 Myself, Akshay Kumar Sodhe, Assistant Professor, Department of Mechanical Engineering, today we will see shear force and bending movement. Learning outcomes at the end of this session, student will be able to apply sign conventions of shear force and bending movement, analyze the shear force and bending movement. So, sign convention for shear force and bending movement, consider a simply supported beam A B carries a point load at its mid of 1000 Newton. As the load acting at the mid of the beam, the reaction at A and reaction at B are equal and the magnitude is 500 Newton each acting vertically upwards, so r A equal to 500 Newton r B 500 Newton. Now in order to calculate the shear force and deciding the sign conventions for the shear force and bending movement, consider the section xx in between A and C. So, by imagining the section xx, the beam A B is divided into two portion that is left side of the section xx and right side of the section xx, so think for a while what do you mean by shear force and bending movement. So, shear force at section xx is defined as it is the algebraic sum of the forces and the reaction acting to the left side of the section or to the right side of the section and therefore, when you consider the left side of the section, the shear force at section xx acting to its left side, there is a only reaction of A acting vertically upwards, so shear force at section xx to the left side is 500 Newton acting vertically upwards. When you consider the right side of the section xx, so shear force at section xx to its right side is equal to 1000 Newton acting in the downward direction and reaction at B which is acting vertically upward consider to be negative and therefore, total shear force acting to the right side of the section is 500 Newton in the downward direction and therefore, shear force at section xx to its left side 500 Newton acting vertically upward and to the right side acting vertically downward. Therefore, shear force at the section xx considering left side of the section all upward forces are considered to be positive and if you are referring the right side of the section, all downward forces are considered to be positive whereas, the resultant of the forces and reaction acting to the left side of the section in downward direction are considered to be negative whereas, if you are referring the right side of the section then all upward forces are considered to be negative. So, shear force at section xx is 500 Newton and shear force is defined as it is the resultant of the force and reaction acting on any part of the beam normal to the axis of the beam that is called as shear force. Now, we will consider the bending moment. So, for calculating the bending moment again consider a simply supported beam AB carries a point load of 1000 Newton at its mid and the total span of the beam is 4 meter. So, as we have calculated the reaction previously, the reaction at A is 500 and reaction at B is also 500. Now, the bending moment at the section is considered to be positive when the moment due to the forces and reaction tends to bend the beam to a curvature having concavity at the top such moments are considered to be positive and they are known as sagging moment whereas, the bending moment at the section which tends to bend the beam to a curvature having convexity at the top such moments are considered to be negative and that moments are called as hogging moment. Now, we will consider the section xx at a distance 1 meter from the left end and we will determine the bending moment at section xx. So, bending moment is nothing but it is the algebraic sum of the moments due to the reaction and forces acting to the left side of the section or to the right side of the section and hence the bending moment at section xx to its left side. So, various moments to the left side there is a only reaction r a acting vertically upward and its distance from the section is 1 meter. So, bending moment to the left of section xx is 500 Newton meter and this moment is in the clockwise direction. Similarly, when we consider the bending moment at section xx to its right side. So, what are the various moments due to the load and reaction to the right side there is a 1000 Newton load and its distance from section xx is 1 meter and this moment is acting in clockwise direction and there is a reaction at b of 500 Newton and its distance from the section is 3 meter. So, 500 into 3 this moment is in the anticlockwise direction. Therefore, the bending moment at section xx referring right side will be equal to 1000 as the clockwise moment is negative and anticlockwise moment is positive. So, minus 1000 plus 1500 that is equal to 500 Newton meter and this is in anticlockwise direction. Therefore, bending moment at section xx is nothing, but it is the algebraic sum of the moments due to the reaction and forces acting to the left side or to the right side of the section and therefore, if we consider the bending moment at section xx the bending moment to the left side of the section if they are acting in clockwise direction and to the right side the moment is acting in anticlockwise direction such a moments tends to bend the beam to a curvature having concavity at the top. Such a moments are considered to be positive and bending moment at section xx when you refer the left side of the section and moment due to the forces and reaction to the left side of the section is acting in anticlockwise direction and to the right side of the section if it is acting in clockwise direction such a moments tends to bend the beam to a curvature having convexity at the top such moments are considered to be negative. This is the sign conventions for shear force and bending moment. Shear force and bending moment diagram a diagram which shows variation in the shear force along the length of the beam is called shear force diagram and it is denoted by SFD. A diagram which shows variation in the bending moment along the length of the beam is called as bending moment diagram and it is denoted by BMD. Important points for drawing shear force diagram and bending moment diagram first consider left or right portion of the section. Add all the forces normal to the beam on one of the portion. If right portion of the section is chosen a force on the right portion acting downwards is positive while a force acting upwards is negative. If left portion of the section is chosen a force on the left portion acting upwards is positive while a force acting downwards negative. Positive values of shear force and bending moment are plotted above the base line and negative values below the base line. Shear force diagram will increase or decrease suddenly that is by a vertical straight line at a section where there is a vertical load. Shear force between two vertical load will be constant and hence shear force diagram between two vertical loads will be horizontal. Bending moment at the support of simply supported beam and at free end of the cantilever will be 0. The material is referred from a book of strength of materials by Dr. R. K. Bansal. Thank you.