I would really appreciate your help on something that has been bothering me for the past week.
I am uncertain on how to derive the deflection curve equation for a certain shaft. Loads are acting on both ends of the shaft, with the reaction forces being provided by two separate bearings that are located towards the middle of the shaft.
Is it correct to assume that by finding the Bending moment equations for each section of the shaft and then double integrating I will find deflection for each section of the shaft? I have attached a picture of my most recent attempt so far.
I am fairly certain that this is the right approach, however I am not sure as to whether or not I need to somehow combine all these moment equations into one equation so that I have a smooth deflection curve as opposed to a disjointed one.
Thank you for your help.