stress transformation and mohr's circle - Foundation Coalition

124 CHAPTER 5. STRESS TRANSFORMATION AND MOHR’S CIRCLE
y-face
(0,0)
σ x ′ y ′
B
C
2.5
5MPa
x-face
z
2.5
y
2.5
σ x ′ x ′
Figure 5.22:
• Maximum shear traction at 45 ◦ from x-axis
• Maximum normal traction along x-axis
Example 5-6
x
45
C B
σxx
σ x ′ x ′ = σn =2.5
σ x ′ y ′ = τ s =2.5
Given: The state of stress at each point in a bar can be represented by the stress tensor [σ]:
Required :
⎡
[σ] = ⎣
z
σxx 0 0
0 0 0
0 0 0
y
⎤ ⎡
⎦ = ⎣
x
Figure 5.23:
a) Construct Mohr’s Circle for the given stress tensor.
10 kN
m 2 0 0
0 0 0
0 0 0
b) What are the traction vectors experienced each face of the cube?
⎤
⎦