frame analysis by hand

[zrck99]

I am designing a frame with tension only diagonal bracing that stops midway up the structure. I am landing on an 8" slab at the base and would like to stick with pinned connections at the base. I'm kind of having trouble wrapping my head around how the upper diagonal braces create rigidity such that there is only shear and axial force in the column at the baseplate. Does anyone have any ideas for a way of explaining this? I've seen approximate methods for dealing portal frames having moment connections at the beam to column connection in the upper corners and am guessing that this is similar but am still having trouble picturing the actual statics of what is happening here. I would appreciate any attempts from people trying to explain this. I think I may be in need of an "Explain it like I'm 5" level of explanation here. I've attached a sketch of the general situation.

Thanks

 

[BAretired]

If the struts are pin connected to the columns, the lower strut carries no moment. The horizontal reactions are P/2 at each column. The vertical reactions are 2Ph/L where L is the distance between columns, tension on the left, compression on the right.

BA

 

[BAretired]

Note: This post has been edited.

Moment in the upper columns varies from Ph/2 to 0. Force in the upper strut is 3P/2 (compression). Force in the tension diagonal is 2P/cosA where A is the angle between horizontal and diagonal. Force in the bottom strut is P (compression).

BA

 

[Agent666]

I think you need to provide a little more information on the connections, the moment diagram you posted suggests the columns have a pin at above the bottom strut, but typically columns would be continuous. Seems like we need some more information to understand the full scenario you have?

 

[BAretired]

The columns are shown to be "full height columns" which would suggest they are continuous. If the lower strut is rigidly connected to each column, the end moments would be approximately Ph/2 as shown.

My calculation above was based on the assumption that the lower strut is pin connected to each column.

BA

 

[zrck99]

Thanks for all the responses.

I've modified the attached sketch to clarify the connection types. I've tried talking this through with my boss and think that he is probably correct but just that I am having a hard time understanding his explanation. I'm hoping to get more explanations to be able to pick up on it from a different angle.

My boss is saying that with the connections as detailed, the upper and lower struts will form a couple which is similar to the couple formed by welding the upper and lower beam flanges to the column in the corner of a portal frame. When looking at a welded portal frame moment connection, I think that recognizing the connection as rigid is pretty intuitive but when looking at the upper and lower struts with tension only bracing, I'm having a harder time "seeing" how it creates a rigid connection.

Does his explanation make sense to you guys? If so, can you try to explain it?

Would you agree that the column will only see small/negligible moments above the lower strut to column connection?

Do you agree that the moments at the lower strut/column connections would be Ph/2?

Thanks in advance for any responses. I appreciate it.

 

[zrck99]

Ok, Following up my previous post because I think that I understand whats going on now. I modeled in Ram Element and see that the moment in the columns varies from 0 at the base to Ph/2 at the middle strut back to 0 at the upper strut connection. That helped everything click. The diagonal tension brace restrains sidesway at the top of both columns and the columns themselves are restrained vertically by their baseplates so from the perspective of the columns, they are pinned at the baseplate and pinned at the upper strut connections. Because we don't have tension bracing in the bottom half, the columns each take half of the point load. So you end up with your moment diagram varying from 0 at the baseplate to Ph/2 at the middle strut to 0 at the upper strut. I'm pretty confident I get it now and appreciate everyone for listening to me think through it all. Ha, thanks everyone.

 

[BAretired]

My boss is saying that with the connections as detailed, the upper and lower struts will form a couple which is similar to the couple formed by welding the upper and lower beam flanges to the column in the corner of a portal frame.

I agree with your boss. The couple is an equal and opposite horizontal force at the upper and lower beam, separated by distance 'h'.

When looking at a welded portal frame moment connection, I think that recognizing the connection as rigid is pretty intuitive but when looking at the upper and lower struts with tension only bracing, I'm having a harder time "seeing" how it creates a rigid connection.

It doesn't create a rigid connection. It creates a rigid frame in the upper tier.

Would you agree that the column will only see small/negligible moments above the lower strut to column connection?

No, the moment in the column is Ph/2 at the lower strut, tapering down to 0 at the upper strut. With the connections you have shown, the struts will see negligible moment.

I modeled in Ram Element and see that the moment in the columns varies from 0 at the base to Ph/2 at the middle strut back to 0 at the upper strut connection.

Correct. Each column has a concentrated load P at midpoint and reaction P/2 at each end.

Because we don't have tension bracing in the bottom half, the columns each take half of the point load.

Actually, the columns each take half of the point load even if you did have tension bracing in the bottom tier.

I really think you've got it, but it would be a good exercise to label the diagram with reactions, moment diagrams and axial forces.

BA