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
