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

INTRODUCTION:

Plot of shear and bending moment values on separate diagrams could be obtained. Magnitude and location of different quantities can be easily visualized.
SFD & BMD are essential for designers to make decisions on the shape and size of a beam.

PREAMBLE:

The advantage of plotting a variation of shear force F and bending moment M in a beam as a function of ‘x' measured from one end of the beam is that it becomes easier to determine the maximum absolute value of shear force and bending moment.

Further, the determination of value of M as a function of ‘x' becomes of paramount importance so as to determine the value of deflection of beam subjected to a given loading.

CONSTRUCTION OF SFD AND BMD:

  • A shear force diagram can be constructed from the loading diagram of the beam. In order to draw this, first the reactions must be determined always. Then the vertical components of forces and reactions are successively summed from the left end of the beam to preserve the mathematical sign conventions adopted.
  • The shear at a section is simply equal to the sum of all the vertical forces to the left of the section.
  • When the successive summation process is used, the shear force diagram should end up with the previously calculated shear (reaction at right end of the beam.
  • No shear force acts through the beam just beyond the last vertical force or reaction. If the shear force diagram closes in this fashion, then it gives an important check on mathematical calculations.
  • The bending moment diagram is obtained by proceeding continuously along the length of beam from the left hand end and summing up the areas of shear force diagrams giving due regard to sign.
  • The process of obtaining the moment diagram from the shear force diagram by summation is exactly the same as that for drawing shear force diagram from load diagram.
  • It may also be observed that a constant shear force produces a uniform change in the bending moment, resulting in straight line in the moment diagram.
  • If no shear force exists along a certain portion of a beam, then it indicates that there is no change in moment takes place. It may also further observe that dm/dx= F therefore, from the fundamental theorem of calculus the maximum or minimum moment occurs where the shear is zero.
  • In order to check the validity of the bending moment diagram, the terminal conditions for the moment must be satisfied. If the end is free or pinned, the computed sum must be equal to zero.
  • If the end is built in, the moment computed by the summation must be equal to the one calculated initially for the reaction. These conditions must always be satisfied.

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