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Assignment 2 FEM

The document contains 30 problems involving the use of finite element methods to determine stress, strain, displacement and rotation distributions in bars and beams with various geometries and load conditions. Solutions are to be found for axial and bending problems involving single and multiple materials with different cross sections, including circular, rectangular, I-shaped, T-shaped, L-shaped and angle sections. Boundary conditions, lengths, forces, moduli and areas are provided for each problem.

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SumitKumar
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445 views8 pages

Assignment 2 FEM

The document contains 30 problems involving the use of finite element methods to determine stress, strain, displacement and rotation distributions in bars and beams with various geometries and load conditions. Solutions are to be found for axial and bending problems involving single and multiple materials with different cross sections, including circular, rectangular, I-shaped, T-shaped, L-shaped and angle sections. Boundary conditions, lengths, forces, moduli and areas are provided for each problem.

Uploaded by

SumitKumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Finite Element Methods Assignment2 Dr. G.

Venkatachalam

1. Find the stress and strain distributions for the bar shown in fig.1. Take F = 100 kN, E1 = 200
GPa, A1 = 4 cm2, L1 = 1.5 m and E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m.

Fig.1
2. Find the stress and strain distributions for the bar shown in fig.2. Take F = 150 kN, E1 = 200
GPa, A1 = 4 cm2, L1 = 1.5 m and E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m. Also take x = 2 mm.

Fig.2
3. Find the stress and strain distributions for the bar shown in fig.3. Take F = 100 kN, E = 200
GPa, A = 4 cm2, L = 1.5 m and x = 0.5 mm.

Fig.3
4. Find the stress and strain distributions for the bar shown in fig.4. Take F1 = 150 kN, E1 = 200
GPa, A1 = 4 cm2, L1 = 1.5 m, F2 = 100 kN, E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m and F3 = 150
kN, E3 = 200 GPa, A3 = 4 cm2, L3 = 1.5 m.

Fig.4

Finite Element Methods Assignment2 Dr. G.Venkatachalam

5. Find the stress and strain distributions for the bar shown in fig.5. Take F = 150 kN, E1 = 200
GPa, A1 = 4 cm2, L1 = 1.5 m and E2 = 70 GPa, A2 = 4 cm2, L2 = 1.3 m. Also take x = 1 mm.

Fig.5
6. Find the stress and strain distributions for the bar shown in fig.6. Take F = 50 kN, E1 = 100
GPa, A1 = 8 cm2, L1 = 2 m and E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m.

Fig.6
7. Find the stress and strain distributions for the bar shown in fig.7. Take F = 50 kN, E1 = 100
GPa, A1 = 8 cm2, L1 = 2 m and E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m. Also take x = 0.5 mm.

Fig.7
8. Find the stress and strain distributions for the bar shown in fig.8. Take F = 150 kN, E = 100
GPa, A = 8 cm2, L = 2 m and x = 0.5 mm.

Fig.8
9. Find the stress and strain distributions for the bar shown in fig.9. Take F1 = 100 kN, E1 = 200
GPa, A1 = 4 cm2, L1 = 1.5 m, F2 = 150 kN, E2 = 70 GPa, A2 = 3 cm2, L2 = 1.3 m and F3 = 100
kN, E3 = 200 GPa, A3 = 4 cm2, L3 = 1.5 m.

Finite Element Methods Assignment2 Dr. G.Venkatachalam

Fig.9
10. Find the stress and strain distributions for the bar shown in fig.10. Take F = 100 kN, E1 =
100 GPa, A1 = 10 cm2, L1 = 2 m and E2 = 70 GPa, A2 = 4 cm2, L2 = 1.3 m. Also take x = 0.1
mm.

Fig.10
11. Find the unknown displacements for the trusses shown in fig.11. Take F = 10 kN, L1 = 2 m,
L2 = 1.5 m, E = 210 GPa and A = 10 cm2.

Fig.11
12. Find the unknown displacements for the trusses shown in fig.12. Take F1 = 10 kN, F2 = 6
kN, L1 = 2 m, L2 = 1.5 m, E = 210 GPa and A = 10 cm2.

Fig.12

Finite Element Methods Assignment2 Dr. G.Venkatachalam

13. Find the unknown displacements for the trusses shown in fig.13. Take F = 10 kN, L = 2 m, E
= 70 GPa, and A = 5 cm2.

Fig.13
14. Find the unknown displacements for the trusses shown in fig.14. Take F1 = 10 kN, F2 = 6
kN, L1 = 2 m, L2 = 1.5 m, E = 210 GPa and A = 8 cm2.

