The steel bar has the original dimensions shown in the...

The steel bar has the original dimensions shown in the figure. If it is subjected to an axial load of $50 \mathrm{kN}$ determine the change in its length and its new cross-sectional dimensions at section $a-a . E_{\mathrm{st}}=200 \mathrm{GPa}, \nu_{\mathrm{st}}=0.29$

Key Concepts

Axial Stress

Axial stress is the force acting along the length of a member divided by the cross-sectional area over which the force is distributed. It is the primary measure used in determining how materials deform under loads and is essential in the analysis of structural components subjected to tension or compression.

Axial Strain

Axial strain is defined as the relative change in length of a material when subjected to an axial load. It is calculated as the change in length divided by the original length, and reflects the material's deformation response under stress.

Hooke's Law

Hooke's law describes the linear relationship between stress and strain in elastic materials, stipulating that the strain is directly proportional to the applied stress as long as the material remains within its elastic limit. This principle is fundamental in predicting how materials elongate or contract under loading.

Young's Modulus

Young's modulus, or the elastic modulus, is a material property that quantifies its stiffness by relating stress to strain in the elastic region. It is a crucial parameter in determining the extent of deformation a material will undergo when subjected to an applied load.

Poisson's Ratio

Poisson's ratio is the ratio of transverse strain to axial strain in a material undergoing deformation. It explains how a material will contract in the directions perpendicular to an applied tensile load and is key to predicting changes in cross-sectional dimensions under axial loading.

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