simple stressses and strains lecture pdf.
scientechnical hub # lecture by ashok.m
simple stresses and strains
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note; kindly refer the youtube classs on simple stresses and strains before going through the notes ,then only you will better understand this class notes.
Stress ; Internal resistance per unit area Stress =External load /area Kn/m² or N/mm²
Types
1.According to the type of body
2.According to the nature of stress
According to the type of body
1.Uni axial
2.Biaxial
3.Triaxial
1.Tensile stress : External force produced elongation of the body in its direction it is termed as external force The stress is called Tensile stress .
2.Compressive stress : External force cause the shortening of the body in the direction of force ,The stress is called Tensile stress.
3.Shear stress :The tangential stress acting along the section of the body.
Strain : It is the measure of deformation produced by the application of external force Denoted with e e=change in dimension/original dimension
Types : 1.Linear strain
2.Lateral strain
3.Shear strain
4.Volumetric strain.
1.Linear strain : Deformation of the bar per unit length in the direction of applied force
2.Lateral strain : Deformation per unit length in a direction right angles to the direction of applied force .
3.Shear strain : Shear strain measured by the angle through which the body distorts.
4.Volumetric strain;Ratio of change in volume to the original volume.
A.Limit of proportionality :this is the point upto which the stress is directly proportional to the strain.
B.Elastic limit :This is the point on the elastic curve ,upto which the material obeys the property of elasticity strain disappear after removal of load
Yield point ;when tensile load further increased ,stress reaches yield stress and matrerial starts yielding.
C.Upper yield d point :stress strain curve suddenly falls showing a decrease in stress The distinct Position where sudden fall to the curve occurs is known as upper Yield point
D.Lower yield point :postion upto sudden fall occurs is known as Lower yield point
E.Strain hardening point :The point where the stress is constant from D to E
F.Ultimate point : Ultimate load is defined as the maximum load which can be placed prior to the breaking of specimen
G.Breaking point : After reaching ultimate point stress strain curve suddenly falls with rapid increase in strain.
Ultimate stress : Resistance against the fracture Is called ultimate stress or tenacity
Working stress : The max permissible stress in a material during its use in any structure is called working stress
Facor of safety ; For brittle materials :ultimate stress /working stress
For ductile materials : yield stress /working stress
Proof stress :0.2%of strain
Hooke’s law : Stress is directly proportional to the strain within the elastic limit .
Modulus of elasticity (E) : Linear stress /Strain
Aluminium -70Gpa
Bronze -80Gpa
Brass-100Gpa
Copper-120Gpa
Steel-200Gpa
Diamond -1200Gpa
Possions ratio: Lateral strain /Longitudinal strain
Steel -0.25 to 0.33
Concrete -0.1 to 0.2
Wrought iron -0.3
Gold :0.440
Incompressible material like clay,rubber =0.5
poissons ratio Range varies from 0 to 0.5
Rigidity modulus : Denoted with C,G or N
Shear stress /Shear strain Bulk modulus :Direct stress /volumetric strain denoted with k
Relation b/n elastic constants
(a) Relationship between E, G and u E= 2G (1 +u).
(b) Relationship between E, K and o E = 3K (1-2u)
(c) Relationship between E, N and K E=9KG/3K+G
(d) Relationship between N. K and u u=3K-2G/6K+2G
Deformation under axial load : Pl/AE
Elongation of tappered bar : 4pl/πd1d2E
Bars of varying sections =P/E(L1/A1+l2/A2+l3/A3)
Principle of super positions ; algebraic sum of strains caused by the individual loads
follow this video for principle of super positions problem
Composite sections • A composite bar is one which is made of two or more than two materials rigidly fixed so that they sustain together an externally applied load.In such cases.
. • (i) Strain in all the materials is same. In other words extension (or) shortening is same in all materials
• (ii) The Total External Load is equal to the sum of the loads carried by the different materials
Temperature stresses and strains when the temperature of a body is raised or lowered, there will be corresponding increase or decrease in its dimensions. If this change in dimensions is prevented by the application of external forces, the body develops stresses in it. Which are called "temperature stresses". These stresses are also known as "Thermal stresses".
The corresponding strains are called "Thermal strains" (or) "Temperature strains". Coefficient of linear expansion: The increase in length of the body per unit rise of temperature in original length is termed as the coefficient of linear expansion and it is denoted by “alpha.
Strain energy : The energy stored in a body by the virtue of strain is called strain energy .
Proof resilience: the maximum strain energy stored in a body without undergoing permanent deformation .
Modulus of resilience : Proof resilience per unit volume F²/2E.
Strain energy due to gradual loading : F²/2E x volume
Strain energy due to sudden applied load :2p/A
Strain energy due to impact = √2Eph/A
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