Chapter 18
Stress and Strain - Axial Loading
Normal Strain under Axial Loading
A rod subjected to a load undergoes elongation. A load-deformation diagram can represent the elongation but cannot predict deformation in different rods.
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Stress-Strain Diagram
Consider a cylindrical specimen placed in a system to measure its tensile strength.
Two gauge marks are inscribed on the central portion of the specimen. ...
Stress-Strain Diagram - Ductile Materials
When a specimen is subjected to loading the length first increases linearly at a slow rate, resulting in an initial straight line with a steep slope on ...
Stress-Strain Diagram - Brittle Materials
Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation ...
True Stress and True Strain
Engineering stress is the ratio of the load and the undeformed original cross-sectional area. Engineering stress approximates strain which represents the ...
Hooke's Law
Hooke's law states that stress applied to a material is directly proportional to the strain it experiences within the elastic limit. For ductile ...
Plastic Behavior
Materials under stress due to tensile loading exhibit elastic and linear behavior until the yield point. Removing the load at the yield point, stress and ...
Fatigue
Fatigue occurs when the materials, under repeated loads for thousands or millions of cycles, rupture at a stress level much lower than the material's ...
Deformation of Member under Multiple Loadings
The deformation of a rod with different materials and cross-sections is computed by dividing it into parts, each characterized by individual parameters.
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Statically Indeterminate Problem Solving
Consider two cylindrical rods, one of steel and another of brass, joined at point B and restrained by rigid supports at points A and C.
Determine the ...
Thermal Strain
A homogeneous rod with a uniform cross-section, resting freely on a horizontal surface, expands when heated.
The expansion is proportional to the ...
Temperature Dependent Deformation
Consider a non-homogenous rod made of steel and brass, restrained at both ends and subjected to a temperature change.
The stress and load on the rod are ...
Poisson's Ratio
When a slender bar is subjected to an axial load, the bar material undergoes axial strain, causing it to deform in the axial direction.
Simultaneously, ...
Generalized Hooke's Law
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an ...
Bulk Modulus
The bulk modulus is a scientific term used to describe a material's resistance to uniform compression. It is the proportionality constant that links a ...
Shearing Strain
In a cubic element with a general state of stress, the shearing stresses can deform a cube into an oblique parallelepiped without affecting normal ...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
A slender bar subjected to an axial load undergoes deformation in the axial and transverse directions. The deformation affects the cubic elements within ...
Saint-Venant's Principle
Consider a member with plates on both ends. When loads are applied centrally on the plates, they move towards each other without rotating, causing the ...
Stress Concentrations
Stress concentration refers to the amplification of stress in a structural member near points of discontinuity, such as holes or abrupt changes in ...
Residual Stresses
When a rod is stretched beyond its yield point, it permanently deforms and doesn't regain its original length.
The stresses created during loading are ...
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