The problems for Sections 2.5-2.8 involve displacements, deformations, and strain states a...

The problems for Sections 2.5-2.8 involve displacements, deformations, and strain states at a point in a structural or machine member. These quantities, as with then stress counterparts, are important in design and failure criteria.

The tension member in Figure P2.53 has the following dimensions: L = 5 m, b = 100 mm, and h = 200 mm. The (x, y, z) coordinate axes are parallel to the edges of the member, with origin 0 located at the centroid of the left end. Under the deformation produced by load P, the origin 0 remains located at the centroid of the left end and the coordinate axes remain parallel to the edges of the deformed member. Under the action of load P, the bar elongates 20 mm. Assume that the volume of the bar remains constant with ϵxx = ϵyy.

a. Determine the displacements for the member and the stale of strain at point Q, assuming that the small-displacement theory holds.

---

b. Determine ϵzz at point Q based on the assumption that displacements are not small.

FIGURE P2.53