1. JNTUW
ORLD
Code No: R05410102 R05 Set No. 2
IV B.Tech I Semester Examinations,December 2011
FINITE ELEMENT METHODS IN CIVIL ENGINEERING
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Write a short notes on plane strain problem
(b) In a plane strain problem, determine the value of stress σz, for the stresses
σx = 150 N/mm2
, σy = −75 N/mm2
, υ = 0.25 [16]
2. Derive the element stiffness matrix for a plane rectangular element. [16]
3. (a) How the node numbering scheme influences the matrix sparsity in banded
stiffness matrix.
(b) Evaluate the function φ = cos πx
2
between x=-1 and x=1 using Gaussian two
and three point rule and check the answer with the exact solution. [6+10]
4. (a) Derive the elemental stiffness matrix for a two noded beam element.
(b) Bring out the differences between a beam element and bar element. [10+6]
5. (a) Derive the element body force vector for an axisymmetric element.
(b) Explain basic concepts of plane stress and plane strain. [8+8]
6. For the truss shown in figure 1. Determine the displacements of all Nodal points
and the element stresses.
Take E=2×105
N/mm2
, v = 0.3. [16]
7. (a) Sketch four types of simple finite elements used in discretization of a body
(b) How will you determine the minimum number of degree of freedom at each
Node for the above elements
(c) Illustrate with sketches the discretization of a structure using each of above
elements. [6+4+6]
8. (a) Sketch the variations of the shape functions of a typical CST element. Check
that N1+N2+N3=1 any where on the element.
(b) The nodal coordinates of the triangular element are shown in figure 2. At
the interior point P, the x coordinate is 3.3 and N1 = 0.3. Determine N2, N3
and y coordinate at point P. [10+6]
1
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3. JNTUW
ORLD
Code No: R05410102 R05 Set No. 4
IV B.Tech I Semester Examinations,December 2011
FINITE ELEMENT METHODS IN CIVIL ENGINEERING
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Derive the elemental stiffness matrix for a two noded beam element.
(b) Bring out the differences between a beam element and bar element. [10+6]
2. For the truss shown in figure 1. Determine the displacements of all Nodal points
and the element stresses.
Take E=2×105
N/mm2
, v = 0.3. [16]
Figure 1:
3. (a) Sketch four types of simple finite elements used in discretization of a body
(b) How will you determine the minimum number of degree of freedom at each
Node for the above elements
(c) Illustrate with sketches the discretization of a structure using each of above
elements. [6+4+6]
4. Derive the element stiffness matrix for a plane rectangular element. [16]
3
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4. JNTUW
ORLD
Code No: R05410102 R05 Set No. 4
5. (a) Write a short notes on plane strain problem
(b) In a plane strain problem, determine the value of stress σz, for the stresses
σx = 150 N/mm2
, σy = −75 N/mm2
, υ = 0.25 [16]
6. (a) How the node numbering scheme influences the matrix sparsity in banded
stiffness matrix.
(b) Evaluate the function φ = cos πx
2
between x=-1 and x=1 using Gaussian two
and three point rule and check the answer with the exact solution. [6+10]
7. (a) Sketch the variations of the shape functions of a typical CST element. Check
that N1+N2+N3=1 any where on the element.
(b) The nodal coordinates of the triangular element are shown in figure 2. At
the interior point P, the x coordinate is 3.3 and N1 = 0.3. Determine N2, N3
and y coordinate at point P. [10+6]
Figure 2
8. (a) Derive the element body force vector for an axisymmetric element.
(b) Explain basic concepts of plane stress and plane strain. [8+8]
4
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5. JNTUW
ORLD
Code No: R05410102 R05 Set No. 1
IV B.Tech I Semester Examinations,December 2011
FINITE ELEMENT METHODS IN CIVIL ENGINEERING
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Derive the element stiffness matrix for a plane rectangular element. [16]
2. For the truss shown in figure 1. Determine the displacements of all Nodal points
and the element stresses.
Take E=2×105
N/mm2
, v = 0.3. [16]
Figure 1:
3. (a) Sketch the variations of the shape functions of a typical CST element. Check
that N1+N2+N3=1 any where on the element.
(b) The nodal coordinates of the triangular element are shown in figure 2. At
the interior point P, the x coordinate is 3.3 and N1 = 0.3. Determine N2, N3
and y coordinate at point P. [10+6]
5
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6. JNTUW
ORLD
Code No: R05410102 R05 Set No. 1
Figure 2
4. (a) Sketch four types of simple finite elements used in discretization of a body
(b) How will you determine the minimum number of degree of freedom at each
Node for the above elements
(c) Illustrate with sketches the discretization of a structure using each of above
elements. [6+4+6]
5. (a) Derive the element body force vector for an axisymmetric element.
