# Homework Help: Concrete bridge pier formwork design

1. Aug 19, 2011

### Joey Jo Jo Jr

1. The problem statement, all variables and given/known data

I have to design the formwork system for an octagonal bridge pier similar to the type shown below, plus a headstock.

[PLAIN]http://img577.imageshack.us/img577/5743/prexconcretebridgecolum.jpg [Broken]

2. Relevant equations

3. The attempt at a solution

I can use any system I want and I have gathered a number that I can choose from. But I really want to use a system like this one (for the pier):

[PLAIN]http://img594.imageshack.us/img594/5471/placeconcretecolumnform.jpg [Broken]
[PLAIN]http://img831.imageshack.us/img831/9784/cleaningcolumnformwork.jpg [Broken]

but I am not certain how to design it to resist the concrete pressure. Does anyone know of any literature that deals with this kind of system in any way?

How do you evaluate the hoop stress of an octagonal pressure vessel like the pier form or iregular shaped and sloping pressure vessel such as the pier cap form? Is the weight of concrete and formwork of the pier cap transferred through the pier form walls axially to the ground? With these two questions answered would I have enough information to pick a steel thickness and grade and also design a connection for the two halves?

Last edited by a moderator: May 5, 2017
2. Aug 19, 2011

### mathmate

As a first approximation, you would consider fresh concrete as a viscous fluid with a density 2.5 times that of water. So hydrostatic pressure (increases with depth) is a primary consideration. The spacing of fasteners of the two halves has to be looked at, as well as local deformation.

Since the wall looks relatively thin, you may want to look at possible bulging of the wall.

The friction between the wall and the concrete will transfer some of the concrete weight through the wall, which means that the bottom part of the wall is under axial compression. "Coke-can" type of buckling should be looked into, but probably not significant because the "hydrostatic pressure" of concrete inside puts the wall in circumferential tension.

Also, add a factor for the vibration of concrete after it is poured.

These are some thoughts, hope they help.

3. Aug 19, 2011

### Joey Jo Jo Jr

Thanks for the reply.

We've been given a value of 2600 kg/m^3 for the concrete density. From my calcs the concrete will be limited by setting so it wont reach the full hydrostatic pressure. So the spacing of the fasteners will get closer as we get closer to the ground and then be evenly spaced where the concrete has begun to set and lose its fluid properties.

So from this I gather the structure has to resist the lateral concrete pressure, as well as it's own weight and the weight of the concrete on the sloping part at the top of the form as well as the concrete adjacent the side walls due to friction. Does that sound right? And since it is thin walled there is a high chance that bulging might be the limiting factor.

I think the "coke-can" buckling you talk about is what we would call twisiting which will be resisted by adding in bracing, which will also resist any other horizontal loads on the structure. And I haven't the code with me but I believe it specifies a factor for vibration of the concrete.

So what my question now is: how could I model this structure? What I really want to do is a few hand calcs that give me an idea of the thickness of steel, and how many bolts I need so that this thing doesn't explode or bulge out into a pear when I fill it with concrete. How can I calculate the state of stress and strain in this structure?

4. Aug 21, 2011

### mathmate

For the setting part, there is usually a limit of how high the concrete can be poured at any one time. The hydrostatic pressure can be calculated based on this height.

If the concrete is in fact poured continuously to the top, some sort of estimate of the concrete setting can be applied, but you want to be extremely cautious in case they pour pea soup in the form!

Unless the whole column is poured in one shot, spacing of the fasteners would likely to be uniform because the pouring could be stopped at any elevation.

The coke-can buckling is what happens when you step on an empty coke-can, when it makes ring like ripples before it flattens completely. See (Theory of elastic Stability, Stephen Timoshenko). This can be strengthened by adding longitudenal ribs (if necessary).

For the design of the wall, one possibility would be to take a horizontal slice and take each face as a uniformly loaded fixed ended beam. Due to symmetry of the 8 sides, each corner should not rotate. The loading is the hydrostatic pressure. You will need to check that the strength of the plate resists the bending moments at the middle of the face (wl^2/24) and at the fixed ends (wl^2/12).

For the bulging, you will have to decide on an acceptable value (1cm, 2cm, etc.) and design the thickness of the plate accordingly.

Due to the cold-forming of the plate (by bending it to an octagon), there may be residual stresses which could give rise to surprises. So you may want to do some experimental testing.

Make allowances for asymmetrical loading. I don't know how to estimate that. Hope your code has something.

These are my thoughts. Check you code to make sure everything has been considered. I am not experienced in formwork design, so if you have a colleague or a superior in the field, have him/her review your design if this is your first.

5. Aug 21, 2011

### nvn

Joey Jo Jo Jr: My current guess, like yours and mathmate's, is that global buckling will be completely insignificant. And, my guess is, axial compressive stress due to wet concrete viscosity will probably be relatively very low and insignificant, compared to the axial compressive stress due to the steel self weight. Just do paragraph 5 of post 4, which sounds like a great idea.

However, also compute hoop stress on the octagon (sigma_h = p*r/t, I think); and add this to the bending stress from paragraph 5 of post 4. Let's see if this idea sounds OK to everyone.

And perhaps see if your thinness ratio, gamma = D/t, is greater than, say, 39, where D = octagon mean (or maximum) diameter = 2*r. If gamma does not exceed 39, I think it might indicate your octagon cross section is locally stable.

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