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...
A linear elastic material is subjected to differing strains. At a strain of 0.2%, the stress is 36 MPa whereas at a strain of 0.75%, the stress is 128 MPa. a) (5 points) Determine the stress in this material at a strain of 0.58% (use linear interpolation) 5, 1. b) (5 points) what is the Young's modulus (elastic modulus) of this material? Use proper units mce
(20%) Question 6. The elastic modulus, yield strength and ultimate strength of a certain material afe 110 GPa 2400 MPa and 265 MPal respectively. If a cylindrical bar of this material 380 mm long is subjected to a uniaxial tension test and its length is increased by an amount áf O.50 mm under a tensile load ót 6660 N.At the same time its diameter decreased by0,28 mm Calculate; a) The initial diameter of the bar, (8%) d b) Under an...
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