 In this problem we need to determine what is the central deflection of the following beam and we need to use superposition principle. As you can see here, this is a simply supported beam at B and C. We have an applied load of 4 kN at point A and at point D and we have an applied force point load of 2 kN at the middle point of this beam. And finally we have a uniform load of 1 kN from B to C. The idea of using superposition principle is that we can divide a complex problem like this one into several problems that are more simple. Then in this case we have a beam with this form but the problem is that in principle we do not have standard solutions for beams like that but we have standard solutions instead for beams like this. So the first step is to transform this problem that we have into a problem with this form. Then what we can do to simplify this problem we can translate these forces applied at A and D to the points B and C. So if we consider the segment for example AB we can see that this applied load here of 4 kN is creating a moment at point B equal to 4 times this distance to meters, 8 kNm. Then we can simplify this problem to, it is convenient to draw the moment in this direction and then to change the design of the magnitude. And finally note also that when we translate this force at point B we translate it as a moment plus a force, right? So in principle we will have to include this force here plus the moment, right? But this force is applied exactly at the support then the support is reacting with the same magnitude and then this pair of forces is not creating any moment or any deflection at the rest of the beam so in order to simplify this problem we can just delete it and the solution of course is exactly the same. Then now we can divide this problem into three soft problems then of course the final solution of this problem is equal to the sum of the individual solutions of these three problems 1, 2, 1, 3. And then now this is much more simple because we have standard solutions for problems like this. So for example for this one we know that the deflection at the central part of this beam is equal to we also have a standard solution for this beam we know that the deflection at this central point is equal to and finally we have that for this problem the deflection is equal to and this is what I said that it was convenient to change the direction of the moment and it is because this formula is given for a moment applied in this direction that you can see here so now we have just to introduce the magnitude of the moment designed inside the formula with the negative sign and that's all. Then now if we substitute the numbers we have that L the length is always equal to 6 meters the distance between B and C in this case B is equal to 2 kN and in this case the intensity of the load W is equal to 1 kN and as I said M is equal to minus 8 kN so if we do this we obtain that then the total deflection of the beam is the sum of all the self-problems then we have that then this is the final solution minus 20.02 mm and it is very important to realize that these standard solutions are defined such that a positive deflection like this one 80 mm it implies a deformation downwards so this beam is being deformed like that so this is why we have a positive deflection this deflection is positive as well so the deflection of this beam is like this and we have here a negative deflection so we have that this beam is deformed like that so the final result is negative so we know that the total deflection, the final deflection of the beam is also upwards