Reinforced Concrete Portal Frame

[benl87]

Hi all,

I massively appreciate any help in advance. I have an exam coming up and am completely stumped on a question regarding reinforced concrete design. The teacher has told us the question is going to be similar to the example he has given us but hasn't gone through it with us. It is a continuous frame constructed of reinforced concrete with a conveyor structure on top (refer attachment). We are to design the beam, columns and footings and to select appropriate reinforcement.

We have been asked to calculate the bending moment of the frame using moment distribution using the self weight of the concrete as a udl and the live and dead loads of the conveyor as two point loads on the structure, assume the column is axially loaded and the footings as being fixed. I'm really not sure how to go about beginning this, if someone could point me in the right direction that would be appreciated!

B

 

[Studiot]

Where to start? I should establish a table of loads and reactions to be applied from the data.

It does look, from the requirements of the question, as though this is meant to be a hand calculation. Are you thinking of a using a computer?

Where does it say this is to be a portal frame in your brief?
From what I can see it is not since the columns & footings are stated to be only axially loaded.

 

[benl87]

Hi Studiot,

Thanks for the reply, unfortunately I constructed that document from things the teacher said in class so it may not be quite correct, but I just had a look through my book again and the column is supposed to carry a design load (half the beam I assume) and a design moment if that makes any sense.

Yes we have to do all our calculations by hand since it's an exam, I may use a computer program before hand to assist making a bit more sense out of it. They have graitec advance concrete and staad pro at uni, do you know anything about these?

I think the main thing I'm stuck on is how to calculate the bending moment diagram for the whole structure, I believe there will be a udl for the concrete which will just be one slab and two point loads which will be the live and dead loads of the conveyor over the span on one slab.

B

 

[Studiot]

the column is supposed to carry a design load (half the beam I assume) and a design moment if that makes any sense.

If the frame is a portal frame then at least the top two corners (column/beam junctions) are rigid.
That is the bending end moment in the beam is carried round into the columns.

So your next decision is about the connections between the columns and the foundations pads.

Either
It is pinned so no moment is transferred to the foundations and these therefore experience only vertical and horizontal reactions,
Or
It is rigid so moment is transferred to the foundation pads. This moment is then distributed across the pads and resisted by soil reactions.

 

[benl87]

I believe the whole structure is rigid because the teacher spoke of the beam being like and encastre beam which would mean it was all fixed right?? Also the footings take the vertical load from the columns so that's to be factored in as well.

 

[Studiot]

It is always a good idea to label the nodes or elements, so I have done so in sketch 1.

Since you say the founds are fully fixed I have shown this case.

In sketch 2 I have shown the effect of having a rigid joint at B (and C). The sagging of the beam section of the frame - BC - causes clockwise rotation at B and induces a moment in the frame at B.

This moment also appears in AB and the only available moment to maintain equilibrium has to be a counterclockwise moment applied at A.

This leads to an uneven distribution of foundation pressure to create this moment, as shown in sketch 3.
You will need to account for this in your pad design.

In this sense the frame is similar to an encastre fixing for a beam.

In order to analyse the frame manually you can use the matrix method, the slope deflection or area moment methods, or moment distribution.

To help with the boundary conditions
Note that A and B are fixed and therefore have no degrees of freedom - that is they suffer zero rotations or horizontal or vertical displacements.
B and C have three degrees of freedom as they can suffer rotation along with horizontal and vertical displacements.
In your design you will need to come up with (guess or trial) suitable section moduli to limit the deflections to acceptable values.

Once you have these you can detail the reinforcement to provide these. You will also need to consider the bracing reinforcement to achieve the required corner fixity at B and C.

This is a significant project.

 

[benl87]

Wow, thanks heaps Studiot. I will do my best with this great information you have provided.

 

[Studiot]

I should have mentioned that the analysis of this frame is similar to that of a continuous beam.

You should also be able to appeal to symmetry for help.

 

[benl87]

Ok thanks heaps, just one thing what is symmetry??

I was also wondering do you think it would make more sense because the span between frames is so large to go without putting a slab in and just have the beams and columns take the load?? It seems like it might be a waste putting in so much concrete longitudinally and might not contribute much to taking much of the load from the beam.

 

[Studiot]

I have sketched the deflected form of the frame and the free body diagram for the beam. Note that the moments are reversed compared to my earlier sketch since they are the reactive moments required to maintain the free body.

As regards to symmetry. Your frame is symmetrical - so you only have to solve one half of it.

You haven't said which calculation method you will go for so here are some general hints.

The frame is simple enough to apply the three moment equation,
you could set up and solve the three simulataneous differential equations for beam and columns
etc

If you were doing this for real, you would need to consider (solve for) the conditions where conveyor F is full and conveyor G is empty, both are full and both are empty and take the most onerous.
You will also need estimates for the self weight of the concrete structure, which I have shown as a UDL.

You would also need to apply the appropriate load factors (partial safety factors) to the various loads before inserting them in the equations, along with the material partial factors for the steel and concrete.

I am sorry I am not familiar with the Australian standards, but I expect they are similar to ours, at least in principle. However you must have some rc experience already, you would have started on a simpler structure.

 

[benl87]

Thanks again Studiot, using your great help I've made a start. I typed it all out to make it a bit easier to understand, I've attached this file am I on the right track?? My next step is to solve the free bm diagrams I believe, and then calculate the moment acting on the frame based on how far below the beam the curve sags.

Ben