1- Consider the unit cube shown in the Figure, which undergoes the deformation: 1 x₁ = a (X₁-X₂), X₂ =BX2₁, X3 = Y X3 2 where a, ß, and y are constants. Determine: (a) the deformed length of diagonal OA, a В (b) the condition that constants a, ß, and y must satisfy if the material is incompressible. 0.6 1.5 Y 1.0

Structural Analysis
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Chapter2: Loads On Structures
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1- Consider the unit cube shown in the Figure, which undergoes the deformation:
1
x₁ = α (X₁- X₂), x₂ =BX2,, x3 = 7X3
2
where a, ß, and y are constants. Determine:
(a) the deformed length of diagonal OA,
a
В
(b) the condition that constants a, ß, and y must satisfy
if the material is incompressible.
0.6
1.5
X₁
Y
1.0
Transcribed Image Text:1- Consider the unit cube shown in the Figure, which undergoes the deformation: 1 x₁ = α (X₁- X₂), x₂ =BX2,, x3 = 7X3 2 where a, ß, and y are constants. Determine: (a) the deformed length of diagonal OA, a В (b) the condition that constants a, ß, and y must satisfy if the material is incompressible. 0.6 1.5 X₁ Y 1.0
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