1. Chapter Introduction 
Concept of Stress

2. Statics Mechanics of Materials  Elasticity  Plasticity
Road Map:
Statics Mechanics of Materials 
Elasticity  Plasticity
Fracture Mechanics
Fatigue
Creep
Mechanics of Materials is important foundation for:
1. Machine Design I & II
2. Advanced Mechanics Courses
3. Elasticity & Plasticity
4. Finite Element Methods

3. Statics: main concern: Equilibrium
Forces
Mechanics of Materials:
1. Equilibrium
2. Deflection (Deformation)
3. Yielding or Failure
Stress
Strain

5. “Mechanics of Materials” is a branch of Mechanics that develops relationships between :
The external loads
Intensity of internal forces
(stress / strain / deformation)

6. 1.3 Stresses in the Members of a Structure
(1.5)
Assumptions:
1. Uniform distribution of stress
2. Uniform material properties

7. Units:
SI Units:
(1.5)
English Units:
psi = lb/in2
ksi = 103 psi

8. 1.5 Axial Loading: Normal Stress
The normal stress:
(1.5)
The more general definition of normal stress is:
(1.6)

9. If the stress distribution is not uniform:
External force
internal force

10. 1. In engineering practice we assume the stress is uniform
This is only true:
If the line of action of the concentrated loads P and P’ passes through the centroid of the section considered.
2. The distribution of the internal stress cannot be uniform if the load is eccentric.

11. 1.6 Shearing Stress
(1.7)

12. 1.7 Bearing Stress in Connections
(1.10)
Bearing Stress in Connections

13. 1.9 Method of Problem Solution
To solve a problem, use the following procedures:
1. Draw FBDs
2. Apply Equations of Equilibrium
3. Determine , , and deformation (deflections)
4. Check your answers.
1.10 Numerical Accuracy
Accuracy Criteria:
1. the accuracy of the given data
2. the accuracy of the computations performed.
For eng. practice, an accuracy of 0.2% is acceptable.

14. Use 4 important figures to record numbers beginnings with a “1”
Use 3 important figures in all other cases.
Examples:
A force of 40 lb. should be read 40.0 lb, and
A force of 15 lb. should be read lb.

15. 1.11 Stress on an Oblique Plan under Axial Loading
(1.12)
(1.13)

16. Since Ao = Acos, or A = Ao/cos
The max normal stress occurs at  = 0o
The max shear stress occurs at  = 45o
At  = 45o the normal stress is

17. 1.12 Stress under General Loading Conditions: Components of Stress

18. Vxz Notation: The plane is ┹ to x-axis
(1.18)
Notation:
The plane is ┹ to x-axis
Vxz
The vector is // to z-direction

19. Notation:
The direction of the component: shear stress is // to y-direction
The surface is ┹ to x-axis

20. All the forces in a system must fulfill the equation of equilibrium:
(1.19)
(1.20)

21. Applying equation of equilibrium
(1.21)
(1.22) 1

22. Therefore, only six components are required to uniquely define the stress state of a material.

23. Max normal stress occurs at  = 0o
Max shear stress occurs at  = 45o
The cube at  = 45o is subjected to the same magnitude of normal and shear stresses at all four sides

24. 1.13 Design Considerations
Concept of Factor of Safety:
Factor of Safety = F.S. =
Factor of Safety = F.S. =
End