Question

6. If the stresses and strains at a point in a linear elastic material are given by
σij = ε
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
=
885 154 0
154 1038 615
0 615 577
0 002 0 001 0
0 001 0 003 0 004
0 0 004 0
MPa; and ij
. .
. . .
.
respectively, determine (i) the total strain energy density in the material, (ii) the hydrostatic
component of the strain energy density, and (iii) the bulk modulus of the material.
7. A curved solid bar with a radius of curvature R = 125 mm is loaded as shown in Figure 2
below. The bar has a circular cross section of diameter 50 mm, and a Young’s modulus
E = 80 GPa. Determine (i) the strain energy due to bending stored in the bar and (ii) the
displacement in the direction of the load, at the point where the load is applied.
8. A clamp is made of two straight members and a curved member, as shown in Figure 3.
The cross-sectional geometry of the clamp, which is also shown in the figure, has a
moment of inertia I = 7 x 10−8 m4, and the material from which the clamp is made has a
Young's modulus E = 200 GPa. If the blocks of wood being clamped exert a force
P = 40 kN on the straight members of the clamp, as shown in the figure, determine (i)
the strain energy due to bending in the clamp and (ii) the movement of the ends where
the loads are applied.
Figure 3 (Qu. 8)

6. If the stresses and strains at a point in a linear elastic material are given by 885 154 0 0.002 0.001 0 Ơi-1154 1038 615MPa; and εί-10.001 0.003 0.004 0 615 577 0 0.004 0 respectively, determine (i) the total strain energy density in the material, (ii) the hydrostatic component of the strain energy density, and (ii) the bulk modulus of the material 7. A curved solid bar with a radius of curvature R below. The bar has a circular cross section of diameter 50 mm, and a Young's modulus E = 80 GPa. Determine (i) the strain energy due to bending stored in the bar and (ii) the displacement in the direction of the load, at the point where the load is applied 125 mm is loaded as shown in Figure 2 8. A clamp is made of two straight members and a curved member, as shown in Figure 3. of the clamp, which is also shown in the figure, has a moment of inertia I 7 x 108 m, and the material from which the clamp is made hasa Young's modulus E 200 GPa. If the blocks of wood being clamped exert a force P 40 kN on the straight members of the clamp, as shown in the figure, determine (i) the strain energy due to bending in the clamp and (ii) the movement of the ends where the loads are applied 10 mm 40 mm 120 mm 5 mm Figure 3 (Qu.8)

Answer 1