- #1
Satonam
- 38
- 1
Greetings,
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.
Comments:
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).
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.
Figure 4.
Figure 5.
Comments:
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).
