Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 6th Sem 2160609 Computational Mechanics Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?VI (NEW) EXAMINATION ? WINTER 2020
Subject Code:2160609 Date:03/02/2021
Subject Name:Computational Mechanics
Time:02:00 PM TO 04:00 PM Total Marks: 47
Instructions:
1. Attempt any THREE questions from Q.1 to Q.6 .
2. Q.7 is compulsory.
3. Make suitable assumptions wherever necessary.
4. Figures to the right indicate full marks.
Q.1 (a) Derive member stiffness matrix of beam member.
03
(b) Derive the relationship AS = RTAM for rotation of axis in 2D.
04
(c) Using member stiffness approach, determine joint displacement for the
07
beam loaded as shown in fig.1. Take EI = 60 kNm2.
Q.2 (a) Explain symmetry and anti-symmetry with neat sketches.
03
(b) Write rotation matrices of plane truss member and plane frame member.
04
(c) Using member stiffness approach, determine joint displacements for the
07
beam loaded as shown in fig.1, if the support `A' rotates by 10o counter-
clockwise. Take EI = 60 kNm2.
Q.3 (a) Evaluate member stiffness matrices of the truss shown in fig.3.
03
(b) Evaluate joint displacements of the truss shown in fig.3.
04
(c) Determine member forces of the truss shown in fig.3.
07
Q.4 (a) Define stiffness and flexibility.
03
(b) Determine member stiffness matrices of the plane frame shown in fig.4.
04
Take EI = 60 kNm2, EA = 3435 kN.
(c) Determine joint displacements and support reactions of the plane frame
07
shown in fig.4. Take EI = 60 kNm2, EA = 3435 kN.
Q.5 (a) Write steps of finite element analysis.
03
(b) Derive shape functions of CST element using Cartesian coordinate.
04
(c) Using FEM, evaluate nodal displacements of the bar shown in fig.5.
07
Take E = 2 ? 105 N/mm2.
Q.6 (a) Write displacement functions for 1D and 2D elements.
03
(b) Using FEM, evaluate nodal displacements of the beam shown in fig.6.
04
Take EI = 60 kNm2.
(c) Using FEM, evaluate nodal displacements and element stresses for the bar
07
shown in fig.7. Take EA = 500 kN.
Q.7 (a) Define plane stress and plane strain problems. Write constitutive matrices
05
of plane stress and plane strain problems.
OR
Q.7 (a) Derive nodal load vector for the 2-noded bar element subjected to surface
05
traction `T' per unit length.
1
10kN/m
10kN/m
(EI)
(EI)
10kN/m
3m
A
90o
3m
B
3m
C
3m
Fig. 1
Fig. 2
10kN/m
5kN
3m
EA
EA 3m
(EA, EI)
36.87o
3m
EA
10kN
(EA, EI)
4m
10kN
Fig. 3
Fig. 4
A=2500mm2
A=1600mm2
A=900mm2
5kN
5kN
1m
1m
1m
Fig. 5
10kNm
10kNm
5kN
5kN
(EI)
(EI)
(EA)
(EA)
3m
3m
1m
1m
Fig. 6
Fig. 7
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This post was last modified on 04 March 2021