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

step 1 Hi friends here it is given. Area protection of the bar is 400 into 10 to the power minus 6 mete

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 triangular axial distributed loading along its length which is 0 at $x=0$ and $9 \mathrm{kN} / \mathrm{m}$ at $x=1.5 \mathrm{m},$ and to two concentrated loads as shown, determine the average normal stress in the bar as a function of $x$ for $0 \leq x<0.6 \mathrm{m}$

Key Concepts

Equilibrium and Free-Body Diagram Analysis

A free-body diagram (FBD) is used to isolate a portion of the member to apply equilibrium conditions. By considering the sum of forces acting on a segment of the bar, one can relate the external loads (both distributed and concentrated) to the internal axial force. This method is critical for developing the function that describes how normal stress varies with position along the member.

Distributed Loading

Distributed loading refers to loads that are spread continuously over a length, area, or volume rather than being applied at a single point. In problems like this, the load intensity can vary along the length (for example, in a triangular distribution), and its effect on the internal force distribution is found by integrating the load intensity over the relevant distance.

Concentrated Loads

Concentrated loads are forces applied at specific points along the member. They create abrupt changes in the internal axial force and must be taken into account along with distributed loads. Accurately incorporating these point loads is crucial for determining the overall stress distribution in the member.

Normal Stress

Normal stress in a structural member is defined as the internal force per unit area acting perpendicular to the cross section. It is calculated by dividing the internal axial force (resulting from external loads) by the area over which the force is distributed. This concept is fundamental in stress analysis for determining the material response under axial loading.

Internal Axial Force

The internal axial force in a member is determined by summing all the external forces acting on a free-body section of the member using equilibrium conditions. This force is essential for computing stresses throughout the member, as it varies along the length due to applied distributed and concentrated loads.

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