Beer Johnston asked 12 months ago
For the given state of stress, determine (a) the principal planes, (b) the principal stresses.
1 Answers
Mazurek Gravity answered 12 months ago
Step: 1
Draw the Schematic diagram of element:
Join
Step: 2
(a)
Calculate the orientation of the principal planes by using the following equation:
Substitute 
for 
.
Therefore, the Principal planes are
.
Step: 3
(b)
Calculate the maximum principal stresses by using the following equation:
Substitute 
for 
, 
for 
, and 
for 
.
Step: 4
Calculate the minimum principal stresses by using the following equation:
Substitute 
for 
, 
for 
, and 
for 
.
Therefore, the maximum principal stress is 
and the minimum principal stress is 
.
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