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Chapter Introduction Concept of Stress
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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
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Statics: main concern: Equilibrium
Forces Mechanics of Materials: 1. Equilibrium 2. Deflection (Deformation) 3. Yielding or Failure Stress Strain
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“Mechanics of Materials” is a branch of Mechanics that develops relationships between :
The external loads Intensity of internal forces (stress / strain / deformation)
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1.3 Stresses in the Members of a Structure
(1.5) Assumptions: 1. Uniform distribution of stress 2. Uniform material properties
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Units: SI Units: (1.5) English Units: psi = lb/in2 ksi = 103 psi
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1.5 Axial Loading: Normal Stress
The normal stress: (1.5) The more general definition of normal stress is: (1.6)
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If the stress distribution is not uniform:
External force internal force
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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.
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1.6 Shearing Stress (1.7)
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1.7 Bearing Stress in Connections
(1.10) Bearing Stress in Connections
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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.
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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.
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1.11 Stress on an Oblique Plan under Axial Loading
(1.12) (1.13)
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Since Ao = Acos, or A = Ao/cos
The max normal stress occurs at = 0o The max shear stress occurs at = 45o At = 45o the normal stress is
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1.12 Stress under General Loading Conditions: Components of Stress
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Vxz Notation: The plane is ┹ to x-axis
(1.18) Notation: The plane is ┹ to x-axis Vxz The vector is // to z-direction
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Notation: The direction of the component: shear stress is // to y-direction The surface is ┹ to x-axis
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All the forces in a system must fulfill the equation of equilibrium:
(1.19) (1.20)
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Applying equation of equilibrium
(1.21) (1.22) 1
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Therefore, only six components are required to uniquely define the stress state of a material.
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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
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1.13 Design Considerations
Concept of Factor of Safety: Factor of Safety = F.S. = Factor of Safety = F.S. = End
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