Compare the moments of a plate on elastic foundation and a simply supported circular plate both subjected to a concentrated load (distributed uniformly over a small circular area). Determine the radius of the simply supported circular plate which has the same moment from a concentrated load as an infinite plate has on elastic foundation. Thickness of the plate is: h = 200 mm, the load is distributed over a circular area the radius of which is: b0 = 50 mm. Material properties are: E = 18.3 GPa and ν = 0.3, the foundation coefficient is: c = 50 000 kN/m3.
It is assumed that at the midplane of the slab the load is distributed uniformly over an area, the radius of which is:
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Radius, R [m]=Solve
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Steps
Step 1. Determine the maximum moment of a plate on Winkler type foundation subjected to concentrated load. Step 2. Write the maximum moment of a simply supported circular plate subjected to concentrated load. Step 3. Compare the above solutions. Express the radius from their equality.Step by step
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Results
The maximum moment of a plate on Winkler type foundation subjected to concentrated load is The maximum moment of a simply supported circular plate subjected to concentrated load is Comparing the above solutions the unkown radius can be expressed:Worked out solution