2/4/2013 1 MECHANICS OF MATERIALS MECHANICS OF MATERIALS CHAPTER TWO STRESS AND STRAIN STRESS AND STRAIN‐AXIAL LOADING AXIAL LOADING Prepared by : Dr. Mahmoud Rababah 1 2.2 2 NORMAL STRAIN UNDER AXIAL LOADING NORMAL STRAIN UNDER AXIAL LOADING Normal strain under axial loading is the deformation per unit length. L In case of non uniform cross-sections, the normal stress will vary along the member. Thus, we consider elements of small length After deformation, element x will increase by . Thus = ..... for infinite elements, = d x dx x dx 2
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2/4/2013
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MECHANICS OF MATERIALSMECHANICS OF MATERIALS
CHAPTER TWOSTRESS AND STRAINSTRESS AND STRAIN‐‐AXIAL LOADINGAXIAL LOADING
Prepared by : Dr. Mahmoud Rababah 1
22..2 2 NORMAL STRAIN UNDER AXIAL LOADINGNORMAL STRAIN UNDER AXIAL LOADING Normal strain under axial loading is the
deformation per unit length.
L
In case of non uniform cross-sections, thenormal stress will vary along the member.Thus, we consider elements of small length
After deformation, element x will increaseby . Thus
Failure occurs due to internal defectsthat initiate a crack perpendicular to thethat initiate a crack perpendicular to thenormal stress.
Failure occurs by slippage of the material along oblique surfaces and is due primarily to shearing stresses (form a cone shape of angle 45o) 5
In the elastic region a linear relationship between stress and strain is existed.
22..5 5 HOOK’S LAW HOOK’S LAW (MODULUS OF ELASTICITY)(MODULUS OF ELASTICITY)
E hook’s law
22..6 6 ELASTIC VERSUS PLASTIC BEHAVIOUR OF A ELASTIC VERSUS PLASTIC BEHAVIOUR OF A MATERIALMATERIAL
Elastic region: The deformation is recovered after releasing the loadThe deformation is recovered after releasing the load. Percentage of deformation is small.
Plastic region: the deformation is permanent. Percentage of deformation is magnificent.
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Local plastic deformationoccurs before reaching the
22..15 15 RELATIONSHIP AMONG RELATIONSHIP AMONG vv, , E AND GE AND G
2(1 )
EG
v
modulus of rigidity
modulus of elasticity
poisson’s ratio
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22..17 17 STRESS AND STRAIN DISTRIBUTION UNDER STRESS AND STRAIN DISTRIBUTION UNDER AXIAL LOADING AXIAL LOADING (SAINT(SAINT--VENANT’SVENANT’S PRINCIPLE)PRINCIPLE)
Axial load applied by rigid plate
Concentrated axial l d li d di lload applied directly
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Saint-Venant’s Principle: The stress distribution isuniform far from the vicinity of the applied loads.
Far means away by at least a magnitude equal to thelargest dimension of the cross-section.
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Stress concentration is independent of the size of the piece. It depends upon the relation between the geometric