 Hello friends, I am Prashant Vishwanath Dinshati, Assistant Professor, Department of Civil Engineering from Walchand Institute of Technology, Sulapur. Today I am here to explain you about the sheer force and bending movement of a beam. Now learning outcome of today's lecture is that at the end of this session, students will be able to know different types of beams and different types of load acting on them and they will be able to calculate the sheer force and bending movement at various section of the beam. Shear force and bending movement, shear force and bending movement diagrams are the tools used in conjunction with the structural analysis to perform structural design. Structural analysis means to find out the shear force and bending movement whereas the structural is design is to find out the minimum size of the member required to resist the force coming on it. So, we know that force and movement that act and the way they act and the geometry, we would be able to compute the analysis and mode of failure. This means that if we know the shear force and bending movements, we will be able to analyze that member and the mode of failure that may take place. So, hence we need to compute the shear force and bending movements. So, we use the findings of shear force and bending movement to know the exact placement of the reinforcement in the structure to counter act the force and movement that is to resist the force coming on it and moment on it. Now, before drawing the shear force and bending movement diagram, we must know about the different types of beams and the types of loads that may be acting on them. The types of beams that may there are many types of beams mainly cantilever beam, simply supported beam, overhanging beam, then fixed beam or built-in beam or encastered beam and lastly is the continuous beam. Now, cantilever beam, a cantilever beam is a beam which is fixed at one end and free at the other end. Now, as this figure shows it is fixed at one end and it is free at the other end. Simply supported beam, a simply supported beam is a beam which is simply resting freely on the supports at its both ends. So, here you can observe two supports are there and the beam is simply resting on it and overhang beam. The beam where the end portion is extended beyond the support. So, here you can see the supports are here and the beam is extended over here that is called as overhang portion. The overhang portion may be large or it may be small. So, that is called as overhanging beam. Fixed beam, so the fixed beam are the beam whose both ends are fixed or built in walls. So, here you can observe these two walls and both the ends are rigidly fixed in the walls. And lastly the continuous beam, it is the beam which is provided with more than two supports. So, here you can observe two supports. So, it may be a two or it may be more than two that is three, four, five, the types of supports that is called as continuous beam. Now, types of loads acting on the beam, there may be a concentrated or a point load uniformly distributed load or it may be called as UDL, then uniformly varying load it may be called as UVL. So, the point load or concentrated load, a concentrated load is the one which is considered to act at a point. So, this is considered to act as a point even though at in actual practice, so there will be no such a point load with having a needle tip. So, there may be some cross sectional area which is going to act on that, from that the force is coming and it is acting on a very small area, so that small area is small compared to with this large area, so it is treated as a point load. Then uniformly distributed load, a uniformly distributed load is the one which is spread over a beam in such a manner that rate of loading is uniform along the length. So, here you can observe this is uniformly distributed load and the unit here is expressed in W Newton per meter, so this at a each meter the load will be W Newton, so it is called as uniformly distributed load. And uniformly varying load, a uniformly varying load is a one which spread over the beam in such a manner that rate of loading varies from point to point. So, here you can see the rate of loading varies from point to point. Now shear force, the algebraic sum of the vertical forces at a section of a beam to the right or to the left of the section is known as shear force and it is briefly written as S F. So, here the shear force is actually sum of vertical forces, the vertical force may be the point loads or number of point loads and the even it is considered the reaction. But only one thing is that either you have to consider the left of the section or right of the section. A shear force diagram is the one which shows the variation of the shear force along the length of the beam. So, here you can see S F D means shear force diagram. It shows the variation of the shear force along the length of the beam. So, here at point A the shear force is positive, it goes it will be remain constant up to this middle point load and again it its value is negative and it is constant up to the next support. Now shear force is the internal force acting perpendicular to the longitudinal axis that is y axis of the structure or a member. So, actually this member is having x axis along its length and perpendicular to it is a y axis. It is the force which is trying to share of the beam at a particular section. Now bending moment, bending moment is the reaction induced in the structural member caused by the external force acting perpendicular to the member and resulting in rotation. So, you know the bending moment is the reaction induced. So, what will be the bending moment at this section? If I take a section at somewhere here, so it is load into this distance and this load is trying to rotate the beam in clockwise direction. So, that is called as bending moment. It is the reaction offered when a beam element is subjected to force at a distance or a moment causing bending moment. So, this is the force which is causing bending moment or sometimes you may have directly the bending moment acting on that beam. So, bending moment diagram is the one which shows the variations of the bending moment along the length of the beam. So, this is the bending moment diagram which shows this variation. So, bending moment goes on increasing up to this point load and then it goes on decreasing to the next support. So, this is the bending moment diagram. Now, what is rectangular or triangular type of loading known as? Here you pause the video and write your answer on a paper. Our rectangular type of loading is known as uniformly distributed load whereas triangular type of loading is uniformly varying load. So, as you have seen the diagram, so uniformly varying load is the intensity of load goes on increasing uniformly whereas in UDL or rectangular type of load the load is constant over the length of the beam. Now, sign convention for shear force and bending moment diagram. A shear force at a section will be considered positive when the resultant of all the forces to the left of the section is upwards or to the right of the section is downward. So, here if I take a section yy, so if I consider the left of the section if it is upward, so the force to the left of the section upward it is considered as positive. So, I have drawn this shear force in the upward portion of this baseline. And if you consider right of the section, so if the right of the section the resultant force now here the resultant force here you can see w by 2 is acting upwards and w is acting downwards. So, the resultant force will be acting downwards. So, from this point load to the right it is negative. So, similarly this is vice versa. So, the shear force at a section will be considered negative if the resultant force to the left of the section is downward. So, if the force to the left of the section if instead of upward it is downward we will treat it as negative and at the right of the section the upward is treated as negative. Now, this sign convention for bending moment. So, the bending moment at a section is considered positive if the bending moment at the section is such that it tends to bend the beam to a curvature having concavity at the top. So, you can see now when a force is applied on this beam the beam bends like this. So, the bending shape of the beam is like this and the concave concavity is at the top. So, when concavity is at the top that is called as a positive bending moment. Similarly, the bending moment at the section is considered negative if the bending moment at the section is such that it tends to bend the beam to a curvature having convexity upwards. So, this happens in case of cantilever beams the beam bends with convexity upward. So, that will be negative and if a concave concavity is up it is a positive bending moment. So, these are the references which I have referred. Thank you. Thank you very much for watching my video.