Plotting Fixed Moment Diagram in PTC Mathcad Prime 7

Question

Plotting Fixed Moment Diagram in PTC Mathcad Prime 7

Ali_003 (Structural)

(OP)

28 Aug 22 21:52

Hello engineers. I wrote a mathcad worksheet using ptc mathcad prime 7 for analysing a three-span continuous beams using three-moment equations. I have calculated the reactions, fixed and free span bending moments. I have also plotted the free span moment diagram. I have not as yet drawn the fixed bending moment diagram. I was wondering if someone could help me to express the fixed bending moment as a function of x, i.e M(x). This will enable me to use the principle of superposition to draw the final bending moment diagram.
The diagram below is basically what I want to plot in mathcad.
Thanks in advance for any suggestions that may help me

in this regards.
Yours truly
Bello Ali

https://files.engineering.com/getfile.aspx?folder=5cb6a9fd-52cd-44bd-8abc-1

structSU10 (Structural) · Answer 1 · 2022-08-30 02:39:22

you can write this as a discontinuous function that is linear within the desired regions. you want for x<l1 the moment to go from M1 to M2 so M1 + x*(M2-M1)/L1 should give you the desired values. You continue that concept through the full length.

Sparweb (Aerospace) · Answer 2 · 2022-08-30 05:28:19

You can do this with an integral. The integral of the shear function is the moment function.
Just make sure the range of integration is continuous.
0 <= x <= 2 and 2 < x <= 4 is continuous from 0 through 4
0 <= x < 2 and 2 < x <= 4 is not.

sticksandtriangles (Structural) · Answer 3 · 2022-08-30 16:19:18

I have gone through this in mathcad 15 and mathcad seems to struggle with integration over a discontinuous function.

I was able to solve this by integrating of the continuous portion of the function and then adding tip to tails to connect the discontinuous regions.

Shear diagram (discontinous function)

Integration over continuous portions:

Adding tips to tails to make a final graph:

You can probably do something similar for your example.

S&T - www.re-tug.com

Ali_003 (Structural) · Answer 4 · 2022-08-31 15:07:00

Thanks @structSU10 for your prompt reply. I have tried your suggestions and was able to plot the fixed bending moment diagram. Thank you once again sir/ma for your heip

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Plotting Fixed Moment Diagram in PTC Mathcad Prime 7