Stress and Strain

Stress and Strain

The Internal Resistance offered by a body on the application of external force is known as Stress The relative change in the size of a body on the application of external force is known as Strain The Linear Elastic Theory is developed to analyse different types of members subject to axial, shear, thermal and hoop stresses. Assumptions made in deriving the expressions of Stresses and Strains - For the range of forces applied Material is Elastic Material is Homogeneous Material is Isotropic

Stress Strain Curve

The stress-strain relation of any material is obtained by conducting tension test The following salient points are observed on the stress-strain curve: Limit of Proportionality (A): It is the limiting value of the stress up to which stress is proportional to strain. Elastic Limit: This is the limiting value of stress up to which if the material is stressed and then released (unloaded) strain disappears completely and the original length is regained. This point is slightly beyond the limit of proportionality. Upper Yield Point (B): This is the stress at which, the load starts reducing and the extension increases. This phenomenon is called yielding of material. At this stage, the strain is about 0.125 per cent.

Stress-Strain Curve (Contd...)

Lower Yield Point (C): At this stage, the stress remains same but strain increases for some time. Ultimate Stress (D): This is the maximum stress the material can resist. This stress is about 370–400 N/mm2. At this stage cross-sectional area at a particular section starts reducing very fast. This is called neck formation. After this stage load resisted and hence the stress developed starts reducing. Breaking Point (E): The stress at which finally the specimen fails is called breaking point. At this strain is 20 to 25 per cent.

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Stress and Pressure

Stress - Internal Resisting force induced at a point in member under load Pressure - Magnitude of External force applied at a point

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Differences between Stress and Pressure

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S-S Curve for Other Materials

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True and Nominal Stresses and Strains

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Factor Of Safety

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The ratio of ultimate stress to working stress is called the factor of safety. For steel – 1.85

Stress is proportional to Strain, up to the Elastic limit. However, no sample follows Hooke's law indefinitely, and here comes a point, called the Limit of Proportionality, where there is no longer a linear relationship between force and extension. After yet more force is applied, the Elastic Limit will be reached. This means that the sample will no longer return to its original shape when the force ceases to be present. Eventually, the force will become so great that the material snaps. This is called the Yield Point.

Hooke's Law

Poisson's Ratio

within the Elastic limit, there is a constant ratio between lateral strain and linear strain. This constant ratio is called Poisson’s ratio. It is denoted by μ. For most of the metals, its value is between 0.25 to 0.33. Its value for steel is 0.3 and for concrete 0.15.

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Volumetric Strain

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When a member is subjected to stresses, it undergoes deformation in all directions. Hence, there will be a change in volume. The ratio of the change in volume to original volume is called volumetric strain. It can be shown that volumetric strain is the sum of strains in three mutually perpendicular directions.

Thermal Stress

When a material undergoes a change in temperature, it either elongates or contracts depending on whether the temperature is increased or decreased of the material. If the elongation or contraction is not restricted, i. e. free then the material does not experience any stress despite the fact that it undergoes a strain The strain due to temperature change is called thermal strain and is expressed as,                                                                                     ε = α(ΔT )      Where α is co-efficient of thermal expansion and ΔT is the change in temperature. The free expansion or contraction of materials, when restrained induces thermal stress in the material given by                                                                                                                                                                                   σ = E (α ΔT) Where E = Modulus of elasticity