(b) Explain basic concepts of plane stress and plane strain. [8+8]
6. (a) Write a short notes on plane strain problem
(b) In a plane strain problem, determine the value of stress σz, for the stresses
σx = 150 N/mm2
, σy = −75 N/mm2
, υ = 0.25 [16]
7. (a) Derive the elemental stiffness matrix for a two noded beam element.
(b) Bring out the differences between a beam element and bar element. [10+6]
8. (a) How the node numbering scheme influences the matrix sparsity in banded
stiffness matrix.
(b) Evaluate the function φ = cos πx
2
between x=-1 and x=1 using Gaussian two
and three point rule and check the answer with the exact solution. [6+10]
6
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7. JNTUW
ORLD
Code No: R05410102 R05 Set No. 3
IV B.Tech I Semester Examinations,December 2011
FINITE ELEMENT METHODS IN CIVIL ENGINEERING
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Sketch the variations of the shape functions of a typical CST element. Check
that N1+N2+N3=1 any where on the element.
(b) The nodal coordinates of the triangular element are shown in figure 1. At
the interior point P, the x coordinate is 3.3 and N1 = 0.3. Determine N2, N3
and y coordinate at point P. [10+6]
Figure 1
2. (a) Derive the element body force vector for an axisymmetric element.
(b) Explain basic concepts of plane stress and plane strain. [8+8]
3. Derive the element stiffness matrix for a plane rectangular element. [16]
4. (a) Write a short notes on plane strain problem
(b) In a plane strain problem, determine the value of stress σz, for the stresses
σx = 150 N/mm2
, σy = −75 N/mm2
, υ = 0.25 [16]
5. For the truss shown in figure 2. Determine the displacements of all Nodal points
and the element stresses.
Take E=2×105
N/mm2
, v = 0.3. [16]
6. (a) How the node numbering scheme influences the matrix sparsity in banded
stiffness matrix.
(b) Evaluate the function φ = cos πx
2
between x=-1 and x=1 using Gaussian two
and three point rule and check the answer with the exact solution. [6+10]
7
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8. JNTUW
ORLD
Code No: R05410102 R05 Set No. 3
Figure 2:
7. (a) Derive the elemental stiffness matrix for a two noded beam element.
(b) Bring out the differences between a beam element and bar element. [10+6]
8. (a) Sketch four types of simple finite elements used in discretization of a body
(b) How will you determine the minimum number of degree of freedom at each
Node for the above elements
(c) Illustrate with sketches the discretization of a structure using each of above
elements. [6+4+6]
8
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![JNTUW
ORLD
Code No: R05410102 R05 Set No. 2
IV B.Tech I Semester Examinations,December 2011
FINITE ELEMENT METHODS IN CIVIL ENGINEERING
Civil Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Write a short notes on plane strain problem
(b) In a plane strain problem, determine the value of stress σz, for the stresses
σx = 150 N/mm2
, σy = −75 N/mm2
, υ = 0.25 [16]
2. Derive the element stiffness matrix for a plane rectangular element. [16]
3. (a) How the node numbering scheme influences the matrix sparsity in banded
stiffness matrix.
(b) Evaluate the function φ = cos πx
2
between x=-1 and x=1 using Gaussian two
and three point rule and check the answer with the exact solution. [6+10]
4. (a) Derive the elemental stiffness matrix for a two noded beam element.
(b) Bring out the differences between a beam element and bar element. [10+6]
5. (a) Derive the element body force vector for an axisymmetric element.
(b) Explain basic concepts of plane stress and plane strain. [8+8]
6. For the truss shown in figure 1. Determine the displacements of all Nodal points
and the element stresses.
Take E=2×105
N/mm2
, v = 0.3. [16]
7. (a) Sketch four types of simple finite elements used in discretization of a body
(b) How will you determine the minimum number of degree of freedom at each
Node for the above elements
(c) Illustrate with sketches the discretization of a structure using each of above
elements. [6+4+6]
8. (a) Sketch the variations of the shape functions of a typical CST element. Check
that N1+N2+N3=1 any where on the element.
(b) The nodal coordinates of the triangular element are shown in figure 2. At
the interior point P, the x coordinate is 3.3 and N1 = 0.3. Determine N2, N3
and y coordinate at point P. [10+6]
1
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