Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 6th Sem New 2160609 Computational Mechanics Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2160609 Date:07/12/2018
Subject Name:Computational Mechanics
Time: 02:30 PM TO 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Draw neat sketch wherever necessary.
Q.1 (a) Explain symmetry and anti-symmetry with neat sketches. 03
(b) Derive SM matrix for beam member. 04
(c) Determine joint displacements for the beam shown in fig.1. Take EI =
constant.
07
Q.2 (a) Formulate combined joint load vector for the grid shown in fig.2. 03
(b) Explain various types of skeleton structures with their internal forces and
deformations.
04
(c) Formulate SMS matrix for grid member. 07
OR
(c) Determine joint displacements for the loaded beam shown in fig.1, if the
support B sinks by 10mm. Take EI = 30000 kNm
2
.
07
Q.3 (a) Determine joint displacements and member forces of the truss shown in
fig.2. All the members have same axial rigidity. Take EA = constant.
14
OR
Q.3 (a) Determine joint displacements and support reactions of the plane frame
shown in fig.3. Take EI = 30000 kNm
2
, EA = 2 ? 10
6
kN.
14
Q.4 (a) Write steps of finite element analysis. 03
(b) Explain plane stress and plane strain problems. 04
(c) Find nodal displacements and element stresses of the bar shown in fig.4.
Take E = 200GPa.
07
OR
Q.4 (a) Explain process of discretization. 03
(b) Using potential energy approach, derive the equation [k]{q}={f}. 04
(c) Find nodal displacements and nodal reactions for the beam shown in fig.5.
Take EI = constant.
07
Q.5 (a) Derive strain displacement matrix of CST element. 07
(b) Evaluate stiffness matrix of the CST element shown in fig.6. Assume plane
stress condition and unit thickness of the element. Take E = 2 ? 10
5
N/mm
2
,
? = 0.3.
07
OR
Q.5 (a) Explain various types of non-linearity with neat sketches. 07
(b) For the plane stress element shown in fig.6, the nodal displacements are
given as u1 = 0.05mm, v1 = 0.02mm, u2 = 0.0mm, v2 = 0.0mm, u3 =
0.04mm, v3 = 0.01mm. Determine the element stresses. Take E = 200GPa,
? = 0.3, Use unit thickness for plane stress element.
07
*************
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2160609 Date:07/12/2018
Subject Name:Computational Mechanics
Time: 02:30 PM TO 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Draw neat sketch wherever necessary.
Q.1 (a) Explain symmetry and anti-symmetry with neat sketches. 03
(b) Derive SM matrix for beam member. 04
(c) Determine joint displacements for the beam shown in fig.1. Take EI =
constant.
07
Q.2 (a) Formulate combined joint load vector for the grid shown in fig.2. 03
(b) Explain various types of skeleton structures with their internal forces and
deformations.
04
(c) Formulate SMS matrix for grid member. 07
OR
(c) Determine joint displacements for the loaded beam shown in fig.1, if the
support B sinks by 10mm. Take EI = 30000 kNm
2
.
07
Q.3 (a) Determine joint displacements and member forces of the truss shown in
fig.2. All the members have same axial rigidity. Take EA = constant.
14
OR
Q.3 (a) Determine joint displacements and support reactions of the plane frame
shown in fig.3. Take EI = 30000 kNm
2
, EA = 2 ? 10
6
kN.
14
Q.4 (a) Write steps of finite element analysis. 03
(b) Explain plane stress and plane strain problems. 04
(c) Find nodal displacements and element stresses of the bar shown in fig.4.
Take E = 200GPa.
07
OR
Q.4 (a) Explain process of discretization. 03
(b) Using potential energy approach, derive the equation [k]{q}={f}. 04
(c) Find nodal displacements and nodal reactions for the beam shown in fig.5.
Take EI = constant.
07
Q.5 (a) Derive strain displacement matrix of CST element. 07
(b) Evaluate stiffness matrix of the CST element shown in fig.6. Assume plane
stress condition and unit thickness of the element. Take E = 2 ? 10
5
N/mm
2
,
? = 0.3.
07
OR
Q.5 (a) Explain various types of non-linearity with neat sketches. 07
(b) For the plane stress element shown in fig.6, the nodal displacements are
given as u1 = 0.05mm, v1 = 0.02mm, u2 = 0.0mm, v2 = 0.0mm, u3 =
0.04mm, v3 = 0.01mm. Determine the element stresses. Take E = 200GPa,
? = 0.3, Use unit thickness for plane stress element.
07
*************
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This post was last modified on 20 February 2020