445.204
Introduction to Mechanics of Materials (재료역학개론)
Chapter 5: One dimensional problems
Myoung-Gyu Lee, 이명규
Tel. 880-1711; Email: [email protected]
TA: Chanmi Moon, 문찬미
Lab: Materials Mechanics lab.(Office: 30-521) Email: [email protected]
Basic considerations
- Equilibrium
- Constitutive equations - Kinematics
- Compatibility conditions
- Other effects: temperature etc
2
Statically determinate problems – Example 5.1
- The forces and stresses in the members can be solved completely independently of the
deformation
Equilibrium conditions
3
Statically determinate problems
Constitutive equations – Hooke’s law
Kinematics
4
Statically determinate problems – Example 5.2
5
1. Centrifugal force with the slice
2. Force at the section at r -> t_rr
3. Constitutive law
6
Statically indeterminate problems – Example 5.5
Equilibrium conditions
7
Statically indeterminate problems - Example 5.5
Constitutive equations
Compatibility
8
Statically indeterminate problems – Example 5.7
Force equilibrium
Statically indeterminate problems – Example 5.7
Compatibility Constitutive equation
Statically indeterminate problems – Example 5.9
- Residual stress: stress existing in the structure after full unloading
Statically indeterminate problems – Example 5.9
Hint: For the elongation 0.025 ft, both members should be plastic!
Also, the material is assumed to be perfectly plastic (or no hardening)
Statically indeterminate problems – Example 5.9
Hint:
- Convert the SS curves to force-strain curves?
- Force equilibrium at full unloading, - Compatibility condition
Statically indeterminate problems – Example 5.9
Thermo-elastic constitutive law
Total strain= mechanical strain + thermally induced strain
mech th
ε ε = + ε
mech
1
ε = E σ
th
L L T
L L T
ε = ∆ = α ∆ = ∆ α
Statically indeterminate problems – Example 5.12
Questions ?