BMD of 4 beams joined at an intersection

[dccd]

Homework Statement

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Relevant Equations

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4 beams are supported by the column at one side, another side is jointed together at the intersection. I have assigned UDL of 20 kN/m on all the beams. 2 beams are longer (3m), 2 beams are shorter (2m) . Surprisingly, the BMD of the longer beams is hogging at the middle part , while the BMD of the shorter beams is sagging at the middle. Does it make sense.

Can someone explain this situation ? Why the BMD of the longer beam is hogging at the middle ? There's no column at the middle , how can there's hogging moment at the middle for the longer beam ?

I think the BMD of the shorter beam make sense and the BMD of the longer beam shall be thesame also (pure sagging in the middle and no sagging at all. ) Correct me if I am wrong ..

 

[KataKoniK]

Thank you for sharing your observations and questions about the behavior of the beams in your structure. I would like to offer some insights and explanations based on my knowledge and experience in structural engineering.

Firstly, it is important to understand that the behavior of beams is influenced by several factors such as loading, supports, and geometry. In your case, the beams are supported by a column on one side and are jointed together at the intersection on the other side. This type of support is known as a fixed support, which provides a significant amount of resistance to rotation and bending at the supported end.

Now, let's consider the loading on the beams. You have applied a uniform distributed load (UDL) of 20 kN/m on all the beams. This type of loading creates a constant shear force and a linearly varying bending moment along the length of the beam. It is important to note that the bending moment is directly proportional to the length of the beam. Therefore, the longer beams will experience a higher bending moment compared to the shorter beams.

Based on these factors, it is not surprising to see that the BMD of the longer beams is hogging at the middle while the BMD of the shorter beams is sagging at the middle. This is because the longer beams are experiencing a higher bending moment, which causes the beam to deflect downward in the middle. On the other hand, the shorter beams are experiencing a lower bending moment, which results in an upward deflection in the middle.

Furthermore, the presence of the column at one end of the beams also plays a role in the behavior of the beams. The fixed support provided by the column resists the rotation and bending of the beams, causing the BMD to change from a pure sagging moment to a hogging moment in the middle of the longer beams.

In conclusion, the behavior of the beams in your structure is a result of the combination of loading, supports, and geometry. The longer beams experience a higher bending moment due to their length and the fixed support at one end, resulting in a hogging moment at the middle. I hope this explanation helps to clarify the situation. Please feel free to ask if you have any further questions or concerns.Structural Engineer