A = 0.04m2. EI and axial rigidity AE are the same for both the members. 07
(b) A rigid frame is loaded as shown in the figure-6, Compute the reactions and draw bending moment, shear force and axial force diagram if the support ‘C’ settles by 10 mm vertically downwards. 07
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Q.4 (a) Determine rearranged joint stiffness matrix for the grid shown in figure-7. Both members have same torsional rigidity and flexural rigidity. Take GJ = 0.8EIL Consider P=10kN and L=4m. 07
(b) Determine the joint displacements of the truss shown in figure-8 by member stiffness method. Assume that all members have the same axial rigidity AE=constant. 07
OR
Q.4 (a) Enlist various steps of finite element method. 03
(b) Derive shape functions for 2-noded bar element. 04
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(c) Derive the equation [k]{q}={f} using minimum potential energy approach. 07
Q.5 (a) Determine the shape functions for a Constant Strain Triangular (CST) element in cartesian coordinate systems. 03
Date: 27/05/2019
Total Marks: 70
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GUJARAT TECHNOLOGICAL UNIVERSITY
(c) For the CST element shown in figure-9, the nodal displacements are given as u1 = 0.05 mm, v1 = 0.02 mm, u2 = 0.02 mm, v2 = 0.01 mm, u3 = 0.03 mm, v3 = 0.04 mm. The element coordinates are given in units of millimeters. Let E =210 GPa, Poisson’s ratio = 0.25 and plate thickness = 10 mm. 04
(c) Three springs are joined together as shown in figure-10. Evaluate nodal displacements and forces in the springs. 07
OR
Q.5 (a) Determine the element stiffness matrix for the element having coordinates as shown in figure-11 in units of mm. Assume plane stress conditions. Consider E=30x103 N/mm2, Poisson’s ratio = 0.25, and thickness t =1mm. The element nodal displacements have been determined to be u1 = 0.0, v1 =0.0025 mm, u2 =0.0012 mm., v2 =0, u3 =0 and v3 = 0.0025 mm.. 07
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(b) For the plane stress CST element shown in figure-11, Determine the element stresses sx, sy, txy. 07
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