UNIT01 SIMPLE STRESSES STRAINS Lecture Number 01 Prof

UNIT-01. SIMPLE STRESSES & STRAINS Lecture Number - 01 Prof. M. N. CHOUGULE MECHANICAL DEPARTMENT SIT LONAVALA Strength of Materials

AGENDA • • Types of Stresses Types of Strains. Hook's Law. Poisson's Ratio(μ). Stress-Strain Diagram Engineering stress VS True stress Numerical Strength of Materials

STRESS? ? Strength of Materials

Types of Stresses • Simple stress can be classified as normal stress, shear stress, and bearing stress. • Normal stress: It develops when a force is applied perpendicular to the cross-sectional area of the material. • Tensile or compressive stresses : depends on stresses acts out of the area or into the area. Strength of Materials

• Bearing Stress : It is the contact pressure between two bodies. (compressive ). Strength of Materials

• Shear stress: It is developed if the applied force is parallel to the resisting area. • Shear stress (τ) acts tangential to the surface of a material. Strength of Materials

Direct , Shear and Volumetric Strain • Direct strain is the deformation per unit of the original length. • Shear strain is measured by angle This is measured in radians. • Volumetric strain is ratio of change in volume to original volume Strength of Materials

Hook's Law • Within elastic limit of material, Stress is directly proportional to strain. Where, E=Constant of proportionality (Modulus of Elasticity) Strength of Materials

Poisson's Ratio(μ) • The ratio of the lateral strain to longitudinal strain is known as the poison's ratio. • Poison's ratio (μ) = lateral strain / longitudinal strain • For most engineering materials the value of m his between 0. 25 and 0. 33. μ material diamond Al Cu Pb Steel rubber cork Strength of Materials 0. 21 0. 33 0. 35 0. 4 0. 29 close to 0. 5 close to 0

Stress-Strain Diagram Strength of Materials

Stress-Strain Diagram (cont) • Proportional Limit (1 – 2) : - The stress is linearly proportional to the strain in this region i. e. Hooks law obeyed. • Elastic Limit (2 – 3) : -The material will return to its original shape after the material is unloaded. • Yield Limit (3 -4) : - The point where permanent deformation occurs. Strength of Materials

Stress-Strain Diagram (cont) • Strain Hardening(5 -6): - Raising the yield strength by permanently straining the material is called Strain Hardening. • Ultimate Tensile Strength (Point 6 ): - It is the maximum stress which the material can support without breaking. • Fracture (Point 7) : - If the material is stretched beyond Point 6, the stress decreases as necking and non-uniform deformation occur. Strength of Materials

Engineering stress VS True stress • Engineering stress - The applied load, or force, divided by the original cross-sectional area of the material. • True stress- The load divided by the actual cross-sectional area of the specimen at that load. Strength of Materials

Stress Strain Diagram for Ductile and Brittle Material • Ductile material: -Having yield point, after ultimate point fracture occurs. • Brittle material: - Brittle materials do not have a yield point, ultimate strength and breaking strength are the same. • Ex- cast iron, glass, stone, concrete etc. Strength of Materials

Q. 01. Find the smallest diameter bolt that can be used as shown in Fig. if P =400 k. N. The shearing strength of the bolt is 300 MPa. Ans. 300 x 2(π/4 x dxd)=400 x 1000 d=29. 13 mm Strength of Materials