Characteristics of the Diagrams Assignment Help

Assignment Help: >> Shear Force and Bending Moment Diagrams - Characteristics of the Diagrams

Characteristics of the Diagrams:

Shear force diagrams (SFDs) & bending moment diagrams (BMDs) are extremely useful which give the apparent picture of the distribution of shear force & bending moment along with the length of the beam. Some significant points regarding these diagrams are as follows :

1. If there is a sudden enhance  or reduce, i.e. a vertical line of SF diagram, it denote that there is either a point load or reaction of the support at that point or in other words, if there is particular point load or reaction, this will cause sudden enhance or reduce in the SF diagram w.r.t. upward or downward direction of point load or reaction, and it shall not cause any distinct variation in the BM diagram.

2. Where the rate of loading is zero, the SF curve shall have constant ordinates and BM curve shall vary linearly. In other terms, if there is no enhance or reduction in SF curve between any two points that means SF line is horizontal & consists of rectangle, it denote that there is no loading among the two points

3. Where the intensity of load is constant, that means uniformly distributed load, the SF curve shall vary linearly and the BM curve shall be a parabola. In other terms, if the SF line is an inclined straight line among any two points, and the BM curve is a parabolic curve among any two points, it denote that there is uniformly distributed load among the two points.

4. Where the loading curve is varying linearly, that means. Uniformly varying load, the SF curve shall be a parabola and the BM curve shall be a cubic parabola. In other terms, if the SF line is a parabolic curve among any two points and BM curve is a cubic parabola among any two points, it denote that there is a uniformly varying load among the points.

5. SF & BM diagrams might be drawn by successive integration for difficult case of loading.

6. The area of loading curve in elementary length shall be equal to change in shear force & area of shear force curve in elementary length will be equal to change in bending moment.

7. The BM shall be equal to zero at the free end of the cantilever & at the simply supported ends.

8. At the intermediate supports, the bending moments are always negative.

9. The maximum bending moment take place at the point where the shear force changes sign & the point of contraflexure is the point where the BM changes sign.

Sometimes, rather than load diagram, a SF diagram shall be given. In such cases, a loading diagram is drawn first. After drawing the load diagram for the beam, the BM diagram might be drawn as usual.

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