Circular Plate Deflection problem

[SMMINCH]

Hello everyone,

My problem today involves understanding circular plate deflection. Online I have found two different equations that include a point and the entire area. I need an area between that. My circular plate is rigidly connected all around the circumference with a weld and has a rod hitting it with x amount of force. This rod is half the diameter of the circular plate. How do I find the deflection and how thin I can get the plate before it breaks. This is a thick plate of steel. the goal is to optimize the thickness of my plate without deflection ruining the weld. Thank you all.

[Kelly_Bramble]

http://www.engineersedge.com/beam_be...te-bending.htm

[SMMINCH]

This looks like it will work but I am unable to define some variables such as q and what units E is in.

[Cragyon]

There's also these webpages - I use them a bunch:

Circular plate, uniform load simply supported edges

Circular plate, uniform load edges clamped

Circular plate, concentrated load floating on another plate

Circular plate, concentrated load edges fixed

[JAlberts]

The following reference addresses your situation (somewhat) by using the equations on pg 448 and Case 5 on pg 450 (it takes a bit of work to understand how to relate these two items). I say "somewhat" because at a point due to the deflecting of the plate your flat bar face load is going to become more of a ring load at the bar's O.D. rather than a distributed load across the face of the bar and I have not found any solutions in this reference for an intermediate ring load configuration.

Note:
1. In Table 5 you will see that between the ro/a (outer radius of load / outside radius of plate) values the maximum stress point shifts from the outer plate edge to the center of the plate.
2. For ro/a values between those given interpolation can be used

Reference Roark's Stress and Strain





One additional caution, you use the term "bar striking the plate with a given force" but generally for dynamic loads of that type an energy solution method is used based upon the moving energy of the striking bar vs. the energy absorption of the deflecting impacted plate because the maximum force of impact is dependent upon the deflection of the plate (i.e. The more the struck plate deflects under load it absorbs more of the striking energy of the bar and therefore the actual striking force is reduced) So the final solution is a bit of a trial and error process of determining the matching force and deflection values.