How do you determine when you receive a problem how many and

How do you determine when you receive a problem how many and from what direction your x values will be? From 9-19FP you only need one but on 9-21 you need two. What\'s the difference? What rule do you follow?

Referencing Structural Analysis 8th Ed. (R.C. Hibbler) Chapter 9

Solution

Solution :

For Problem F9-19: The given problem is related to simply supported beam and the values required are for slope at the support and deflection at the center of the beam. Inoder to determine slope you have to have strain energy for the entire beam and for that you need to apply unit moment at the same support. In doing so you will notice that the strain energy equation for the entire beam will be same. Now to find deflection at the center of the beam you have to apply a unit load at the center and develop the equations. In doing so you will notice that the equations are same for each half and so you dont have to use two coordinates. Equaitons are same because the loading is symmetric and for right half portion you can develop equation considering right side of the section and similarly for left half considering left side of the section.

For Problem F9-21: The given problem is related to cantelever beam and the values asked are for the slope and deflection at the center of the Beam. LIke the previous case in this again you have to develop strain energy equations. For the slope you have to apply a unit moment at the center and for deflection a unit force at the center. In each case you will notice that bending moment eqaution will vary for each half of the beam and so you have to take x coordinates to determine total virtual strain energy.

I hope I was clear enough.

Thanks