Horizontal force transferred to a plate as a vehicle drives over it?

[bobkjr]

If I have a flat, 1/2" thick metal plate that is through-bolted onto the surface of a concrete slab, how do I calculate the horizontal shear force applied to the anchor bolts as a vehicle hits the plate and drives up over it? Above the bottom 1/16" of plate thickness, the plate edge is beveled at a 30° angle from horizontal.

I know the vehicle's weight, speed and wheel diameter. Considering the size of the wheel is approximately 20x the thickness of the plate, my gut thought is that if the wheels don't slip prior to contact, then the majority of the force is downward and not horizontal. But I'm having one of those days and I can't justify it mathematically.

Thank you in advance for any light you can shed on this.

 

[djw2k3]

hmmm - heres my go

As pneumatic tyres deform the foot print is say a sqaure with side equal to the tyre width.

Usually the weight of the vehicle is supported by normal reactions to the flat ground.

So say you had a region of tyre that is not acting normal to the ground but normal to the 30 deg surface as you say - this means there will be some component of horizontal force....?

Dave

 

[ivymike]

If the vehicle is moving quickly, you'll need to know quite a bit about the dynamic behavior of the vehicle suspension and tyres. If the vehicle is moving very slowly, the horizontal force will be small but also difficult to calculate.

Regardless of vehicle speed, if there is sufficient friction between the plate and the slab, the bolts will see no shear whatsoever (design it this way if possible).

 

[JStephen]

Assume the vehicle stops on the plate, then spins the tires taking off. That should get you an easier design case that is probably fairly realistic.

 

[diamondjim]

I would assume the greatest force is when the
vehicle first hits the plate and would think
a 45 degree angle of approach might be in line.
When the tire is on the plate, it exerts an
axial force helping to resist any horizontal
movement force.

 

[GregLocock]

Kerb impact problems are difficult to solve accurately, but, assuming you have a normal automotive tire, a 2 degree of freedom model using a disk model of the tire will typically get you within a factor of 2.

In this case the angle of impact is almost vertical, hence only a small amount of the force will be resolved horizontally. here's the inputs for a typical model. You may not need all of them.

Kerb height m 0.013
Tyre stiffness N/mm 180
Vehicle speed kph 50
Wheel stiffness N/mm 16000
unsprung corner mass kg 35
sidewall height mm 114
sprung corner mass kg 365
rolling radius mm 292
Roadspring rate N/mm 16.9
Shocker rate N/m/s 600



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[zekeman]

If you have the vehicle, you could run a static test to see the path of the centerline of the wheel as it pases over the plate. It would look like an "S' curve. Using the radius of curvature of the the upward radius ,r1 the formula for acceleration would be :
a=V^2/r1
(The downward curvature, r2 is not of interest since gravity would dominate the dynamics and the forces on the vehicle would be opposite and smaller).
From this acceleration of the front wheel centerline you could obtain the forces and thus the horizontal forces required.
These results would be fairly conservative since under dynamic conditions, the path of the centerline would have larger radii of curvature owing to the increased forces and deflection of the tire thus leading to as smaller value of acceleration.

 

[zcp]

How about you take 50% of the vehicle weight on the number of tires on the plate and apply it as a horizontal force to simulate braking? Instead of spinning out on the plate, design it for the stopping case. (With the rubber tires, there is little chance of getting to the 50% in real life.) I am guessing your anchor bolts will be fine.

ZCP

http://www.phoenix-engineer.com

 

[sreid]

Simply as a "Gut Check," 1/2 inch steel plates are thrown over trenches in roadways during construction so autos can temporarilly drive over the trench.