stress, strain, stress at a point, stress tensor

1. V K Jadon, Professor, Mechanical Engineering
Concept of Stress

2. 𝜎𝑥𝑥 𝜏 𝑥𝑦 𝜏 𝑥𝑧
𝜏 𝑦𝑥 𝜎 𝑦𝑦 𝜏 𝑦𝑧
𝜏 𝑧𝑥 𝜏 𝑧𝑦 𝜎𝑧𝑧
State of Stress at a point on 3-D element Stress at a point on 2-D element
A stress is positive, if its direction and the direction of the
normal to the face on which it is acting are both in positive
or negative direction; otherwise, the stress is negative.
V K Jadon, Professor, Mechanical Engineering
Stress is always computed at a point
Stress is a tensor quantity
State of Stress represents the stress components at a point
There can exists only two types of Stresses at a point

3. 𝜎 =
𝐹
𝐴
Bending Stresses
V K Jadon, Professor, Mechanical Engineering
Axial Stress 𝑏
ℎ
𝑙
𝑴 𝑴

4. V K Jadon, Professor, Mechanical Engineering
More on Bending Stresses
𝑏
ℎ
𝑙
𝐹
𝐹
𝑀 = 𝐹. 𝑙
x
y
z

5. Applied TM
Resisting TM
𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑎𝑖𝑛
𝜃
𝑀𝑡
𝑀𝑡
𝐴
𝐵
𝐵′
𝑂
𝜏
𝑟
=
𝐺𝜃
𝑙
=
𝑀𝑡
𝐽
=
𝜏 𝑚𝑎𝑥
𝑟 𝑚𝑎𝑥
Torsional Stresses

6. There are only TWO types of stresses
- Normal Stress
- Shear Stress
Stress is always calculated at a point
Double subscript notation
- First subscript represents plane
- Second subscript represents direction
SUMMARY
 Axial stress
 Bending Stress
 Circumferential stress
 Hoop stress
 Radial stress etc.
 In-plane shear stress
 Transverse shear stress
 Torsional shear stress
Static Equilibrium
Stress-strain Relations
V K Jadon, Professor, Mechanical Engineering

7. References