\r\n Have you ever wondered why is it so easy to poke a hole in a piece of paper with the tip (front-end) of a pen\r\n but not so much with the back-end of the pen?\r\n
\r\n The answer lies in the notion of stress. Stress describes how much force a body experiences per unit area, and is an important notion in mecahnics of material.\r\n Stress depends upon not only the magnitude of applied force but also the area onto which\r\n the force is applied. Thus, the same magnitude of force applied over different areas can result in different values of stress.
\r\n For example — when you poke a piece of paper with the tip of a pen, the entire applied force is concentrated over the tiny area of the tip. As a result, the paper experiences a large stress — making it easier to poke a hole in it.\r\n On the other hand, when you poke a piece of paper with the back-end of the pen, the applied force is spread over a much larger area, resulting in a much lower stress on the paper, and as a result, poking a hole is not so easy that way.\r\n
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There are two types of stress in mechanics.
\r\n\n Let's consider a sqaure bar with a uniform cross-section area \\(A \\) as shown below. The bar is subjected to a pair of equal forces with magnitude \\(F\\) — both acting along its axis but in opposite directions. Next, consider a cut perpendicular to the length of the bar. Upon force balance, we obtain the internal force acting on the cross-section as \\(F\\).\r\n
\r\n\n Thus, the stress acting on that cross-sectional area of the bar can be obtained as:\r\n $$\\sigma = \\frac{F}{A}$$\r\n This exercise can be repeated for any cut through the bar, and it can be shown that the stress remains uniform throughout the length of the bar (given that the cross-sectional area of the bar remains constant).\r\n
\r\n\n Through this MagicGraph, we will explain the notion of stress by means of a simple illustration.\r\n In this illustration, a cylindrical bar with cross-sectional area varying along its length is subjected to equal but opposite forces\r\n at its ends, as a result of which, a tensile stress is developed.\r\n Because the bar has different cross-sectional area at different points, it experiences varying magnitude of stress along its length - higher stresses at locations that have smaller cross-sectional area and smaller stress at locations with larger cross-sectional area. Drag point 'A' along the length to examine the stress at different points along the length of the bar. Note the locations along the bar that have maximum and minimum stresses.\n
\r\n\n To get started:\r\n