A rectangular block having dimensions 20 cm X 30 cm X 40 cm is subjected to a hydrostatic stress of -50 kPa (i.e. under compression). Calculate the change in length of each side…

Question

asked Aug 7, 2020 151k views

1 Answer

Jaehong · Answer 1 · 2020-08-12T21:41:19+0000

Answer:

$\Delta a=-0.166 cm$

$\Delta b=-0.249 cm$

$\Delta c=-0.332 cm$

Step-by-step explanation:

Given that E=600 KPa

Poisson ratio=0.45

We know that for hydroststic stress ,strain given as

$\varepsilon =(\sigma)/(E)(2\mu -1)$

Here given that
$\sigma =-50 KPa$

Now by putting the values

$\varepsilon =(50)/(600)(2* 0.45 -1)$

$\varepsilon =-0.00833$

Negative sign indicates that dimensions will reduces due to compressive stress

We know that strain given as

$\varepsilon =(\Delta L)/(L)$

Lets take a=20 cm,b=30 cm,c=40 cm.

So
$\Delta a=-0.00833* 20 cm$

$\Delta a=-0.166 cm$

$\Delta b=-0.00833* 30 cm$

$\Delta b=-0.249 cm$

$\Delta c=-0.00833* 40 cm$

$\Delta c=-0.332 cm$