The bar has a cross-sectional area of 400(10^-6) m^2. If it is subjected to a uniform axial dist

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The bar has a cross-sectional area of 400(10^-6) m^2. If it...

The bar has a cross-sectional area of $400\left(10^{-6}\right) \mathrm{m}^{2}$. If it is subjected to a uniform axial distributed loading along its length of $9 \mathrm{kN} / \mathrm{m},$ and to two concentrated loads as shown, determine the average normal stress in the bar as a function of $x$ for $0.6 \mathrm{m}<x \leq 1.5 \mathrm{m}$

Key Concepts

Axial Normal Stress

Axial normal stress refers to the internal force per unit area within a structural member that arises due to axial (tensile or compressive) loading. It is calculated by dividing the internal axial force by the cross-sectional area, providing a measure of how the material is loaded and is crucial for assessing whether the material will yield or fail under the applied loads.

Distributed Loading

Distributed loading is a type of force applied continuously over a length, area, or volume of a body rather than at a single point. In the context of a bar, a uniform axial distributed load applies a consistent force per unit length along the bar, and its contribution to the internal force at any cross-section can be determined by integrating the load intensity over the relevant length segment.

Concentrated Loading

Concentrated loads are forces applied at specific, discrete points along a structure. These instantaneous loads contribute directly to the internal axial force in the bar at and beyond the point of their application. Their effect, combined with that of distributed loads, must be accounted for in an equilibrium analysis to accurately determine the stress distribution.

Force Equilibrium and Section Analysis

Force equilibrium involves cutting the bar at an arbitrary section and summing the forces acting on the segment to ensure static equilibrium. By accounting for both distributed and concentrated loads, the resulting internal force at any section is obtained. Dividing this net force by the cross-sectional area gives the average axial stress, which varies along the length of the bar depending on the load contributions from the portion of the bar being considered.

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