# Thread: how to find the internal forces of a bookshelf??

1. i have calculated the forces of a bookshelf but i don't know how to find internal forces.can u help me?
the following is my calculation
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iii) Free-body diagram iv) Calculations
Assumptions:
Weight of the applied loads (books): 100 N
Weight of the wood: 30 N
Total weight : 130 N
The width of the wood : 0.5 m

+→ ∑ Fx = 0; Ax=0

+ ↑ ∑ Fy = 0; Ay - mg = 0
Ay = mg
Ay = 130 N

For the weight of the books acting through the woods center of gravity:

Taking counterclockwise as positive,

∑ Ma = 0; Ma  mg(r) = 0
Ma = (130N) ( 0.25)
Ma = 32.5 N

For the weight of the books acting through other positions:

Taking counterclockwise as positive,

∑ Ma = 0; Ma  (30)(0.25)  (100)(R) = 0 , where R = distance from the
fixed point A

Example:

If the weight of books acts through the position 20cm from the fixed point A, the calculation is:

Taking counterclockwise as positive,
∑ Ma = 0; Ma  (30)(0.25)  (100)(0.2) = 0
Ma = 27.5 N

v) Taking the subcomponents
Taking each individual piece from the bookshelf, the free body diagram for each piece is below:   2.

3. I see a bunch of problems.

Firstly, you don't have a single free body diagram. You have a nicely drawn image of the system, but that is not an FBD. Wiki's image is wrong, don't use it.

A FBD assumes everything is a point and then draws associated forces acting on that point (usually the Center of Mass--but doesn't take into account the distance from the point to any force).

Secondly, your system ignores the end walls of the book shelf. If there are no sides to the shelves then you are missing supports underneath, or the system is unstable.

Thirdly, you're ignoring torque. (Or I'm missing it in your images.) (This also means you're missing a measurement of distance between book and wall.)

In addition, I'm not sure what your white arrows represent, but there doesn't seem to be a calculation for them anyway. If they are torques, you're calculating them incorrectly and have them going in the wrong directions.

Finally, on your second set of "FBDs" you are missing the other forces, such as the force holding it to the wall (Ax), and holding it up from the wall (Ay).

Hope this helps some.  Bookmarks
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