Floor Plate with Wheel Load - Sanity Check

[CTW]

I've used Roark's in the past for floor plates with relatively short spans and felt comfortable with the outcome. However, I could use a sanity check for the floor plate outlined below.

The plate is 20 ft wide with a 10.2 ft span. Simply supported along the 20 ft edges only. The applied axle load is 32 kips and the spacing between wheels on the axle is 6 ft. Using the method in Roark for determining the effective width of the plate, I get the following.

b = 20 ft
a = 10.2 ft
b/a = 1.96 (say 2)
e/a = 0.656 (for c=0)
e = 0.656 x 10.2 ft = 6.69 ft

Assuming a 2 inch thick plate
P = 32 kips/2 = 16 kips
I = 6.69 ft x 12 in/ft x (2^3)/12 = 53.52 in^4
E = 29000/(1-0.3^2) = 31860 ksi
L = 10.2 ft = 122.4 in
Deflection = (P x L^3)/48EI = 0.36 inches

I know the numbers say the deflection is 0.36 inches, but it doesn't seem practical. I would have expected the deflection to be much greater with a 16 kip concentrated load applied to a 10.2 ft span, 6.69 ft effective width and 2 inch thick plate. I realize the deflection will be a little larger since the effective widths under each wheel overlap each other, but it still doesn't seem right.

I'm interested in other opinions of this.

 

[BAretired]

Perhaps an effective width of 6' would be more realistic provided that a wheel does not come closer than 3' from the end. If one wheel is closer to the end than 3', deflections will be higher.

A 10' x 20' x 2" plate sounds a bit extreme. Couldn't you use a few beams and a thinner plate?

BA

 

[CTW]

Thanks BA. That's exactly my point. A 10' x 20' x 2" plate does sound a bit extreme. The original plan was to use a stiffened plate but I was just curious what thickness of plate would be required to span that distance. I guess I'll research to find out if there has been any real world testing of plates based on the equations in Roark. I just can't believe that a 16 kip load is only going to deflect that plate about 3/8".

 

[rb1957]

i guess i'm alittle confised with your calc ... PL^3/48EI is for a centrally applied load, no? haven't you got a beam (plate) 10.2' wide with two 16 kips loads applied 6' apart ?

Quando Omni Flunkus Moritati

 

[jayrod12]

I believe the two point loads act along the 20' length and therefore could theoretically be looked at individually