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 square plate, 1 m long on a side, is loaded in a state of plane strain and is deformed as shown in Figure P2.64.

a. Write expressions for the u and v displacements for any point on the plate.

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b. Determine die components of Green strain (Eq. 2.62) in the plate.

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c. Determine the total Green strain (Eq. 2.61) at point B for a line element in the direction of line OB.

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d. For point B, compare the components of strain from part b to the components of strain for small-displacement theory (Eq. 2.81).

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e. Compare the strain determined in part c to the corresponding strain using small-displacement theory.

FIGURE P2.64

 (2.61)

 (2.62)

 (2.81)