Strength of material:-
Strength of material could be a subject that deals with however solid bodies react once subjected to varied types of loading.
Elasticity:-
The property of bound materials of returning back to their original position, once removing the external force is understood as elasticity.
A body is solid to be perfectly elastic, if it returns back completely to its original shape and size, after the removal of external forces.
If the body doesn't come back completely to its original form and size, once the removal of external force, it's known as partially elastic.
Ex- Rubber Band
Stress:-
Resistance per unit area of deformation is known as stress.
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| Figure- Stress |
Mathematically,
σ=P/A
Where, σ= Stress
P= Load or internal resistance force
A= Area
Units- Pascal(Pa)
1 Pa = 1 N/mm^2
Strain:-
-Deformation per unit length is understood as strain.
-Change in dimension upon original dimension.
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| Strain |
Mathematically,
ϵ=ΔL/L
Where,
L = original length
ΔL= Change in length
ϵ= Strain
Units- Dimensionless.
Type of stresses-
Normal Stress
Shear Stress
Normal Stress:-
-Perpendicular to the surface.
-Classified in two types-
Tensile stress
Compressive stress
1. Tensile stress:-
-When subjected to 2 equal and opposite pulls and therefore the body tend to increase its length.
-Cross-sectional area of the body gets reduced.
2. Compressive stress:-
-When subjected to 2 equal and opposite pushes and also the body tend to decrease its length.
-Cross-sectional area of the body gets increased.
Note-Sign convention: The tensile forces are termed as (+ve ) while the compressive forces are termed as negative (-ve).
Shear stress:-
-Parallel to the surface.
-Also Known as parallel stress/ Tangential stress.
-Mathematically
τ = P/A
Unit- N/m^2
Ex- Cesar
Types of strain-
Strain is also classified in two types-
Normal Strain
Shear strain
NORMAL STRAIN-
Strain developed in Perpendicular direction.
Classified in two types-
Tensile strain ( Strain developed by tensile stress)
Compressive strain( Strain developed by compressive stress)
Shear Strain-
Strain developed in Parallel direction.
Elastic limit:-
In section, there's a limiting value of forces up to and at interval that the deformation entirely disappears on the removal of force.
The value of intensity of stress similar to this limiting force is called elastic limit of the material.
Beyond the elastic limit, the material gets into plastic stage and trough this stage the deformation does not entirely disappear on the removal of the force.
Hooks law:-
When a material is loaded, at intervals its elastic limit the stress is directly proportional to the strain.
Mathematically,
Hook’s law holds for tension as well as compression.
Modulus of elasticity (Young’s Modulus “E”)-
The quantitative relation of the stress and strain on that Hook’s law holds.
Mathematically,
E=σ/ϵ
Where,
E= Modulus of elasticity or Young’s modulus
σ= stress
ϵ=strain
Material | Modulus of elasticity |
| Steel | 200-220 |
| Wrought iron | 190-200 |
| Cast iron | 100-160 |
| Copper | 90-110 |
| Brass | 80-90 |
| Aluminum | 60-80 |
| Timber | 10 |
Deformation of a body because of force acting on it think about a body subjected to a tensile stress,
Let -
P= load or force acting on body
L= length of the body
A= cross-sectional area of the body
σ= stress induced in the body
E= Young’s modulus
ϵ= strain
ΔL= deformation of the body
We know
Stress σ=P/A & Strain ε=ΔL/L=σ/E=P/AE
ΔL=σL/E=PL/AE