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I'm attempting to create a suspended shelf. I need to determine the horizontal force at point A to determine whether or not the fasteners will fail. All members are rigid and the supports at A and B are fixed.

I am very rusty on statics and your help would be greatly appreciated! I would attach the work I've attempted, but quite frankly, it's embarrassing.

enter image description here

Thanks for your time.

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  • $\begingroup$ Can you assume that a bolted connection acts like a pinned connection? A bolted connection would prevent rotation and result in a moment while a pinned connection would not. Also, how did you determine that A and B don't both have vertical reactions? $\endgroup$
    – IForgotStatics
    Commented Sep 14, 2017 at 11:19
  • $\begingroup$ The connection, pinned or bolted, sees the same forcevector prior to any rotation occurring. Since you are looking for the static solution, it doesn't matter which you choose. $\endgroup$
    – Carl Witthoft
    Commented Sep 14, 2017 at 15:38
  • $\begingroup$ So I can't comment because I don't have enough reputation. Thanks for adding my comment earlier Fred. If I summed the moments about C, wouldn't I get: 300(14) = Ax(14) - By(14) Also, I would expect the resulting forces at A and B to be less than the applied force at C. What is wrong with my thinking here? Thanks for all the responses. It's very appreciated! $\endgroup$
    – IForgotStatics
    Commented Sep 14, 2017 at 16:28

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The horizontal force in A is solved by summing up moment at B.

$$300 (14) = Ax (14)$$

therefore, $$Ax = 300lbs.$$

Note: If your construction is to be bolted in the wall, the support condition shall be assumed to be pinned connection. It is safe to assume that point B will be hinged and point A to be horizontal reaction only.

See image below

or the point A to be hinged and B is horizontal reaction only.

See image for another possible support condition

Either way, the value of horizontal reaction at A will still be the same. :)

Edit: Other supplemental info based on OP's comment.

  1. A bolted connection is GENERALLY a pinned connection. Examples of this are in BRIDGE TRUSS connections. This is because rigid connections in dynamic systems are catastrophic as it is prone to extreme fatigue due to constant deformation and back to its original shape..

  2. The vertical reaction can be checked (if you are checking/designing for/vs the shearing of bolts) by distributing the vertical force equally into Ay and By. This is not static problem anymore but more on the design method. Therefore, by designing the shearing strength of bolts, you can assume that BOTH point A and B carries the same amount of shear caused by 300lb load, that is equal to 150lb per joint. This is contrary to the assumption in static check that only one of the two points carry the load.

  3. If you want to get the exact force in each point, you might want to use indeterminate methods in solving for the reactions such as force method, virtual work methods, etc. These usually use displacement as 4th parameter as there will be four unknowns in the system. But taking your question as a simple static problem (because this is a shelf), I suggested the simplest approach to your problem. This is the **real** indeterminate FBD of your system.

Still, by summing up moments at B, the value of Ax remains the same.

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  • $\begingroup$ Adding the comment the OP wrote in an answer box, which should have been posted as a comment. Can you assume that a bolted connection acts like a pinned connection? A bolted connection would prevent rotation and result in a moment while a pinned connection would not. Also, how did you determine that A and B don't both have vertical reactions? $\endgroup$
    – Fred
    Commented Sep 14, 2017 at 12:01
  • $\begingroup$ Please see edits. I added the answer to OP's questions. $\endgroup$
    – Jem Eripol
    Commented Sep 15, 2017 at 0:14

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