 Myself, Mr. Akshay Kumar Naminath Sobhre, Assistant Professor, Department of Mechanical Engineering. Today, we will see shear force and bending moment diagram. At the end of this session, the student will be able to determine and draw shear force and bending moment diagram. So, shear force and bending moment diagram for a beam carrying a couple. When the couple is acting on a section of a beam, then there is a sudden change in the bending moment where the couple acts. The sudden change in the bending moment at the section where couple acts is equal to the magnitude of the couple acting at the section. The section where couple acts, there is no change in the load and therefore, shear force value remains constant and diagram will remain horizontal. Therefore, sudden change in the bending moment at the section where couple acts that can be calculated by determining the reactions at the support as well as the bending moment at the section where couple acts. So, consider a simply supported beam of span 6 meter hinged at A and B and from support A a couple of 24 kilo Newton meter acting in clockwise direction draws shear force and bending moment diagram. Now, before starting to solve the problem, we will see the sign conventions for the shear force and bending moment. If you consider the left side of the section, then all upward forces are considered to be positive and all downward forces are considered to be negative. Whereas, if you consider the right side of the section, then all upward forces are considered to be negative and all downward forces are considered to be positive. Whereas, the bending moment at the section where if the moment due to the forces and reaction acting to the left side of the section is in clockwise direction and to the right side of the section in anti-clockwise direction considered to be positive. Whereas, the bending moment at the section if it is acting in anti-clockwise direction to the left side of the section and to the right side of section in clockwise direction, then such moments are considered to be negative. Now, think for a while what will be the effect of the couple which is acting at point C on beam AB. The effect of the couple at support A is the portion AC will get lifted up at A. Therefore, the reaction at A will act in the downward direction. Whereas, the effect of the couple which is acting in clockwise direction at support B is to depress the portion CB in the downward direction. Therefore, the reaction at B is acting in the upward direction. So, the reaction at A is acting in the downward direction whereas, the reaction at B is acting in the upward direction. So, first of all calculate the reaction at A and B. Therefore, some of the forces acting in the upward direction rA plus rB is equal to total load acting on the beam which is equal to 0. So, rA plus rB is equal to 0. This is my equation number 1. Secondly, taking the moment about point A, we will get taking the moment about point A rB into 6 is equal to 24 and therefore, reaction at B is equal to 4 kilo Newton acting in the upward direction. So, reaction at A is equal to minus 4 kilo Newton which is acting in the downward direction. Therefore, reaction at A is 4 kilo Newton. Reaction at B is also a 4 kilo Newton acting in the upward direction. The section where the couple acts, there is no change in the load. Therefore, shear force value will remain constant and diagram will remain horizontal. Therefore, first of all we will calculate the shear force calculation. Shear force at point A, as at point A there is a downward point load acting in the downward direction. So, shear force at point A according to the sign convention, it is minus 4 kilo Newton. The section where couple acts, there is no change in the load. Therefore, shear force value will remain constant at point C and diagram will remain horizontal. Shear force at point B, as at point B there is a upward reaction. So, shear force at point B is also minus 4 kilo Newton. So, first of all for drawing shear force diagram draw a base line. All positive values are plotted above the base line and all negative values are plotted below the base line. So, at point A the shear force value is minus 4 kilo Newton. Therefore, shear force value will suddenly drop from 0 to minus 4 by vertical straight line. Between A to C there is no load. Therefore, shear force value will remain constant and diagram will remain horizontal. Whereas, the section where couple acts the shear force will remain constant and diagram will remain horizontal and at B the shear force value is also minus 4 kilo Newton and it goes on decreasing to 0. So, the shear force diagram is a rectangle. Now, we will calculate the bending moment. So, bending moment calculation as in case of simply supported beam at the support the bending moment is always 0. Therefore, bending moment at point A and at point B is equal to 0. So, the section where couple acts at that section we will consider the bending section just before point C and just after point C. So, when we consider the section just before point C and calculate the bending moment due to the reaction and forces. So, there is a reaction of A acting in the downward direction and its distance from point C is 2 and therefore, bending moment at point C just to its left side is equal to minus 4 into 2 which is equal to 8 kilo Newton meter. Whereas, bending moment at point C just to its right side. So, bending moment just to the right side of the section. So, there is a reaction R B acting vertically upward and its distance from point C is 4 meter and therefore, bending moment just to the right side of B is 4 into 4 moment is positive. So, it is 16 kilo Newton meter whereas, the bending moment at point C just to its left side is minus 4 into 2 it is minus 8 kilo Newton meter. Therefore, the bending moment diagram all positive values are plotted above the base line and all negative values are plotted below the base line. So, at point A the bending moment is 0 at point C just to the left of point C the bending moment is minus 8 kilo Newton meter. So, it decreases from 0 to minus 8 kilo Newton meter linearly and due to the couple acting at point C there is a sudden change in the bending moment and that change in the bending moment is take place from minus 8 to plus 16 kilo Newton meter and from 16 kilo Newton meter the bending moment goes on decreasing to 0 at point B. So, the section where couple acts at that section there is a sudden change in the bending moment and that change in the bending moment is equal to the magnitude of the couple acting at that particular section. Therefore, while calculating the reactions at the support A and B only the magnitude of the couple is to be taken into account. So, from this what we can learn the section where couple acts at that section there is a sudden change in the bending moment take place and the change in the bending moment at the section where couple acts is equal to the magnitude of couple acting at that section. At the section where couple acts the shear force value remains constant and diagram will remain horizontal. The material which is referred for this from the book of strength of material by Dr. R. K. Bansal as Chan and cooperated limited and also strength of material by SS Bhavikatti. Thank you.