CH2 Shear Force And Bending Moment PDF

1 ROYAL UNIVERSITY OF BHUTAN 1 1 COLLEGE OF SCIENCE AND TECHNOLOGY PHUNTSHOLING: BHUTAN TSM 202: STRENGTH OF MATERIAL Lecture 2.1 Shear Force and Bending Moment 1...

1 ROYAL UNIVERSITY OF BHUTAN 1 1 COLLEGE OF SCIENCE AND TECHNOLOGY PHUNTSHOLING: BHUTAN TSM 202: STRENGTH OF MATERIAL Lecture 2.1 Shear Force and Bending Moment 1 07/09/2020: Nimesh Chettri 8/8/2022  Introduction 2 The algebraic sum of the vertical forces at any section of a beam to the right or left of the section is known as shear force. It is apparently represented as S.F. The algebraic sum of the moments of all the forces acting to the right or left of the section is known as bending moment. It is apparently represented as B.M. In this chapter, the shear force and bending moment diagrams for different types types of beams(i.e. Cantilevers, simply supported, fixed, overhanging, etc.) for different types of loads (i.e., point load, uniformly distributed loads, varying loads etc.) acing on the beams, will be considered. 8/8/2022 3 SHEAR FORCE AND BENDING MOMENT DIAGRAMS A shear force diagram is one which shows the variation of the shear force along the length of the beam. And a bending moment diagram is one which shows the variation of the bending moment along the length of the beam. Before drawing the shear force and bending moment diagram, it is essential to know the different types of beams and different types of load acting on the beams. TYPES OF BEAMS The following are the important types of beams: 1. Cantilever beam, 2. Simply supported beam, 3. Overhanging beam 4. Fixed beams, and 5. Continuous beam 8/8/2022  Cantilever Beam: A beam which is 4 fixed at one end and free at the other end, is known as cantilever beam. Such beam is shown in Figure 1. Simply Supported Beam: A beam Figure 1 supported or resting freely on the supports at its both ends, is known as simply supported beam. Such beam is shown in Figure 2 Figure 2 8/8/2022  Overhanging beam: If the end portion of a 5 beam is extended beyond the support, such beam is known as overhanging beam. Overhanging beam is shown in Figure 3. Fixed Beams: A beam whose both ends Figure 3 are fixed or built-in walls, is known as fixed beam. Such beam is shown in Figure 4. A fixed beam is also known as a built-in or encastred beam. Continuous Beam: A beam which is provided more than two supports as Figure 4 shown in Figure 5 is known as continuous beam. 8/8/2022 Figure 5  TYPES OF LOAD 6 A beam is normally horizontal structural components and the loads acting on the beams are generally vertical. The following are the important types of load acting on a beam: 1. Concentrated or point load, 2. Uniformly distributed load, and 3. Uniformly varying load. Concentrated or Point Load: A concentrated load is one which is considered to act at a point, although in practice it must really be distributed over a small area. Figure below shows the point load. 8/8/2022  Uniformly distributed Load: A uniformly distributed load is one 7 which is spread over a beam in such a manner that rate of loading ‘w’ is uniform along the length (i.e., each unit length is loaded to the same rate) as shown in Figure below. The rate of loading is expressed as ‘w’ N/m run. Uniformly distributed load is apparently represented as u.d.l. For solving the numerical problems, the total uniformly distributed load is converted into a point load, acting at the centre of uniformly distributed load. 8/8/2022  Uniformly Varying Load: A uniformly varying load is one which is 8 spread over a beam in such a manner that rate of loading varies from point to point along the beam as shown in Figure below in which load is zero at one end, and increases uniformly to the other end. Such load is known as triangular load. For solving numerical problems the total load is equal to the area of the triangle and this total load is assumed to be acting at the centre of 2 mass of the triangle i.e., at a distance of rd length of beam from left 3 end. 8/8/2022 9 SIGN CONVENTIONS FOR SHEAR FORCE AND BENDING MOMENT Shear Force Diagram: For the section under consideration, the clockwise moving forces gives positive shear force and vice versa. Bending Moment Diagram: The force bending the beam with concavity at the top of beam gives positive bending moment and the one which creates convexity at the top of beam gives negative bending moment. 8/8/2022  IMPORTANT POINTS FOR DRAWING SHEAR FORCE AND BENDING MOMENT DIAGRAMS 10 We know that the shear force diagram is one which shows the variation of the shear force along the length of the beam. And a bending moment diagram is one which show the variation of the bending moment along the length of beam. In these diagrams, the shear force or bending moment are represented by ordinates whereas the length of the beam represents abscissa. 1. Consider the left or the right portion of the section. 2. Add the forces (including reaction) normal to the beam on one of the portion, for the chosen portion if a force on the right portion moving clockwise direction gives positive SF and vice versa. The forces creating concavity at the top of beam gives positive BM and one creating convexity at the top of beam gives negative BM 3. The positive values of shear force and bending moments are plotted above the base line, and negative values below the base line. 4. The shear force between any two vertical loads will be constant and hence the shear force diagram between two vertical loads will be horizontal. The shear force diagram will increase or decrease suddenly i.e., by a vertical straight line at a section where there is a vertical point load. 5. The bending moment at the two supports of a simply supported beam and at the free end of a cantilever will be zero. 8/8/2022 11 THANK Y0U 8/8/2022