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Grillage model problem

Grillage model problem

Grillage model problem

(OP)
Hello,

As the title says, I'm having some difficulties when developing the grillage model for a bridge slab.

The slab is simply supported and composed of 8 longitudinal RC beams and several transverse elements (shear-key deck).

The longitudinal beams are as below:



So, beacuase the centres of gravity of different parts of the longitudinal beams are different I was using a function, on my computer model, that allows me to offset each individual bar to its "real" position (like in the image above). The way the program does that is by creating virtual vertical bars (infinitely rigid) to offset those elements.

What this does on the other hand, is it creates huge horizontal reaction on the supports due to the now "portal-like" behaviour of the structure.

My question is, would a structure like this (statistically indeterminate) in reality have any horizontal reactions due to the fact that it has a variable centre of gravity along its length, or should the always be 0 no matter what?

Thanks!

RE: Grillage model problem

If your grillage support restraints are as shown in your diagram you should have zero horizontal reaction at all Section C nodes. There will be non-zero horizontal reactions at Section A, but the total horizontal force must be zero, or equal to the applied horizontal force if any.

The offset centroids will affect the bending moments in all the longitudinal members, so you will have to take account of that in your section design. I would suggest doing the analysis with the centroids all in the same plane, then do a check with the offset centroids to make sure it all makes sense.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Grillage model problem

Quote (OP)

What this does on the other hand, is it creates huge horizontal reaction on the supports due to the now "portal-like" behaviour of the structure.

Are you sure that there's actually a roller modeled at one end of this? As IDS intimated, if the supports are modeled correctly, you should be getting horizontal reactions.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Grillage model problem

(OP)
I should have clarified that, the supports are as shown in the diagram and there is no horizontal loads applied. If I offset the elements to their "real" centroid position I get huge horizontal reactions for this support conditions, and if I leave the centroids in the same plane, I get horizontal reactions = 0. I'm just not sure if leaving them all in the same plane is a correct reproduction of reality.

Imagining that the supports would be fixed on both sides and I would have only 1 longitudinal beam instead of 8 and no transverse members at all. Would it be correct to ignore the offsets and have the centroids all in the same plan (therefore having horizontal reaction as 0) or should I offset them and have H reactions different than 0?

That is ultimately my question. In the real world, in a statistically indeterminate bar with variable section, will you have horizontal reaction different than 0 if you only have vertical forces applied?

Thanks again for your help!

RE: Grillage model problem

Quote:

That is ultimately my question. In the real world, in a statistically indeterminate bar with variable section, will you have horizontal reaction different than 0 if you only have vertical forces applied?

With a single beam with restraints as shown there will be no horizontal reactions.

With a single beam fixed at the base at both ends there will be equal and opposite horizontal reactions at the ends, for a uniform beam or a stepped beam as shown. The uniform beam would have larger horizontal reactions because the offset from the support to the centroid is greater.

For a grillage with supports as shown there should be no horizontal force at Section C in the model, or in "reality" (i.e. reality with totally frictionless bearings). At Section A there will be horizontal reactions because the different slopes in the beams will generate a torsion in the end transverse beam. This also applies to both stepped and uniform beams. I would not expect these forces to be "huge".

In practice these horizontal forces are usually ignored, both in a grillage analysis, and more simplified analysis methods, such as applying a load distribution factor.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Grillage model problem

(OP)

Quote (IDS)

At Section A there will be horizontal reactions because the different slopes in the beams will generate a torsion in the end transverse beam.

Could you explain this in a bit more detail please.

I think I understand the main idea, but I'm struggling to understand how, in a fully fixed bar, an horizontal reaction is created because of the offset of the centroids (i.e. due the variable cross section).

RE: Grillage model problem

Quote:

Could you explain this in a bit more detail please.

I'd suggest doing some sketches of the deflected shape of two beams, one under uniform load and the other with no load or much less load.

Start with uniform beams with no transverse connection, then consider how the ends of the beams can be brought into strain compatibility when the only external horizontal force is applied by the bearings at the base of the beams. If there was an infinitely rigid transverse diaphragm at the ends, this would impose the required restraint without any external horizontal force, but if the diaphragm has a finite stiffness there must be torsional strains, so there will be horizontal forces generated on the fixed bearings.

Obviously the stepped beams will behave differently in detail, but the source of the forces (the differential rotation of the ends) is the same.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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