Expert answers to "The homogeneous plate ABCD is subjected to a..."

e1s2kat26

Answered question

2021-03-28

The homogeneous plate ABCD is subjected to a biaxial loading asshown. It is known that

σ_{z} = σ_{o}

and that the change in length of the plate in the x direction must be zero, that is

ϵ_{x} = 0

. Denoting E the modulus of elasticity and by v Poisson's ratio, determine (a) the required magnitude of

σ_{x}

, and (b) the ratio

\frac{σ_{o}}{ϵ_{z}}

gotovub

Skilled2021-03-30Added 98 answers

a) Strain in x-direction,

ϵ_{x} = \frac{σ_{x}}{E} - V \frac{σ_{z}}{E}

But given,

ϵ_{x} = 0, σ_{z} = σ_{o}

\frac{ϵ_{x}}{E} - V \frac{σ_{o}}{E} = 0

Then find

σ_{x}

b) Strain in Z-direction,

ϵ_{Z} = \frac{σ_{Z}}{E} - V \frac{σ_{x}}{E}

ϵ_{Z} = \frac{σ_{0}}{E} - V \frac{σ_{x}}{E}

Then find

\frac{σ_{0}}{ϵ_{z}}

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