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created by - **premprakash**

LESSON

## the definition of beams

## types of support

## types of beams

## types of loading

## concept of shear force and bending moment.

## sign convention.

## shear force diagram and bending moment diagram

## variation of shear force and bending moment

## the relation between load, BM,SF

## multiple-choice questions.

- beam a structure member that has a
*long length as compare to breath or dia**.* - it subjected to
*transverse loads, couple.*

TYPES OF SUPPORT

- roller support
- pin support
- fix support

- allows rotation.
- allows translation.
- have 1 vertical reaction.

- allows rotation
- have 2 reaction- one vertical, one horizontal

- no rotation
- no translation
- have 3 reactions- one vertical, one moment, one horizontal reaction.

## rest on roller support at one end and pinned support at another end.

## fixed at one end and free at another end.

- both ends of the beam are fixed.

- rest on more than two support throughout its length.

- extends from its support either one side or both sides.
- it has features of simply supported and cantilever beam.

a beam may be subjected to either or in combination of the following loads.

- concentrated or point load-
*it is load acting on a single point.* - uniformly distributed load(UDL)-
*it is load uniformly spread over the beam and in calculation assumed acts at c.g. point throughout its length.* - uniformly varying load(UVL)-
*it is load varying at one end to the other end and sometimes is known as a triangular load.*

- algebraic sum of all transverse forces either to the left or right hand of the section.
- it is written as a symbol as S.F. or F only.

- algebraic sum of
*moments of all transverse force*either to the left or right of the section. - it is written as symbol B.M. OR M only.

## calculation of shear force at section or point, generally we take all the sum of forces either left or right of the section that is SF at that section.

- if assume we take the sum of all forces right of the section then upward forces are taken negative and downward forces are taken as positive in calculation of shear force.

- in calculation of bending moment, we take the sum of all the moment either right or left of at section or point that is bending moment at that section.
- assume we take the right side of forces in calculation of bending moment, if that force cause sagging of the beam then called positive bending moment.

*draw of shear force throughout the length of the beam is called shear force diagram(SFD)*

*draw of bending moment throughout, length of the beam is called bending moment diagram(BMD)*

types of loading | variation of shear force | variation of moment |

point | rectangle | linear |

uniformly distributed | linear | square parabola |

uniformly varying | parabolic | cubic parabola |

parabolic | cubic | fourth-degree polynomial |

couple or moment | no shear variation | a vertical step at point of application |

*rate of change of shear force is equal to load.*- dF/dx = W
*rate of change of bending moment is equal to shear force*- dM/dx = F
*bending moment is maximum when the shear force is zero or change sign.**point of contra flexure where bending moment is zero or change sign.*

MULTIPLE CHOICE QUESTIONS PART 1

*if a cantilever beam is subjected to point load at its free end then shear force under the load is - equal to the load.**the bending moment at the free end of a cantilever beam carrying any type of load is - zero**the bending moment at the center of a simply supported beam carrying a uniformly distributed load is - wl*^{2}/8*when the shear force at that point is zero, the bending moment at**that point will be - max**the point of contra flexure is a point where - bending moment change sign**the shear force in a beam subjected to pure positive bending is - zero**the number of independent reaction components for a hinge or pinned support is - 2**the shape of the shear force diagram for a cantilever subjected to a couple at its free end is - no shear force in any part of the beam.**the bending moment in a beam is maximum where - shear force change sign or zero.**match the list 1 and list 2*

*thankyou created by premprakash*

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