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Chapter 1 Introduction 

Chapter 1 Introduction . Concept of Stress. 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

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Chapter 1 Introduction 

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

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

  5. 1.3 Stresses in the Members of a Structure (1.5) Assumptions: 1. Uniform distribution of stress 2. Uniform material properties

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

  7. 1.5 Axial Loading: Normal Stress The normal stress: (1.5) The more general definition of normal stress is: (1.6)

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

  9. 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.

  10. 1.6 Shearing Stress (1.7)

  11. (1.10) 1.7 Bearing Stress in Connections

  12. 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.

  13. 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 15.00 lb.

  14. 1.11 Stress on an Oblique Plan under Axial Loading (1.12) (1.13)

  15. 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

  16. 1.12 Stress under General Loading Conditions: Components of Stress

  17. (1.18) Notation: The plane is ┹ to x-axis Vxz The vector is // to z-direction

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

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

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

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

  22. 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

  23. 1.13 Design Considerations Concept of Factor of Safety: Factor of Safety = F.S. = Factor of Safety = F.S. = End

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