Fig.14
15. Find the unknown displacements for the trusses shown in fig.15. Take F = 10 kN, L = 2 m, E
= 100 GPa, and A = 8 cm2.

Fig.15
16. Find the unknown displacements for the trusses shown in fig.16. Take F = 20 kN, L1 = 3 m,
L2 = 2 m, E = 100 GPa and A = 10 cm2.

Finite Element Methods Assignment2 Dr. G.Venkatachalam

Fig.16
17. Find the unknown displacements for the trusses shown in fig.17. Take F1 = 20 kN, F2 = 15
kN, L1 = 2 m, L2 = 2 m, E = 210 GPa and A = 10 cm2.

Fig.17
18. Find the unknown displacements for the trusses shown in fig.18. Take F = 25 kN, L = 1.5 m,
E = 70 GPa, and A = 8 cm2.

Fig.18
19. Find the unknown displacements for the trusses shown in fig.19. Take F1 = 20 kN, F2 = 10
kN, L1 = 3 m, L2 = 2 m, E = 210 GPa and A = 10 cm2.

Fig.19
20. Find the unknown displacements for the trusses shown in fig.20. Take F = 15 kN, L = 1 m, E
= 100 GPa, and A = 10 cm2.

Finite Element Methods Assignment2 Dr. G.Venkatachalam

Fig.20
21. Find the unknown displacements & rotations for the beam shown in fig.21 (a). Take E = 210
GPa, F = 5 kN and L = 2 m. The cross section of the beam is shown in fig.21 (b) [a, c = 30 mm
& b, d = 100 mm].

Fig.21 (a)
Fig.21 (b)
22. Find the unknown displacements & rotations for the beam shown in fig.22 (a). Take E = 210
GPa, F = 5 kN and L = 2 m. The cross section of the beam is shown in fig.22 (b) [a = 30 mm &
b, c = 100 mm].

Fig.22 (a)
Fig.22 (b)
23. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.23 (a) & (b). Take E = 210 GPa, F = 5 kN and L = 2 m. Take A (solid circular) = A
Hollow circular), d = 50 mm and do = 1.8di.

Fig.23 (a)

Fig.23 (b)

Finite Element Methods Assignment2 Dr. G.Venkatachalam

24. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.24 (a) & (b). Take E = 210 GPa, F = 5 kN and L = 2 m. Take (i) for L section a, d
= 100 mm & b, c = 25 mm (ii) for I section a, c = 100 mm & b, d, e = 30 mm.

Fig.24 (a)
Fig.24 (b)
25. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.25 (a) & (b). Take E = 210 GPa, F = 5 kN and L = 2 m. Take (i) for T section a, c
= 20 mm & b, d = 100 mm (ii) for section a = 20 mm & b, c = 100 mm.

Fig.25 (a)
Fig.25 (b)
26. Find the unknown displacements & rotations for the beam shown in fig.26 (a). Take E = 70
GPa, F = 10 kN and L = 2 m. The cross section of the beam is shown in fig.26 (b) [a, c = 20 mm
& b, d = 100 mm].

Fig.26 (a)
Fig.26 (b)
27. Find the unknown displacements & rotations for the beam shown in fig.27 (a). Take E = 70
GPa, F = 4 kN and L = 2 m. The cross section of the beam is shown in fig.27 (b) [a = 10 mm &
b, c = 100 mm].

Finite Element Methods Assignment2 Dr. G.Venkatachalam

Fig.27 (a)
Fig.27 (b)
28. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.28 (a) & (b). Take E = 100 GPa, F = 2 kN and L = 2 m. Take A (solid circular) = A
Hollow circular), d = 50 mm and do = 1.5di.

Fig.28 (a)
Fig.28 (b)
29. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.29 (a) & (b). Take E = 70 GPa, F = 2 kN and L = 2 m. Take (i) for L section a, d =
80 mm & b, c = 30 mm (ii) for I section a, c = 80 mm & b, d, e = 20 mm.

Fig.29 (a)
Fig.29 (b)
30. Find and compare the unknown displacements & rotations for the beam and its cross sections
shown in fig.30 (a) & (b). Take E = 70 GPa, F = 1 kN and L = 2 m. Take (i) for T section a, c =
30 mm & b, d = 150 mm (ii) for section a = 30 mm & b, c = 90 mm.

Fig.30 (a)

Fig.30 (b)

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