In a plane strain problem, we have: ax = 30,000 psi, ay = —15,000 psi, E = 30 x106 psi, v = 0.3....

Question

In a plane strain problem, we have: ax = 30,000 psi, ay = —15,000 psi, E = 30 x106 psi, v = 0.3. Determine the value of the stress az.
Q2. A typical displacement field is described by u = (x3 + 4y2 — 16xy)10-6 v = (y2 — 5x + 8y)10-4 Determine ez,ey, yzy at the point P (1.0).
(1 mark)
(2 mark)
Q3. A rectangular region ABCD undergoes deformation to the state A'B'C'D' , as shown in Figure 1 below.
D D' „„
C C'
•

005_9uazo-0n5hbbhg.pdf

David · Accepted Answer

Solution: 1 
Strain in x and y direction is given as: 
   
 
 
(      )
      
*      (          )+            
   
 
 
(       )
      
*(          )  (      )+          
σz is given by the formula: 
   
 
   
*
 
    
(     )+
     
[
   
  (     )
(          (       ))]
Solution: 2 
Given displacement field: 
  (           )     
  (        )     
   
  
  
 (       )     
At point P (1, 0): 
   ( ( )
      )            
And 
   
  
  
 (    )     
At point P (1, 0): 
   (     )  
          
And 
    
  
  
 
  
  
 
    (      )  
   (  )     
At point P (1, 0): 
    (        )  
   (  )
Solution: 3 
(a) Displacement field is given as:

In a plane strain problem, we have: ax = 30,000 psi, ay = —15,000 psi, E = 30 x106 psi, v = 0.3. Determine the value of the stress az. Q2. A typical displacement field is described by u = (x3 + 4y2 —...

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