Posted by: Scott1975 ® 04/05/2010, 08:59:31 Author Profile eMail author Edit

Hi everyone, This is my first post; I don't know if it is possible to determine the maximum stress in a flat circular plate of constant thickness, with fixed edges, but with a large thru hole on either side of the centre axis? The whole plate is under a uniform distributed load! I've attached an image of what I mean. I've looked at Roark's Formulas under flat plates but the examples don't cover more than just a concenric hole (i.e. a ring). Also, ASME Section 8, Division 2, Paragraph 4.6.4 describes a method of determining the stresses at an opening in a flat circular head (plate), but again this is for a centrally located opening, not one each side of the centre axis like I need to analyse. Does anyone have any suggestions as to how to calculate the maximum stress in this configuration or is this really only suitable for an FEA? Thanks Scott

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: maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes?
: maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes? -- Scott1975	Post Reply	Top of thread	Engineering Forum

Posted by: zekeman ® 04/05/2010, 15:31:01 Author Profile eMail author Edit

Unless you get extremely lucky, you are not bound to find an analytic expression for this. In theory, you would have a chance if the plate had circular symmetry, i.e. the solution independent of theta, the angle around the center.

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: : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes?
: : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes? -- zekeman	Post Reply	Top of thread	Engineering Forum

Posted by: Pinkerton ® 04/05/2010, 17:42:28 Author Profile eMail author Edit

I have been thinking about this since this morning and have come up blank. Providing the plate material isn't $1,000 per cubic inch, you could try something like a flat bar (red rectangle in pic) and regard the un-calculated section as the "safety factor" I think you are going to have to fudge and/or assume for some parts of this. How big and what pressures are we talking about? Dave

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: : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes?
: : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes? -- Pinkerton	Post Reply	Top of thread	Engineering Forum

Posted by: Scott1975 ® 04/06/2010, 03:32:05 Author Profile eMail author Edit

Hi, thanks for the reply, I have some information below regarding the plate. The material is Aluminium 6061-T6, Tensile Strength = 42,000psi Yield Strength = 35,000psi Plate Thickness = 2 inches OD of plate = 7.910 inches ID of 2 x holes = 2.04 inches (centre of each hole is 1.25 inches off-centre of the 7.910 inch OD circular plate) Distributed Pressure = 1500psi Can this really be simplified to that of a beam? How do you account for the holes? Regards Scott

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: : : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes?
: : : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes? -- Scott1975	Post Reply	Top of thread	Engineering Forum

Posted by: Scott1975 ® 04/06/2010, 05:04:14 Author Profile eMail author Edit

What I'm trying to calculate is the maximum bending stress at the two holes. Roark's Formula's 7th Edition, Page 464, Table 11.2, Case 2a, is for a fixed edge circular plate, with a hole cut in the middle. That case advises the maximum moment is a tangential moment at the ID of the hole. If the moment is calculated using the formula provided, it can then be substituted into the plate bending formula = 6M/t^2. The resulting stress can then be compared to some failure criteria, to determine a factor of safety That is the closest comparison to what I have (I have two holes offset by same amount from centre axis of circular plate). Thanks for the help so far, Scott

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: : : : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes?
: : : : : maximum stress in a flat circular plate of constant thickness, with fixed edges, under uniform distributed load, but with two large thru holes? -- Scott1975	Post Reply	Top of thread	Engineering Forum

Posted by: Pinkerton ® 04/06/2010, 11:23:57 Author Profile eMail author Edit

Hi Scott, >> What I'm trying to calculate is the maximum bending stress at the two holes. I am pretty much out of ideas and the flat bar was just to hopefully "jog" a thought process for you. Even then the calculations will be "interesting," as the strength of the bar would be determined by the two thinned areas between the edge of a hole and the edge of the bar. However having two holes the web between the two holes would have to come into play as well. Sorry, not being much help I know but it is an interesting problem to ponder. I wonder if you can find a motor racing design forum that might be better able to help you. They are very fond of making lots of holes in stuff! Dave

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