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2.3 TYPES OF SUPPORTS AND THEIR REACTIONS

Though there are many types of supports, yet the following are important from the subject point of view:

  1. Simple supports or knife edge supports
  2. Roller support
  3. Pin-joint (or hinged) support
  4. Smooth surface support
  5. Fixed or built in support

2.3.1 Simple Support or Knife Edge Support. A beam supported on the knife edges A and B is shown in Fig. 2.18(a). The reactions at A and B in case of knife edge support will be normal to the surface of the beam. The reaction RA and RB with free-body diagram of the beam is shown in Fig.2.18(b).

Fig.2.18

2.3.2 Roller Support. A beam supported on the rollers at points A and B is shown in Fig.2.19(a). The reactions in case of roller supports will be normal to the surface on which rollers are placed as shown in Fig. 2.19 (b)

Fig.2.19(b)

2.3.2. Pin Joint (or Hinged) Support. A beam, which is hinged (or pin-joint) at A, is shown in Fig.2.20. The reaction at the hinged end may be either vertical or inclined depending upon the type of loading. If the load is vertical, then the reaction at the hinged end will be inclined.

Fig.2.20

2.3.4 Smooth Surface Support. Fig.2.21 shows a body in contact with a smooth surface. The reaction will always act normal to the support  as shown in Fig.2.21 (a) and 2.21(b).

Fig.2.21

Fig.2.22 shows a rod AB resting inside a sphere, whose surface are smooth. Here the rod becomes body and sphere becomes surface. The reactions on the ends of the rod (i.e., at point A and B) will be normal to the sphere surface at A and B. The normal at any point of the surface of the sphere will always pass through the centre of the sphere. Hence reactions RA and RB will have directions AO and BO respectively as shown in Fig.2.22.

Fig.2.22

2.3.5. Fixed or Build-in-Support. Fig.2.23 shows the end A of a beam, which is fixed. Hence the support at A is known as a fixed support. In case of fixed support, the reaction will be inclined. Also the fixed support will provide a couple.

Fig.2.23

2.3.6. Types of Loading. The following are the important types of loading :

a)      Concentrated or point load,

b)      Uniformly distributed load, and

c)      Uniformly varying load.

a)      Concentrated or point load. Fig.2.24 shows a beam AB, which is simply supported at the ends A and B. A load W is acting at the point C. This load is known as point load (or concentrated load). Hence any load acting at a point on a beam, is known as point load.

In actual practice, it is not possible to apply a load at a point (i.e., at a mathematical point) as it must have some contact area. But this area in comparison to the length of the beam is very very small (or area is negligible)

Fig.2.24

c)      Uniformly distributed load. If a beam is loaded in such a way, that each unit length of the beam carries same intensity of the load, then that type of load is known as uniformly distributed load (which is written as U.D.L.). Fig.2.25 shows a beam AB, which carries a uniformly distributed load.

For finding the reactions the total distributed load is assumed to act at the C.G. of the load.

c)     Uniformly varying load. Fig.2.26 shows a beam AB, which carries load in such a way that the rate of loading on each unit length of the beam varies uniformly. This type of load is known as uniformly varying load. The total load on the beam is equal to the area of the load diagram. The total load acts at the C.G. of the load diagram.

Fig.2.26