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50.2: Longitudinal (Normal) Stress

  • Page ID
    92316
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    In longitudinal (or normal) stress, the applied force is normal (perpendicular) to the surface.

    Imagine a metal rod, for example: pulling on both ends of the rod (so as to stretch it to a longer length) is called tensile stress. If instead we push the ends of the rod together (so as to compress the rod to a shorter length), it is called compressional stress. In either case, the area \(A\) in Eq. 50.1.2 is the cross-sectional area of the rod; the longitudinal stress is then the force applied to either end of the rod divided by the rod's cross-sectional area.

    Strain

    When applying a longitudinal stress to the rod, it changes from its original length \(L_{0}\) to a new deformed length \(L\). Then the longitudinal strain \(\varepsilon\) is defined by

    \[\varepsilon=\frac{\Delta L}{L_{0}}\]

    where \(\Delta L=L-L_{0}\) is the change in the length of the rod from its original length, and will be positive for tensile stress and negative for compressional stress.

    Young's Modulus

    In the case of a longitudinal stress, the appropriate elastic modulus is the Young's modulus \(Y\) :

    \[Y=\frac{F_{n} L_{0}}{A \Delta L}\]

    Here \(F_{n}\) is the force applied normal to the area \(A, L_{0}\) is the original (unstressed) length of the rod, \(L\) is the stressed length of the rod, and \(\Delta L=L-L_{0}\).


    50.2: Longitudinal (Normal) Stress is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.