Westergaard Support Reactions for Wheel Loads 2

[cap4000]

I have the paper by Westergaard titled the Computation of Stresses in Bridge Slabs Due to Wheel Loads from March 1930. In it Table 10 indicates the left reactions for various spacings as a function of the simple span. Can anyone verify the left reaction value for a 20 kip load placed 1 foot away from the left support for 7 foot wide concrete slab? The table indicates extremely small reaction values on the order of 0.0117 x 20 kips per foot or 234#/ft? Any tips will be greatly appreciated.

 

[miecz]

Without the paper, it's hard to say. Sounds like it would be closer to 234#/inch.

 

[cap4000]

As long as the units stay in feet it should come out in feet. The problem is the actual formula involves calculus with hyperbolic sine and cosine functions.Takes for the tip.

 

[jike]

cap4000:

I do not have the paper here at work but I will try to remember to dig it up tonight and check back with you tomorrow.

 

[tkowalczyk]

Where did you find Westergaard's paper? I looked for it everywhere.

 

[miecz]

Me, too. I finally gave up.

 

[jike]

I order it thru my local library. I believe they got it from the University of Illinois library.

 

[jheidt2543]

You can also order a copy of the paper for $16.00 from:

Linda Hall Library
5109 Cherry St.
Kansas City, Missouri 64110-2498
Phone: 816-363-4600

 

[miecz]

I got a copy of Westergaard's paper from the Linda Hall Library. The 0.0117 factor from Table 10 is the reaction per lineal foot at y/u=4. This corresponds to 234#/ft, as you say. But it's not the peak shear, it's the shear at 4*u or 4 feet away from the load. The shear adjacent to the load is 0.4535P, which corresponds to 9070#/ft. See the attached pdf, where I derived the coefficients in table 10, together with the corresponding shears, from formula 119.

 

[cap4000]

miecz

I have already done a shell analysis on it with Ram Advanse. Real Nice Job. Done Deal. Thanks.

 

[jheidt2543]

cap4000:

Would you like to describe how you set up your model in Advance and what kind of results you got compared to Westigards method? I've not tried modeling a bridge deck as a shell in RAM Advanse.

 

[cap4000]

jheidt

I don't really have a bridge problem. What I do have is a 7 foot square slab over a 17 foot deep hole in the middle of a driveway where fire trucks and other AASHTO H25 wheel loads will travel over. I was only looking for a "check" against Westergaards paper. Ram Advanse solved 120 simultaneous equations in a micro second to get me the deflections, shears and bending stresses. It also gave me the rebar required. I then checked the results against a book by Cook and Young for classical plate theory.