20 Kip Point Load over a 7' Square Concrete Slab 2

[cap4000]

Do anyone has the formula for a point load on a simply supported slab using the "theory of elasticity". AASHTO has a very simple formula but it is around 25% conservative. Essentially there are both torsional moments and bending moments that resist the point load. The crossing beam analogy is the simplest most conservative way to determine the moments in both directions. Any tips will be greatly appreciated.

 

[Lion06]

Do you have a copy of Roark?

 

[cap4000]

No

 

[Lion06]

What are your boundary conditions, and slab dimensions?

 

[cap4000]

Simply Supported on 4 sides, 7 foot square slab, 10 inches thick, 20 kip load in center.

 

[Lion06]

I'm coming up with a bending stress of 256psi - using Roark. I am assuming your 20k point load is spread over a 16.8"x16.8" area to conform to the table.

 

[cap4000]

I am looking for the bending moment in kip-feet.

 

[Lion06]

About 29.9K-ft

 

[cap4000]

Seems quite high to me. If you take the 20 kip load and divide that by 2 you have PL/4 or 10*7/4 = 17.50 kip-ft.
This is based on a simplified 2 way distribution of the load.

 

[cap4000]

Per AASHTO formula 3.24.6 for conc.load in center of a square slab distributes 50% each way. The formula is p=b^3/a^3+b^3 where a and b are the same dimensions for a square.

 

[miecz]

Cap4000-

I agree with EIT and get around 260 psi using Roarke and another method. For a bending moment, I get a peak moment of 4.4 k'/ft. The 17.5 k' is a average over the entire width of the plate.

 

[cap4000]

miecz

I agree with the 260psi but I disagree with the 4.4k-ft/ft.

 

[cap4000]

miecz

AASHTO E = 4 + 0.06(S) or E = 4.42ft as the effective width
Using 10k/4.42' = 2.26K Load. PL/4 = 3.95k-ft/ft
Does this really apply to a 7' x 7' area??

 

[miecz]

cap4000

I don't believe the AASHTO provision (3.24.3.2) is really meant for two way slabs. I think it is meant for one way slabs with the supporting stringers perpendicular to the direction of traffic. That said, I think it can give a close enough approximation the way you use it. We only differ here by 10%, 4.4 k'/ft vs 3.95 k'/ft. I have one other reference that gives 4.4 k`/ft and another (Seeley & Smith Advanced Mechanics of Materials Article 74) that gives 3.6 k'/ft.

 

[cap4000]

miecz

Thanks Alot. Done Deal.