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.

A state of plane strain exists at a point in a beam, with the nonzero strain components ϵxx = −2000 μ, ϵyy = 400 μ, and ϵxy = −900 μ.

a. Determine the principal strains in the (x, y) plane and the orientation of the rectangular element on which they act. (See Example 2.10.)

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b. Determine the maximum shear strain in the (x, y) plane and the orientation of the rectangular element on which it acts.

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c. Show schematically the deformed shape of a rectangular element in the reference orientation, along with the original undeformed element. (See Example 2.10.)

Example 2.10.