Question

A cylindrical tank holding oxygen at 4000 kPa pressure has an outside diameter of 500 mm and a wall thickness of 10 mm. It has been determined that a critical point on the tank is subjected to the tensile stress of 464 MPa in x-direction, compressive stress of 340 MPa in y-direction and shearing stress of 600 MPa. By using Mohr’s Circle;

1. Sketch the plane stresses element for the critical point.
2. Determine the principal stresses and their locations.
3. Determine the maximum shearing stresses and their locations.
4. If the critical point on tank is rotated to an angle of 24° clockwise from the x-axis, determine the normal and shear stresses on the plane.

Answer 1

i)

340 MPa σχ =464 MPa T= 600 Mpa

ii)

Given:
= 464 MPa
                  
-340 MPa ˇ
          
= 600 MPa

340 = 62 MPa

A= (G-'Txy)2(464, 600)

B=(oy,Txy)-(-340, 600)

We create axis , where normal stress is horizontal , +ve along right and shear stress is vertical +ve up

The points A, B and center C are plotted and the Mohr’s circle is drawn as shown below:

464.00 20- 62.00 340.00 01 784.22 02660.22

$\sigma_1 = 784.22 \ MPa$

$\sigma_2 = -660.22 \ MPa$

$\theta = 56.18 / 2 = 28.09^o$

iii) Again from the Mohr circle

464.00 Tmax 33.82/ 20- 62.00 340.00 01 784.22 02660.22

$\tau_{max}=722.22 \ MPa$

$\theta = -33.82 / 2 = -16.91^0$

iv)

Then another line is drawn at 24^o CW to line AB to represent oriented element. The measures of the new stress are then measured from the circle

,-721.78 MPa
                           
oy--597.78 Mpa
                
Trlyi-293.75 Mpa

340.0064.00 I x1y1 62.00 Ơx1 597.78721.78