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### Shearing Force, And Bending Moment In A Straight Beam 1

Date : 2016-06-23 12:24:21

STRAIGHT BEAM:

The application is designed for calculations of straight, maximum three times static indefinite beams with constant axis-symmetrical profiles. The software solves the following tasks:

• Simple definition of the type of beam and its loading with visual check.
• Calculation of area characteristics of 20 types of cross sections.
• Calculation of reactions in supports.
• Calculation of minimum / maximum bending moment, stress and deflection of the beam.
• Calculation and graphic illustration of the moment, stress, deflection and bending angle of the loaded beam.

Fig 1: Straight beam

RELATION BETWEEN THE INTENSITY OF LOADING, THE SHEARING FORCE, AND THE BENDING MOMENT IN STRAIGHT BEAM:

Consider a straight beam under any system of lateral loads and external couples, Fig 2; an element length of the beam at a distance z from one end is acted upon by an external lateral load, and internal bending moments and shearing forces. Suppose external lateral loads are distributed so that the intensity of loading on the elemental length is w.

Fig 2: Shearing and bending actions on an elemental length of a straight beam

Then the external vertical force on the element is ,  fig 2 this is reacted by an internal bending moment M and shearing force F on one face of the element, and on the other face of the element. For vertical equilibrium of the element we have

If delta z is infinitesimally small

Suppose thls relation is integrated between the limits z, and z,, then

If F, and F, are the shearing forces at z = z, and z = z2 respectively, then

Then, the decrease of shearing force from z, to z2 is equal to the area below the load distribution
curve over this length of the beam, or the difference between F, and F2 is the net lateral load over
this length of the beam.