Mechanics
It is a branch of science which deals with the study of effect of forces on material
Mechanics of materials
It deals with the study of resisting capacity of materials due to the application of external load or forces
Types of materials
- Non deformable (rigid objects)
- Deformable
Non Deformable
These are the materials which do not under go any change in its size or shape due to the application of external loads
Deformable
These are the materials which undergo change in its size or shape on application of external loads
In mom all materials are treated as deformable materials
- Elastic materials
- Plastic materials
- Elasto plastic materials
Elastic Materials
The materials which can undergo change in its size or shape when ever subjected to external forces and has the tendency to regain its original shape and size soon after the external forces are removed such materials are known as elastic material and property is called elasticity
Plastic Materials
The materials which can undergo change in its size or shape when ever subjected to external forces and has no tendency to regain its original shape and size soon after the external forces are removed such materials are known as plastic material and property is called plasticity
Elasto Plastic Materials
The materials which can regain partially its original size or shape soon after the removal of external forces acting on them
In mom all the materials are assumed to be elastic materials
Homogeneous Materials
Materials which consists of same matter distributed uniformly through out and having same physical mechanical property through out are called homogeneous materials
Isotropic Materials (red hot material)
These are the materials which has same elastic properties in all the direction at a given point
Anisotropic Materials
These are the materials having different elastic properties in all the direction at a given point
Homogeneous And Isotropic Materials
These are the materials which has same elastic properties in all the direction at all the points
In mom all the materials are assumed to be homogeneous and isotropic
Ductile Materials
The materials which can sustain large deformation with out failure under tensile loads are known as ductile materials and its property is said to be ductility
Eg: copper, aluminum, steel, mild steel
Brittle Materials
These are the materials which can sustain small deformation under tensile loads
Eg: glass, cast iron, brass, ceramics
Stress [Sigma “σ” Unit: N/ mm2]
It is the resistance offered by material / unit area of cross section against any loads, This stress is known as average or mean stress or simple stress
Normal Stress or Direct Stress
Stress induced in the materials, due to the application of forces normal to the area of cross section are known as normal or direct stress
Axial Stress
Stress induced in the material due to the application of axial forces
Stress
- Tensile stress
- Compression stress
Tensile Stress
It is the resistance offered by material / unit area of cross section against tensile forces is known as tensile stress
Compressive Stress
It is the resistance offered by materials / unit area of cross section against compressive forces is called compressive stress
Bending Stress
It is the resistance offered by materials / unit area of cross section against bending due to transverse loads
Shear Stress / Tangential Stress [Tow “τ” Unit: N/ mm2]
It is the resistance offered by materials / unit area of cross section against shearing or application of tangential forces
Strain [Epsilon “Ε or ϵ ” Unit: no unit ]
It is the measurement of deformation in the material by comparing the change with its originality.
Types of strains
- Linear Strain / Primary
- Lateral strain / Secondary
- Volumetric strain
Linear Strain / Primary
It is the strain measured in a material in the direction of application of the force
Linear strain = change in length / original length {dl / l}
Lateral strain / Secondary
It is the strain measured in a material in the direction perpendicular [to the line of action of the force
Lateral strain = db / b or dt / t
Volumetric Strain
It is the strain measured with respect to change in volume in the material due to combined effect of lenear and lateral strains
Volumetric strain = change in volume / original volume {dv / v}
[change in volume, dv = final volume – original volume
final volume = (l+dl) (b-db) (t-dt) ]
Relation b/w stress and strain
Hooks Law
For elastic materials stress is directly proportional to the strain with in elastic limit
The constant of proportionality 
is called the Modulus of Elasticity 
or Young's Modulus and is equal to the slope of the stress-strain diagram
is called the Modulus of Elasticity or Young's Modulus and is equal to the slope of the stress-strain diagram
Young’s modulus or elastic modulus
+ve slope of stress - strain with in elastic limit
E = stress / strain {with in elastic limit}
Stress Strain Behavior Of Ductile Material In Tension
The strains are measured along with corresponding stress using extensometer or strain guage
From graph it can be observed that the portion “OA” is a straight line and linear indicating that the material obeys hook’s law. The point A in the graph corresponds to proportional limit, little beyond A still behaves as elastic material but hook’s law need not to valid. the point A’ is the elastic limit. Very close to A’ the material begins to yield @ B with out any appreciable increase in stress but corresponding increase in strain. Yielding continues up to point C is called lower yield point. After yielding there will be appropriate raise in strain corresponding increase in stress and the curve seen rising up to point D the point D corresponds to ultimate point after this the specimen develops failure by forming a neck @ this stage even if the loads are decrease the strain is continuously increase, decrease in stress till it breaks. The point E is the break point.
Proportional limit = stress @ A {load @ A / original area of cross section}
Elastic limit = stress @ A’
Yield stress = stress @ C
Ultimate / maximum stress = stress @ D
Safe Stress / Design Stress / Working Stress
The structure or mechanical component is always design the stress less than maximum or ultimate stress
For ductile material with yield point
Factor of safety (FOS) = yield point / (safe/working/design stress)
For brittle material with out yield point
Factor of safety (FOS) = ultimate stress / (safe/working/design stress)
Assumptions on Material in MOM
Material must be elastic
Material must be homogeneous and isotropic
It must be of uniform cross section through out (prismatic)
It must be subjected to axial force
Hooks law must be valid
Stress In Composite Section Connected In Parallel
A composite section is one which is made up of more than one different type of materials connected in parallel in these sections the stress in each material will be different but the amount of deformation that each material undergo are equal, these type of sections are preferred for safety strength and economical reasons
Eg: RCC structure (Reinforced cement concrete)
Modular Ratio
It is the ratio of greater value of young’s modulus of one material to the smaller value of young’s modulus for the other material this ratio is used to relate the stress and area of cross section in different materials which helps in designing the economical sections
Elastic Constants
- Young’s modulus
- Poisson’s ratio
- Bulk modulus
- Shear modulus / rigidity modulus
Poisson’s Ratio [ Nue “ν” or mue ‘μ’]
When ever a material are strained to one direction it will be always accompanied by corresponding strains in the mutual perpendicular direction also this strain is known as lateral or secondary strain
Simon.d.poisson showed that there exists a constant ratio between the lateral and leaner strain with in the elastic limit this ratio is known as poison’s ratio which is defined as the ratio of lateral strain to leaner strain
μ = ( db / b or dt / t ) / (dl / l)
For most material μ value will be 0.25 to 0.45 and
If it is > 0.5 it will be for rubber and “0” zero for cork material
Bulk Modulus [“K” Unit: N/ mm2]
It is the measure of resistance against change in volume, it is defined as the ratio of identical or hydrostatic stress to the volumetric strain in the material. Bulk modulus is denoted by letter “K”
Shear Modulus / Rigidity Modulus [“G” Unit: N/ mm2]
It is the measure of resistance against rigidity or stiffness as per hooks law
τ = shear stress
Φ = shear strain
G = τ / Φ
Compound Stress
The normal stress and tangential stress on any given oblique plane are called compound stress. The normal stress are develop in an element due to bending moment and tangential force are develop due to shear force
Principle Planes and Principle Stress
There are the planes which carry only normal stress with out any shear stress, hence the principle planes are also known as shear less planes.
Generally there are 2 principle planes which mutually perpendicular to each other and known as major and minor principle planes
The normal stress on the principle planes are called principle stress
the plane which carries maximum normal stress is called major principle plane and the plane which carries minimum normal stress is called minor principle plane, correspondingly the normal stresses are called major principle stress and minor principle stress
