1. Chapter 1 Introduction Concept of Stress

2. 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 Mechanics of Materials: 1. Equilibrium 2. Deflection (Deformation) 3. Yielding or Failure Forces 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 Assumptions: 1. Uniform distribution of stress 2. Uniform material properties (1.5)

7. Units: SI Units: (1.5) English Units:psi = lb/in 2 ksi = 10 3 psi

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

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)

13. 1.9 Method of Problem Solution 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. 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.

14. 1.Use 4 important figures to record numbers beginnings with a “1” 2.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 15.00 lb.

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

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

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

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

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

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

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

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

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

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