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9 December, 15:42

How many sets of equations (V and M equations) would you need to describe shear and moment as functions of x for this beam? In other words, how my segments of the beam need to be analysed separately? There is a uniform distributed load (w) on the left and a concentrated force P applied to the beam

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  1. 9 December, 16:08
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    Shear and moment as functions of x is described below.

    Explanation:

    1. Beam is the slender bar that carries transverse

    loading; that is, the applied force are perpendicular to the bar.

    2. In a beam, the internal force system consist of a shear force and

    a bending moment acting on the cross section of the bar.

    3. The shear force and the bending moment usually vary continuously

    along the length of the beam.

    4. The internal forces give rise to two kinds of stresses on a

    transverse section of a beam:

    (1) normal stress that is caused by

    bending moment and

    (2) shear stress due to the shear force.

    Knowing the distribution of the shear force and the bending

    moment in a beam is essential for the computation of stresses

    and deformations.

    Shear - Moment Equations

    The determination of the internal force system acting at a given

    section of a beam : draw a free-body diagram that expose these

    forces and then compute the forces using equilibrium equations.

    The goal of the beam analysis -determine the shear force V and the bending moment M at every cross section of the beam.

    To derive the expressions for V and M in terms of the distance x

    measured along the beam. By plotting these expressions to scale,

    obtain the shear force and bending moment diagrams for the

    beam.

    The shear force and bending moment diagrams are convenient

    visual references to the internal forces in a beam; in particular, they identify the maximum values of V and M
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