To draw shear force and bending moment diagram for a simply supported beam under point and distributed loads.
APPARATUS USED :- Apparatus of simply supported beam.
THEORY :-
BEAM :- It is a structural member on which the load act perpendicular to axis. It is that whenever a horizontal beam is loaded with vertical loads, sometimes it bends due to the action of the loads. The amounts by which a beam bends, depends upon the amount and types of loads, length of beam, elasticity of the beam and the type of beam. In general beams are classified as under :
1. Cantilever beam :- It is a beam whose one end is fixed to a rigid support and the other end is free to move.
2. Simply supported beam :- A beam supported or resting freely on the walls or columns at its both ends is known as simply supported beam.
3. Rigidly fixed or built-in beam :- A beam whose both the ends are rigidly fixed or built in walls is called a fixed beam.
4. Continuous beam :- A beam support on more than two supports is known as a continuous beam. It may be noted that a continuous beam may not be overhanging beam.
TYPES OF LOADING :
1. Concentrated or point load :- A load acting at a point on a beam is known as concentrated or a point load.
2. Uniformly distributed load :- A load, which is spread over a beam in such a manner that each unit length is loaded to a same extent.
3. Uniformly varying load :- A load, which is spread over a beam, in such a manner that its extent varies uniformly on each unit length.
SHEAR FORCE :- The shear force at the cross-section of a beam may be defined as the unbalanced vertical forces to the right or left of the section.
BENDING MOMENT :- The bending moment at the cross-section of a beam may be defined as the algebraic sum of the moment of forces, to the section.
IMPORTANT POINTS :-
1. If loading is uniformly distributed load then shear force diagram will be a curve of first degree and B.M. diagram will be a curve of second degree.
2. If the loading is point load then its corresponding S.F. diagram would be a curve of zero degree and the B.M. diagram would be a curve of first degree.
3. If the loading is uniformly varying load its S.F. diagram would be curve of second degree and BMD will be of third degree.
4. Bending moment is maximum where shear force is zero.
5. In case of simply supported beam the first step is to calculate the reactions at the support, then we proceed in usual manner.
6. In case of cantilever beam there is no need of finding reaction and start from the free end of the beam.
7. Point of flexural is the where BM changes its sign.
8. B.M. at the support is zero for simply supported beam.
Example :- A simply supported beam 4m. long is subjected to two point loads of 2KN & 4KN each at a distance of 1.5m and 3m from the left end draw the S.F & B.M diagram for the beam.
RESULT :-
CONCLUSION :-
VIVA-QUESTIONS :-
· What is the point of contraflexture ?
· What are sagging & hogging moments ?
· Define a beam. What is a cantilever a fixed beam and an overhang beam ?
· Define S.F. & BM.
· When bending moment will be maximum?