A question about the vertical part of the beam

I am solving beam type of problems finding reactions, moments...my question is how do I represent the F2 force that is acting on the vertical part of the beam (on the stick).

Usually there is only a beam on supports, forces in the x and y direction a moment, maybe sometimes an angled force or distributed load, this is the first time I see this kind of problem.

Does the F2 on the stick create a counter clockwise moment or is it just a force acting in the x direction, I need to know so I know in which of the equilibrium equations I put it.

2 Answers

Treat it the usual way. Slice the beam and find the force/moment balance.

For example:

\begin{aligned} N - F_2 & = 0 \\ S + B_y & = 0 \\ M + x B_y + a F_2 & - 0 \end{aligned}

Then use the $$N(x)$$, $$S(x)$$ and $$M(x)$$ as needed.

• Why the reference to "deflections".? Isn't this a statics problem and not a mechanics of materials problem? – Bob D Jan 23 at 15:38
• @BobD - point taken. I edited the answer. – John Alexiou Jan 23 at 15:41
• Your first equation is incorrect. Roller supports like B do not support horizontal loads. That means N has to be zero. And if N=0 your equation says F2 =0, which is obviously incorrect since it is a given horizontal load. I'm not even sure what the second two equations mean. – Bob D Jan 23 at 18:25
• @BobD - No it is correct. There is no $B_x$ in the first equation. $F_2$ does transfer through the beam to be reacted by $N$. $N= F_2$ is the expected behavior as the roller support does not alter the loading in the horizontal sense. – John Alexiou Jan 23 at 19:15
• Sure the expected behavior at the roller does not alter the loading in the horizontal sense. But as I understand it this is supposed to be a statics problem. The objective is to determine the reactions at the supports. As such the compression of the beam due to the N (the reaction at A) and F2 is irrelevant. All we care about at B is $B_y$ and the moment contribution about B due to F2 as well as the moments contributions about B due to the vertical reaction at A and the couple. But look, the OP is happy with the answer, so there is no need to debate it further. Sorry if I was a bother. – Bob D Jan 23 at 20:04

Does the F2 on the stick create a counter clockwise moment or is it just a force acting in the x direction, I need to know so I know in which of the equilibrium equations I put it.

Yes, it creates a counter clockwise moment on the beam and it is also a force in the x direction. It's not clear from the drawing what is going on at the left side of the beam, but it looks like the application of a force-couple (pure moment).

In any event, the fact that there is a vertical extension of the beam and a horizontal force on it, does not complicate the problem. Just treat it as another force that contributes a moment.

The problem is actually quite simple, mainly because roller supports cannot support horizontal loads. Consequently, the horizontal reaction at roller B has to be zero. That gives you the horizontal reaction at the pin A. From there, simply set the sum of the moments about A or B equal to zero (not forgetting the moment contribution of $$F_2$$) to get the vertical reaction at A or B. Then take the sum of the vertical reactions and $$F_1$$ to get the vertical reaction at the other support.

From here you should be able to proceed independently.

Hope this helps.