 Myself, Mr. Akshay Kumar Suvade, Assistant Professor, Department of Mechanical Engineering. My dear students, today, we will study strain energy and impact loading. Learning outcome, at the end of the session, students will be able to understand the concept of strain energy and estimate the strain energy stored due to sudden load. Now, before starting the derivation of strain energy stored due to sudden load, we will take a pause and think what is mean by suddenly applied load and what are the various examples of sudden load. So, examples of sudden loads are if I kept a bundle of 20 books on a table, then it is an example of suddenly applied load or a weight of 50 kg is placed on a weighing balance. In this case, the load is suddenly applied. So, these are the examples of suddenly applied load. Now, we will consider that the load is applied suddenly over the body and therefore, suddenly applied load P will be constant throughout the deformation process of the body. From the load extension diagram, where the body is subjected to sudden load, we will find out the stress induced in the body due to sudden applied load and strain energy. So, as shown in the load extension diagram, the load P which is applied suddenly this load will remain constant throughout the deformation or extension of the body and therefore, load extension diagram is a rectangle in shape. So, difference between gradually applied load and suddenly applied load is that in gradually applied load, the load is applied in step of 5 Newton or 10 Newton whereas, in case of sudden applied load, the load is suddenly applied and hence, this load will remain constant throughout the deformation. Sigma is the stress developed in the body due to sudden applied load. E, Young's modulus of elasticity, A, cross sectional area of the body, P, sudden applied load which will be constant throughout the deformation of the body, X, deformation of extension of the body, L, length of the body, V, volume of the body which is equal to product of area multiplied by length of the body that is A into L. U, strain energy stored in the body. When the body will be loaded within the elastic limit, the work done by the load in deforming the body will be equal to strain energy stored in the body and therefore, strain energy stored in the body is equal to work done by the load in deforming the body which is also equal to area of load extension diagram. So, from load extension diagram, we can calculate the area under the curve that is the area of rectangle and strain energy stored in the body is nothing but the load P multiplied by extension. So, P into X is nothing but the load P multiplied by extension but strain energy stored in the body. This is equation number one. Now, in general strain energy stored in the body is given by sigma square upon 2 E into V where V is the volume and that is equal to A into L and therefore, strain energy U is equal to sigma square upon 2 E into A into L but equation one gives the strain energy stored in the body due to sudden applied load which is equal to P into X. Putting the value of strain energy in the above equation, you will get P into X is equal to sigma square upon 2 E multiplied by A into L. The value of extension X in terms of stress length of the body and Young's modulus of the body can be determined by using Hook's law. So, as per the Hook's law when the material is stressed within the elastic limit, the stress is directly proportional to strain and therefore, stress is equal to Young's modulus multiplied by strain that is equal to sigma is equal to E into strain. So, putting the value of strain as you observe in the load extension diagram, the load is applied suddenly, the extension of the body takes place by amount X and hence, strain induced in the body is the ratio of extension to the original length and therefore, sigma is equal to sigma is equal to E into L. Young's modulus multiplied by X upon L and from this equation, we can determine the extension X is equal to sigma multiplied by L upon E. This is equation number two. So, putting the value of extension which we have determined from equation two, we will get X upon L P into sigma upon E into L is equal to sigma square upon 2 E into A L. So, cancelling the terms from both side, E will get cancelled, L will get also cancelled and therefore, P is equal to sigma multiplied by A upon 2 and therefore, stress sigma is equal to 2 times P by A. So, this particular equation will give us the stress induced in the body when the load is applied suddenly and now, if you remember the stress induced in the body due to gradually applied load is equal to P by A and therefore, from these two equations, we can conclude that maximum stress induced in the body due to sudden applied load will be twice the stress induced in the body with same value of load applied gradually. And by determining stress, you can calculate the strain energy stored in the body is referred from a book of Strength of Materials by Dr. Avgai Bansal and SS Bhavi Katti. Thank you.