Question

Problem 2.1 A plate is secured from any displacement along sides AB and BC. A loading is applied along AD and CD such that point D displaces 1" to the right and 1" upward. On the basis that the deflections appear linear along AD and CD, assume for plate displacements the equations: u = a0 + a1 x + a2 y + a3 xy v = b0 + b1 x + b2 y + b3 xy where the constants ai and bi i = 1 to 4 are evaluated from the displacement conditions at the four corners. Doing this, what is obtained are the displacement equations over the extent of the plate. From these equations evaluate the strains in the plate, namely, ?x = ?u/?x ?y = ?v/?y ?xy = ?u/?y + ?v/?x by differentiation. Having now equations for the strains, what are the strain values at point E? Has the angle ? shown at E increased or decreased in size?

          Problem 2.1

A plate is secured from any displacement along sides AB and BC. A loading is applied along AD and CD such that point D displaces 1" to the right and 1" upward. On the basis that the deflections appear linear along AD and CD, assume for plate displacements the equations:

u = a0 + a1 x + a2 y + a3 xy

v = b0 + b1 x + b2 y + b3 xy

where the constants ai and bi i = 1 to 4 are evaluated from the displacement conditions at the four corners. Doing this, what is obtained are the displacement equations over the extent of the plate. From these equations evaluate the strains in the plate, namely,

?x = ?u/?x  ?y = ?v/?y  ?xy = ?u/?y + ?v/?x

by differentiation.

Having now equations for the strains, what are the strain values at point E? Has the angle ? shown at E increased or decreased in size?

Problem 2.1

A plate is secured from any displacement along sides AB and BC. A loading is applied along AD and CD such that point D displaces 1" to the right and 1" upward. On the basis that the deflections appear linear along AD and CD, assume for plate displacements the equations:

u = a0 + a1 x + a2 y + a3 xy

v = b0 + b1 x + b2 y + b3 xy

where the constants ai and bi i = 1 to 4 are evaluated from the displacement conditions at the four corners. Doing this, what is obtained are the displacement equations over the extent of the plate. From these equations evaluate the strains in the plate, namely,

?x = ?u/?x ?y = ?v/?y ?xy = ?u/?y + ?v/?x

by differentiation.

Having now equations for the strains, what are the strain values at point E? Has the angle ? shown at E increased or decreased in size?

Added by Bradley H.

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