Vehicular Centifugal force on bridge

[4Boomers]

For a bridge structure on a horizontal curve does the centrifugal force result in an additional horizontal force and/or vertical force on the structure. I understand that the force is a horizontal force @ 6' above the deck, but am a little unsure if it results in an additional downward vertical load on the deck or if it is a horizontal force transmitted through the deck to the bearings, or both.


Any thoughts would be greatly appreciated.

Thank you.

 

[Lomarandil]

I've never used that load provision in practice, but if they specify it being 6' above the surface, then it must result in a vertical component as you uncouple the moment arm...

I imagine that additional downward force is neglected in the deck and most superstructure members by the majority of designers. But I could see it being significant at bearings.

 

[Leftwow]

My knowledge of this is derived from dynamics class in college.

Centrifugal Force = (mass of vehicle)(velocity^2)/radius of curve

Now, with this knowledge, I also know that this vector is applied at the center of mass. Which causes a moment on the vehicle. Perhaps not that significant when a small car is driving at 60 miles/hr versus 18,000 lbs ESAL truck loads are applied it would cause an eccentricity on the road, and therefore cause the truck to increase force on one side of the bridge decking which would infact increase your vertical load on one side and reduce it on the other. There is also a shear lateral force that occurs in the connections causing horizontal forces. I would assume that roadway engineers take this into account.

How would I approach this? I do know that the centrifugal force CANNOT exceed the coefficient of friction between tires and roadway. Now this is something I am not versed in so, I would assume that the dynamic friction and static friction should be a parameter that should be observed and studied. Also, dynamic friction could possibly be neglected in that situation I'm not sure. But applying that centrifugal force formula should give you your horizontal shear force conservatively (not to mention you should be adding appropriate safety factors in accordance with your local codes ((ours is aashto))).

Now the moment causing a differential distribution of forces, you should be able to account for a standard truck mass, compare it to your centrifugal force, find the center of mass, then apply the load to figure out how much eccentricity is actually occurring. Apply it to your reactions.

 

[GregLocock]

" I do know that the centrifugal force CANNOT exceed the coefficient of friction between tires and roadway. Now this is something I am not versed in so, I would assume that the dynamic friction and static friction should be a parameter that should be observed and studied. Also, dynamic friction could possibly be neglected in that situation I'm not sure"

Correct. You don't need to worry about dynamic friction, if you assume static friction is 1.0 you'll be good to go. In practice trucks drive at about 0.3g max. In order to resolve the forces directly you need the cg height of the vehicle and the track. There will be no net change in vertical load, but you will have a horizontal force.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[XR250]

What if the truck has track tires and some wings for downforce :> ?

 

[azcats]

F1 trucks make so much downforce that they can drive inverted.

 

[ACtrafficengr]

4Boomers, the net vertical force from the vehicle isn't increased by the cornering force, but there is some weight transfer to the tires on the outside of the curve.

Leftwow, that should be "the centrifugal force CANNOT exceed the coefficient of friction between tires and roadway plus the superelevation of the roadway." The Green Book recommends using side friction factor of 0.15 above 50 mph. Combine that with an e_max of 10%, and you could get lateral forces considerably higher than from friction alone.

GregLocock, would the vertical component of the superelevation force be enough to need consideration?

 

[Leftwow]

Yea Super elevation will, good point

 

[canwesteng]

F1 cars make more downforce than they weigh, idk if they can actually drive inverted though. They need that downforce plus the weight of the car on the tires to maintain traction.

 

[cal91]

Isn't it static friction, not dynamic friction?

The point of the tire in contact with the road is not moving relative to the road at that point in time, unless there is some slip.

 

[bridgebuster]

I have an example I can post later today; gotta run to a meting right now.

 

[Leftwow]

I don't understand how it's not dynamic friction in my mind, even if it is rolling.

 

[cal91]

Static friction occurs between objects A and B when A is not in motion relative to B. Once the static friction force increases past it's maximum, A will begin to move with respect to B and it is now dynamic friction (which is less then the maximum static friction).

Car wheels on pavement have static friction, unless the wheels are not gripping the pavement and are slipping. (Even when rolling.)

 

[SwinnyGG]

Isn't it static friction, not dynamic friction?

The point of the tire in contact with the road is not moving relative to the road at that point in time, unless there is some slip.

In theory, yes, but in the real world, no. When the tire meets the road it deflects, and the concrete-rubber interface is subject to creep without slip. This effect is large enough to be measureable on a normal street car, and visually evident in slow motion video of something like a drag racing vehicle with soft tires and a lot of power.

In short, tires are really complicated.

 

[Archie264]

You mean like this?

 

[Compositepro]

I would think that friction is not an important factor here. The vehicle will be steered along a certain path so velocity and position are all that matter.

Also, weight is the only vertical component of force.

 

[SwinnyGG]

You mean like this?

yup.

I would think that friction is not an important factor here. The vehicle will be steered along a certain path so velocity and position are all that matter.

I would say it's definitely not on the bridge engineer to calculate cornering forces.

If the type of traffic is known, this is pretty light work- you could use Greg's number of .3g for an average truck. For passenger vehicles, 1g would be going really really fast. .5g or something similar would be more realistic as a worst case I would think.

 

[drawoh]

4Boomers,

Some standard road vehicles can corner at 1g. You can engineer your bridge to withstand this. If you are going to protect the car, you will have to re-think your guard rails for when the car rolls over.

--
JHG

 

[GregLocock]

OT : Sedans won't roll unless tripped. SUVs and light trucks will generally be capable of untripped rollover, so these days they are fitted with Roll Over Mitigation, an electronic intervention that encourages one wheel to skid rather than tripping the vehicle.

On topic - the tire is nominally at zero velocity where it is in contact with the road when it is rolling. But that is not really true, as the local velocities in the contact patch actually create the in-plane forces. As such the high school friction model is a gross simplification, and 1.0 is good enough.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[bridgebuster]

Appendix D has an example for the centrifugal force.