Trying to duplicate a formula

Question

Hello guys,In me previous discussion I was trying to set-up my own equation.It worked out eventually thanks to you guys.But, I have been dealing with an other problem.I have been trying to duplicate a formula from the beginning till the end.I have found the original formula on some forum on the internet.The formula seems correct because the same formula is written in roarks' book.I have been trying to prove the formula with the use of mathcad and the weird (in my opinion) statements on the engineerings forum.Can you please help me towards the correct direction?It is about the deflection of a thin ring under a point load.Here is a quote from the forum regarding the formula: "You do this with the energy application using Castigliano which is far easier than curved beam theory. You first split the the ring in quarters using the second quadrant assuming the force is north south. If the load is north P, then you have a built in edge on the north point and a moment M1, undetermined and a south vertical force of P/2 at the west position. You write the energy integral M^2/2EI*rd@ over the 90 degrees where M=m1-(P/2)r(1-cos@)The partial derivative with respect to M1 would be the slope at the west position is zero due to symmetry and the partial with respect to P is the vertical displacement, your problem. After all this I gety=Pr^3(pi/4-2/pi)/EI"Regards,Tim van Lunteren

AlanStevens · Accepted Answer

Perhaps more like the attached?Alan

Werner_E · Answer

Are you sure about what you are doing? And I am not speaking of your attempts to work in Mathcad.

You define M as a function and then at the end you are trying to "find" M!! You can find variables but not functions and as you have defined it yourself you won't have to search for it anyway.

In the solve block you use a function dMdm1(th) you haven't defined. What do you think Mathcad should do with it? If you want the derivative dM(th)/dm1 then use the derivative operator here as Richard an me have shon in that other thread.

Richard also had already told you that you have to use the boolean equal sign - you still use the numeric evaluation = in the first and the assignment := in the second equation.

If in your first equation dMdm1 is meant the derivative as I wrote above - you yourself had evalauted it and got shown that it is (no surprise) 1. That means that the interal in your first equation would yield 1/(2*EI)*R*th and evalauted from 0 to pi/2 this would give R*pi/(4*EI). You demand this to be zero anf that gives us R=0.

So the Integral in your second equation is an integral of zero over th from 0 to pi/2 - the result is of course zero and that means that delta has to be zero. Thats exactly what Mathcad gives you as result. Garbage in - garbage out.

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