How to connect two line bodies?

Hi. I'm trying to design L-shaped beam as shown in this picture:

But when I simulate it, it acts as two separate bodies so I added a connection between two vertices as shown:

However, this doesn't connect the whole touching faces as you can see in one of the mode shapes:

What is the best way to make it act as one body? I mean to have fixed connection between the two touching faces?


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