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May 08, 2020
08:46 PM

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May 08, 2020
08:46 PM

Mathcad quadratic equation of an arch

Hi PTC Community,

I would like to find a solution and better understand of how I can define this type of equation and how to get the results for the arch height at different points. I am attaching a sketch for a better understanding.

I thank you all!

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6 REPLIES 6

May 09, 2020
01:14 AM

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May 10, 2020
11:25 AM

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May 10, 2020
11:25 AM

Thank you so much!

May 09, 2020
09:21 PM

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May 09, 2020
09:21 PM

Here is a way to do it using the symbolic "solve"

May 10, 2020
11:45 AM

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May 10, 2020
11:45 AM

Thank you so much!

For my own learning, if you have the time, could you explain to me the solve statement, or at least how the programming line and "Local Assignment Operator" works in this statement.

Such a beautiful community, never thought this way of solving an equation, like yours or @terryhendicott

May 10, 2020
12:36 PM

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May 10, 2020
12:36 PM

@george_geo56 wrote:

Thank you so much!

For my own learning, if you have the time, could you explain to me the solve statement, or at least how the programming line and "Local Assignment Operator" works in this statement.

To use the symbolic "solve" you have to put all equations of the system line by line in a vector and then apply the symbolic solve where you have to state which variables you want it to solve for.

The local assignment operator was necessary to be able to evaluate the first derivative at position L.d/2. Unfortunately Mathcad 15 does not provide an operator like the prime symbol in MC-Prime (one of the few advantages of Prime) where we simply could write y'(L.d/2)=0.

Another way, which also may look cleaner, is to define the derivative as a function yourself. I had chosen the name "y1(x)" but of course you may make it look like "y'(x)" using the Ctrl-K feature.

The red error stems from the numeric because its moaning about the variable(s) not defined. A probably more correct but also more elaborate approach which makes the numeric happy, too, is this:

Because this last approach also is compatible with Mathcads numeric engine, you may use a numeric solve block to get the very same results:

The symbolic engine in Mathcad is rather weak compared to Maple or Mathematica and if at the end you are only after numeric results, it may be better to use numeric methods, only. Chances are that the symbolic "solve" will choke in case of more complex/complicated equations.

May 10, 2020
03:06 PM

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May 10, 2020
03:06 PM

Solution without units is not solution!

And second/

Try to solve a problem symbolic and than numeric!