Mathcad usage

[NM_10165576]

Hello everyone,
eff.K shown in picture is radius of curvature along beam length and X is the array for sectional points.
I have to double integrate eff.K to get deflection. How can i do it in Mathcad? Attached Mathcad 10 sheet.

[terryhendicott]

Hi,

two steps.

1) turn the effK into a continuous function using the interp() function.

2) make a function to do the double integration.

Then plot the result

[AlanStevens]

Terry, shouldn't your outer integration be with respect to x?

[terryhendicott]

Hi Alan,

If the second integral is wrt x it would be an area integration.  It should be two integrals wrt length along the beam?

To be meaningful for deflection of the beam the slope at the ends of the beam needs to be included?

Cheers

Terry

[Werner_E]

I have no expertise whatsoever in your field of work but the double integral as you had set it up

would mean that the evaluation of the inner definite integral would yield an expression in x. Variable y is gone and the subsequent integration wrt y would mean just a multiplication by y.

Given the limits 0 to x of the outer integral this would mean that you could replace the outer integration just by a multiplication with x.

So we could spare the outer integral speeding up the calculations. But is this really as it should be???

Here are is your formula and the equivalent one (with just the multiplication by x) compared with Alan's suggestion, which sure looks more like a parabola:

I have no knowledge about beams and deflection but I also guessed that either the variable of integration of the outer integral should not be y and/or that one of the integral limits should be different.

PS: While mathematically not correct in notation, the following would yield the very same result as my delta3 above and is maybe what you had in mind?:

[NM_10165576]

Thank you.
please send me the mathcad file.

[NM_10165576]

Thank you for the answer. 
But the curve doesn't look like a beam deflected shape for simply supported beam. Shouldn't it be like parabola?

[terryhendicott]

Hi,

But the curve doesn't look like a beam deflected shape for simply supported beam. Shouldn't it be like parabola?

Correct.  Allowance needs to be made for the slope of the simply supported beam at the supports.  Not enough information is given in the post to calculate this.

Cheers

Terry

[NM_10165576]

beam length is 5.46m and the supports are at 0.1m from left and 0.1m from right. Calculate for this new data, if possible.Deflected curve looks like in the image below. Attached the mathcad sheet.

[terryhendicott · Accepted solution]

Hi,

See enclosed file.

[NM_10165576]

This works. Thank you😊

[AlanStevens]

Here's a simple numerical integration: