formula for concentrated load on a slab 1

[cve60069]

Hello

I am trying to find a formula that I could use in a spreadsheet for the bending-moments of a simply-supported two-way slab under a concentrated-load (similar to equations 10 and 12 of BS8110). The load is 300-mm square.

Any references or guidance would be appreciated.

Regards

 

[BAretired]

Are the spans equal? Is the load at midspan in both directions? Are the slab corners tied down or free to lift up?

BA

 

[msquared48]

"Formulas for Stress and Strain" by Roark and Young, Fifth Edition, Table 26, page 386 gives one situation of a simply supported plate at the edges, with a uniformly loaded area of radius r0 in the center that you might be able to use.

Could not see any adaptations of similar loading for plates with various combinations of fixed edges.

Mike McCann
MMC Engineering

 

[Bagman2524]

Winter & Neilson, Design of Concrete Structures has this type of information in it. There are tables that give coefficents in calculating the end moments. The coefficents vary depending on end support conditions and type of loading.

 

[cve60069]

Thanks for the response.

The slab is simply-supported and allowed to lift at edges. The spans are not equal ranging from 1:1 to 1:4. I am designing a slab 1500:1900mm (1:1.3) but I want to be flexible and cover all ratios, hence a formula.

I have looked at Roarke and the situation I am modelling is referenced under Table 11.4 1cg503. If I cannot get a formula I will have to adapt the table for my situation. This is the first time I have used Roarke. Poissons ratio is 0.2 for concrete and the table is for 0.3; how may I adjust for the difference, please? Am I able to extrapolate between the three ratios to obtain a ratio of 1:1.3. I have tested the table and the extrapolation will not be linear.

As a beside; I was given a formula for a concentrated-load on a slab by an engineer I am no longer able to contact. The formula was similar to the BS8110 equations 10 and 11 in that alpha.sx and alpha.sy were the same but nl[sub]x[/sub][sup]2[/sup] was replaced with 2.nl[sub]x[/sub](1/0.3+0.6l[sub]x[/sub]). I am unable to locate a reference to this formula anywhere but I do recognise the 0.3 being the width of the load and the 0.6l[sub]x[/sub] referring to the effective-width from clause 3.5.2.2. I am unable reluctant to use the formula without a reference.

Regards

 

[cve60069]

Dear all

I have spoken to the engineer that provided the revised equations 10 and 11. Chris (the engineer) worked out the equivalent-UDL for the concentrated-load and supplemented the equivalent-UDL into equations 10 and 11. I have not done the check but the solution is very elegant. Any load shape on a two-way-slab could be analysed using revised equations 10 and 11 without referring to tables.

Regards