Concentrated Loading on Concrete Decks

[Buzzbromp]

I was wondering if anyone had any advice where to look for how to analyze concentrated loads on concrete decks. I've seen in AASHTO information on wheel loads. Specifically it mentions two cases, one case for a tire load with reinforcement parallel to the traffic path and one case for reinforcement perp. to the traffic path. The perpendicular case uses a a formula (something like ((S+2)/32)*P(tire) to calculate a moment to use on the 1 ft width that is typically analyzed for available strength. I believe this is specific to wheel loads (H15 and H20 trucks) that must be a certain distance away from the edge of the bridge.

I've seen another case where using the footprint of the loading area (0.01P in AASHTO for tires), a formula (width of footprint + 2*0.6*(distance from load to end of slab)) that calculates an effective width to use for flexural strength of slab for the concentrated loading. The 0.6 apparently is from the common ratio of the angle at which the load path takes from the point to the edge of the slab tan-1 (0.6). This came from structural design handbook i believe. Does anybody use this formula? If so, can i use the same effective width for shear strength, or do i just analyze punch through? If my loading is less than effective width/2 from an edge of the slab, i'd imagine my width would be effective width/2 + distance from loading to edge?

If anyone has any references I'd appreciate it

 

[Galambos]

example:

http://www.njb-united.com/usd/examples/example1.pdf

taken from:

http://www.njb-united.com/usd.htm

 

[csd72]

Galambos beat me to it.

There is also another sheet on the same site that gives the theory and the formulas.

 

[miecz]

See thread507-112794.

 

[Buzzbromp]

Thanks for the info. It seems that the formula listed on the njb-united.com link is limited by 8.9*t/h and is a function of both thickness of slab and location of loading. While the formula i found in a structural engineering handbook (width of load + 2*0.6*a) where a is location of loading on span and the formula on miecz link b_ef = b_load + 2.4*a*(1.0 – a/L_n) are not dependant on thickness. Plus they don't have a limitation on effective width of slab. This can result in a large difference.

I have a fixed-fixed slab with an axle loading which yields the largest moment at a certain location. Say one tire is 3 feet from fixed end A and second tire is 9 feet from fixed end A, and the span is say 12 feet. I ended up analyzing each load separately, so the moment created from the load 3 feet from the end was divided by an effective width of (tire width + 2*0.6*3ft). Since this load yields the higher negative moment at the fixed end and has a lower effective width due to its distance from the end, it results in a significantly larger moment/ft-width of slab. I then did the same thing for the load 9 feet out with an effective width of (tire width + 2*0.6*9ft). These two moments per ft-width were added and compared to the allowable of the deck. You can see that the effective width of the load 9 feet out will be larger than 9 feet, ended up being over 10 feet in some instances, but this is its distance to the support with the largest moment, not the support closest to it. Any opinions on this methodology??

Thanks a again for your input.