In a linearly elastic material, direct strain at a point in any direction s proportional to Displacement perpendicular to that direction Displacement in that direction Rate of displacement in that direction Rate of displacement perpendicular to that direction

“The displacement vector is not a tensor quantity”. Is this statement true or false? The engineering strain matrix is not a tensor quantity”. Is this statement true or false?   "The directions of principal stresses coincide with those of principal strains in isotropic materials". Is this statement true or false?

4.7. Show that the direct strain-component in the y-direction is given by (Fig. 4.6). Figure 4.7 (Evv)s an ay Ay A x Ax Ay D' any Ay Figure 4.6 1 Ax

A metal wire is 2.5 mm diameter and 2m long. A force of 12 N is applied to it and it stretched 0.3 mm. Determine the stress, strain and tensile modules of the wire.

Q3

A rectangular steel block is 300mm in the x direction, 200mm in the y direction and 150mm in the z direction. The block is subjected to a triaxial loading consisting of three uniformly distributed forces as follows: 250kN tension in the x direction, 320kN compression in the y direction and 180kN tension in the z direction. For steel, v=0.30 and E=200,000MPa. Determine the total strain in the x direction due to the forces applied in the three directions.

2) Which of the following strain fields are possible for a solid structure. Explain. (a) ɛ, = k(x+ y), 8, = k, 8, = kx, Y = ky, 7z = k, Y =0 (b) ɛ, = k(x² + y²), ɛ, = ky, ɛ, = 0, 7y = kxy, Y3z = 0, 7x = 0 (c) ɛ, = kz(x² + y²), 8, = ky²z, 8, = 0, 7 = kxyz, Yyz = 0, 7= = 0

struggling with this one help would be appreciated  thanks!

Can the normal strain on the free surface of a body be measured in aparticular direction using an electrical resistance strain gage? Give an example?

3. A square steel plate is 10.0cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0 x 10^5 N is applied parallel to each of the side. (b) Find the displacement x in centimeters.