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In the textbook "Engineering Mechanics: Statics (7th edition)" by James L. Meriam and‎ L. G. Kraige, Chapter 3: Equilibrium, in the section titled: "Examples of Free Body Diagrams", I found an example which seemed quite confusing to me.

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The force at $P$ can be resolved into two components, one along the horizontal and one along vertical. To balance the horizontal component shouldn't there be a horizontal component of force at $B$ i.e. $\vec{B_x}$, just like $\vec{A_x}$ at $A$?

I'm not sure why they neglected $\vec{B_x}$ in the free body diagram.

2 Answers2

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It is because of the supports they are using.

From the diagram, point $A$ appears to be a simple pinned support, which generally means it can supply reaction forces in the $X$ and $Y$ planes. Also, because it is a pin, the structure could be free to rotate if a moment were applied. The pinned support itself can not supply a reaction moment (which makes sense, the whole structure in theory could spin around the pin if moments were unbalanced).

The support at point $B$ is some sort of sliding/roller support. In this case, the support is also pinned; but it is not fixed to the ground like a simple pinned support is. Instead, the support at B is free to move in the horizontal plane ($X$ in this case). Because of this freedom of movement, the support cannot provide a reaction force in the $X$ direction. It is still sitting on the ground though, so it provides a vertical reaction force in the $Y$ direction.

This type of support is very common in engineering problems, because it is fairly realistic. When designing structures like this, realistically it will change shape somewhat as the members become stressed and deform (this is especially true due to temperature changes, which can vary the overall length of a long beam fairly significantly) having a support free to move horizontally prevents internal stresses from building up in the structure when members have to expand or contract.

JMac
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They have set up the problem to specify that the force at B is vertical. Notice the rounded bottom of the support there.

Ben51
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