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Static Analysis Of Bolted Joints

  1. Feb 14, 2019 #1

    I'm an Undergraduate Mechanical Engineering student. I want to design bolted joints on Figure 1, I'm trying to perform a basic static analysis of the structure to understand the forces acting on its members and its current stress state. I've included dimensions and position of its components in Figure 2. Units are in inches. The structure is divided into three levels, each consisting of two beams which share a combined load of 480-lbs. Assuming they share an even 240-lbs per beam and taking the line of action to be perpendicular to the beam's centerline, I've included my free-body diagram and calculations in Figure 3 and Figure 4.

    Figure 1.

    Figure 2.

    This structure rests on the floor as support. I never realized until now, but college courses never use the floor as a support in assignments, so I'm not entirely sure how to approach it. It's hard to see, but Figure 1 shows that the two beams of the bottom level aren't touching the ground. The entire structure is supported by the two 58" beams on the bottom.

    My intuition says that the reaction forces from a planar supporting surface, like the floor, will create a distributive force with its peak acting along the line of action and progressively diminishing at distances away from said point. (Figure 5) In the example shown in Figure 5, these distributive reaction forces can then be simplified as two concentrated forces acting on or near the line of action of its loads.

    Due to the symmetry of applied loads shown in the free-body diagram of Figure 3, I'm expecting two reaction forces a distance u and u' from the origin. I also expect 14" < u < 20", where u' = u if measured from the right.

    Figure 3.
    Note: In FBD 2 of Figure 3, the bottom member is not in contact with the floor, only the edges (which represent beams going into the page). The 2R reaction force in the center represent the two reaction forces in FBD 1 as viewed from the Y-Z plane. I'm not sure whether it would be more appropriate to place the reaction force in FBD 2 on z = 0 since that is where contact is made.

    Figure 4.

    Figure 5.


    In hindsight, while writing this post, I noticed some mistakes I made. For instance, in FBD 1 of Figure 3, I only acknowledged two reaction forces, but there should actually be four reaction forces because FBD 1 only represents half of the system. Furthermore, in FBD 2, it's probably more accurate if I put the 2R reaction force at z = 0" and add another 2R at z = 32". However, perhaps I can still represent it as 4R at z = 16" ? (I'm thinking the answer is no)

    With that said, are there any other mistakes I've made concerning this task? Would correcting the reaction forces to account for the other half of the system solve my predicament? I feel like this should be easy for me, but applying academic knowledge to real-world conditions seem to be more challenging than I thought. I think part of the problem is that we never see how a problem statement is formed, we're only ever told that a beam is simply supported, which is just an idealized model representing real-life situations -but we don't know how that looks in real life (except for obvious cases).

    Attached Files:

  2. jcsd
  3. Feb 14, 2019 #2
    Welcome to the world of static indeterminacy!! This is just reality. You can deal with it by FEA, incorporating some assumptions ab out the flatness of the floor, the nature of the loading, etc., or you can make some simplifying assumptions.
  4. Feb 15, 2019 #3


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    Bear with me, but the reason for determining the 'reaction' forces at u and u' is unclear.
    Are you possibly thinking of putting another support at these particular locations for added load bearing capability?
    If the floor has a hill at u and u' then that would make sense to me.
    What if the floor has a valley at those two locations and the contact points with the floor are somewhere else?

    What I see is four columns supporting the load from the top two layers, and the horizontal beams supporting the load from the bottom layer.
    The beam may or may not rest on an even floor.
    It is conceivable that the floor may have a topography, and the structure rigid enough, such that only three contact points are possible.
    The structure will have a wobble.
    A structure flexible enough may eliminate the wobble as it settles into the features of the floor.
  5. Feb 15, 2019 #4
    Thank you for the reply!

    I'm actually trying to simulate a static analysis with SolidWorks, but because I have little experience with simulation, I wanted to validate the results I received from the program by doing some hand calculations. If I can't confirm my results manually due to static indeterminacy, how else would I validate results from a simulation? How do I know it's safe to make decisions based on what the program spits out?

    I was assuming that the floor was perfectly flat. I know there are irregularities, but does it make that big of a difference if there are no obvious hills and valleys? (honest question)

    I'm not planning on placing supports at u and u', the reason I was trying to determine u and u' was to check myself. If my assumption that 14" < u < 20" was accurate, then that would have meant that I could trust my reasoning.
  6. Feb 15, 2019 #5
    Imagine a simple, rectangular, four legged table, with all the legs exactly the same length. On a perfectly flat floor, we might feel safe in saying that all four legs carry 1/4 of the weight of the table. But now, shorten one leg (just one!) by 10^(-100000) mm. That leg no longer touches the floor at all! It cannot possible carry 1/4 of the table weight. So yes, it really does make that big of a difference!
  7. Mar 15, 2019 at 4:01 PM #6
    I never realized how difficult it is to design a bolted bracket I can confidently prescribe to employers. Perhaps that's just because I'm inexperienced. Would you guys be able to help guide me in the right direction?

    Here's my game plan:

    Objective: Design brackets for a beam with a single load.
    • Determine forces and moments at supports for a statically indeterminate problem.
    • Use resulting reaction forces and moments to determine required dimensions and material properties of bracket.
      • Bracket Components
        • Sheet Metal
          • thickness
          • material
          • length
        • Bolts
          • diameter
          • length
          • quantity
          • distance between bolt centers
          • material
    My main challenge right now is actually trying to determine what kind of "support" a bracket represents. I know a welded joint is considered a fixed support, but what about bracket joints? It seems to me that the different between bolted and welded joints is that welded joints sustain reaction forces and moments while a bracket distributes them. For instance, depending on the orientation, the sheet metal resists bending moment while the bolts support reaction forces.

    If I can figure out what kind of support a bolted joint represents, then I can determine the correct beam deflection equations to complete the first task. As for the second task, I'll have to analyze how the bolts are transmitting the forces between the sheet metal and "wall". The bolt may be experiencing tension or shear while the sheet metal may be experiencing a moment or transmitting the shear.

    Any help would be appreciated!
  8. Mar 15, 2019 at 4:09 PM #7
    You speak about "a bolted joint," but there are many applications of bolts, each giving rise to different types of loading on the bolt. You need to post a clear figure showing your bracket and the expected loads (even if you cannot evaluate them, you know they are there). Then it may be possible to help you further.
  9. Mar 16, 2019 at 11:04 PM #8


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    ...and during that wobble there will be two legs supporting the load, not the first impression of three. (Oops)
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