Chapter 7


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Chapter 7

  1. 1. 11/18/2011 Jaydeep Patel School of Technology,7-1 Beams Members that are slender and support loads applied perpendicular to their longitudinal axis.7-2 1
  2. 2. 11/18/2011 Forces are acting on the girder or on the beam due to supported loads over it. These forces are balanced by the reactions given by the walls or by the pillars to the beam or girder. Wall supports or the pillar supports provide reactions to the beam to keep the forces acting on the beam in equilibrium.7-3 Types of Beams Depends on the support configuration Simply Supported Beam: When both end of a beam are simply supported it is called simply supported beam Such a beam can support load in the direction normal to its axis.7-4 2
  3. 3. 11/18/2011 Cantilever Beam: If a beam is fixed at one end and is free at the other end, it is called cantilever beam. Over-hanging Beam: If a beam is projecting beyond the support. It is called an over-hanging beam. The overhang may be only on one side or may be on both sides.7-5 Beam with One End Hinged and the Other on Rollers: If one end of a beam is hinged and other end is on rollers, the beam can resist load in any direction Propped Cantilever: It is a beam with one end fixed and the other end simply supported. Continuous Beam: A beam is said to be continuous, if it is supported at more than two points.7-6 3
  4. 4. 11/18/2011 Statically Determinate or Indeterminate beams In the case of simply supported beams, beams with one end hinged and the other on rollers, cantilever and over-hanging beams, it is possible to determine the reactions for given loadings by using the equations of equilibrium only. In the other cases, the number of independent equilibrium equations are less than the number of unknown reactions and hence it is not possible to analyse them by using equilibrium equations alone. The beams which can be analysed using only equilibrium equations are known as Statically Determinate beams and those which cannot be analysed are known as Statically Indeterminate beams.7-7 Types of Loading Concentrated Loads: If a load is acting on a beam over a very small length, it is approximated as acting at the mid point of that length and is represented by an arrow as shown in Fig. Uniformly Distributed Load (UDL): • Over considerably long distance such load has got uniform intensity. • It is represented as shown in Fig (a),(b). • For finding reaction, this load may be assumed as total load acting at the centre of gravity of the loading (middle of the loaded length). • For example, in the beam shown in Fig., the given load may be replaced by a 20 × 4 = 80 kN concentrated load acting at a distance 2 m from the left support.7-8 4
  5. 5. 11/18/2011 UniformlyVarying Load: • The load shown in Fig. varies uniformly from C to D. • Its intensity is zero at C and is 20 kN/m at D. • In the load diagram, the ordinate represents the load intensity and the abscissa represents the position of load on the beam. • Hence the area of the triangle represents the total load and the centroid of the triangle • Represents the centre of gravity of the load. Thus, total load in this case is (½)× 3 × 20 = 30 kN and the centre of gravity of this loading is at (1/3) × 3 = 1 m from D, i.e., 1 + 3 – 1 = 3 m from A. • For finding the reactions, we can assume that the given load is equivalent to 30 kN acting at 3 m from A.7-9 General Loadings: Figure shows a general loading. Here the ordinate represents the intensity of loading and abscissa represents position of the load on the beam. For simplicity in analysis such loadings are replaced by a set of equivalent concentrated loads. External Moment: • A beam may be subjected to external moment at certain points. • In Fig. the beam is subjected to clockwise moment of 30 kN-m at a distance of 2 m from the left support.7 - 10 5