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### Beam

• 1. Chapter No. 3 Beam Page 1 CHAPTER No. 3 BEAMS AND SUPPORT REACTIONS CONTENT OF THE TOPIC: - Definition of statically determinate beam o Types of beam supports o Types of Beams o Type of Loading - Procedure To Find The Support Reactions Of Statically Determinate Beam - Compound beam - Concept of virtual work Definition of Beam: A beam is horizontal or inclined member carrying transverse or inclined loads and supported at ends or anywhere. It is a structural member for the frame or structures of steel or concrete which has one dimension (length) considerably larger than the other two dimensions. If support reactions can be determined by using the conditions of equilibrium only, then the beam is known as statically determinate beam. If support reactions cannot be determined by using the conditions of equilibrium only, then the beam is known as statically indeterminate beam. Definition of span: Centre to centre distance between the two end supports is called span. Types of beam supports: 1) Simple support: It is a theoretical case in which the ends of the beam are simply supported or rested over the supports. The reactions are always vertical as shown in Fig.1 below
• 2. Chapter No. 3 Beam Page 2 Fig.1 Simple Support It opposes downward movement but allows rotation and horizontal displacement or movement. 2) Pin or hinged Support: In such case, the ends of the beam are hinged or pinned to the support as shown in Fig.2 below. Fig.2 (A) Hinged Support Fig.2 (B) Hinged Support The reaction may be either vertical or inclined depending upon the type of loading. If the loads are vertical the reaction is vertical as shown in Fig. 2 (A) and when the applied loads are inclined the reaction is inclined as shown in Fig. 2 (B). The main advantage of hinged support is that the beam remains stable i.e. there is only rotational motion round the hinge but no translational motion of the beam i.e. hinged support opposes displacement of beam in any direction but allows rotation. 3) Roller Support: In such cases, the end of the beam is supported on roller as shown in Fig. 3 below. Fig. 3 Roller Support
• 3. Chapter No. 3 Beam Page 3 The reaction is always perpendicular to the surface on which rollers rest or act as shown in Fig. 3. The main advantage of the roller support is that, the support can move easily in the direction of expansion or contraction of the beam due to change in temperature in different seasons. 4) Fixed Support: It is also called as Built-in-supports. It is rigid type of support. The end of the beam is rigidly fixed in the wall as shown in Fig. 4 below. Fig. 4 Fixed Support It produces reactions Ra in any direction and a moment Ma as shown in Fig. 4 above. Types of Beams: The types of beam are depends upon the types of supports over which it will rest. 1) Simply Supported Beam: A beam supported or rested freely on the supports at its both ends is known as simply supported beam. Such beam can support load in the direction normal to its axis. The support reactions are always vertical (as shown in the Fig. 5 Ra and Rb). Fig. 5 Simply Supported Beam 2) Cantilever Beam: One end of the cantilever beam is rigidly fixed in the wall as shown in Fig. 6 below. Such supports are known as fixed support (as explained in above). It is a type of rigid support. It produces reactions Ra in any direction and a moment Ma as shown in Fig. 6.
• 4. Chapter No. 3 Beam Page 4 Fig. 6 Cantilever Beam 3) Overhang Beam: The beam is supported on hinged support and roller support. The beam has overhang on one end i.e. to the right or left of the beam and on both sides as shown in Fig. 7 below. Fig. 7 (a) Overhang Beam (overhang on both sides) Fig. 7 (b) Overhang Beam (to right) (c) Overhang Beam (to left) 4) Continuous Beam: Such beams are supported at more than two points as shown in Fig.8 below. It is also called as multi-span beam.