Heavy duty grating deflection formula 2

[wudaijie]

Does anyone know how the formula come from?
I checked into the Manufacturer's Catalog and found out the deflection equation is
D = P*[(2L^3)-(a^2*L)+(a^3/4)]/96EI.
Where
P=load per bearing bar
L=Clear Span
a=Partial Load contact parallel to span
Considering AASHTO H-20 vehicular load.
Many thanks.

 

[paddingtongreen]

How many spans?

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[SlideRuleEra]

The formula is based on the AASHTO Standard Specifications for Highway Bridges. See the attached explanation taken from an Ohio Gratings catalog:

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[wudaijie]

It's single span. Thank you.

 

[paddingtongreen]

For a simple span, that is the formula for the deflection of a partially loaded beam when the load is in the middle.

Michael.
Timing has a lot to do with the outcome of a rain dance.