Download GTU B.Tech 2020 Winter 6th Sem 2160609 Computational Mechanics Question Paper

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Subject Code: 2160609

GUJARAT TECHNOLOGICAL UNIVERSITY

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Instructions:

1. Attempt any THREE questions from Q.1 to Q.6.

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2. Q.7 is compulsory.
3. Make suitable assumptions wherever necessary.
4. Figures to the right indicate full marks.

Q.1

1. (a) Derive member stiffness matrix of beam member. (03)

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2. (b) Derive the relationship As = R^TAw for rotation of axis in 2D. (04)
3. (c) Using member stiffness approach, determine joint displacement for the beam loaded as shown in fig.1. Take EI = 60 kNm². (07)

Q.2

1. (a) Explain symmetry and anti-symmetry with neat sketches. (03)
2. (b) Write rotation matrices of plane truss member and plane frame member. (04)

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3. (c) Using member stiffness approach, determine joint displacements for the beam loaded as shown in fig.1, if the support ‘A’ rotates by 10° counter-clockwise. Take EI = 60 kNm². (07)

Q.3

1. (a) Evaluate member stiffness matrices of the truss shown in fig.3. (03)
2. (b) Evaluate joint displacements of the truss shown in fig.3. (04)
3. (c) Determine member forces of the truss shown in fig.3. (07)

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Q.4

1. (a) Define stiffness and flexibility. (03)
2. (b) Determine member stiffness matrices of the plane frame shown in fig.4. Take EI = 60 kNm², EA = 3435 kN. (04)
3. (c) Determine joint displacements and support reactions of the plane frame shown in fig.4. Take EI = 60 kNm², EA = 3435 kN. (07)

Q.5

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1. (a) Write steps of finite element analysis. (03)
2. (b) Derive shape functions of CST element using Cartesian coordinate. (04)
3. (c) Using FEM, evaluate nodal displacements of the bar shown in fig.5. Take E = 2 x 10⁵ N/mm². (07)

Q.6

1. (a) Write displacement functions for 1D and 2D elements. (03)

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2. (b) Using FEM, evaluate nodal displacements of the beam shown in fig.6. Take EI = 60 kNm². (04)
3. (c) Using FEM, evaluate nodal displacements and element stresses for the bar shown in fig.7. Take EA = 500 kN. (07)

Q.7

1. (a) Define plane stress and plane strain problems. Write constitutive matrices of plane stress and plane strain problems. (05)
2. (b) OR Derive nodal load vector for the 2-noded bar element subjected to surface traction ‘T’ per unit length. (05)

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Date: 03/02/2021
Total Marks: 47

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