Mathcad Community Challenge January 2022

[#1]

Mathcad Contest Idea - January 2022

Plane Truss Mechanics

Can you use Mathcad to solve this problem?

This comes from page 88 of “An Introduction to the Mechanics of Solids,” by Stephen H. Crandall, Norman C. Dahl, and Thomas J. Lardner. This was the text for the first mechanical engineering class (2.01 Mechanics) that I took my sophomore year at MIT way back in 1989. You can find the book for as little as $5 on Amazon. It shows three different solutions for the problem, including:

• closed-form solutions involving equilibrium of forces and the beam-deflection equation
• a computer program called IBM STRESS
• Castigliano’s theorem which solves via elastic energy.

Any introductory mechanics text or a Schaum’s Outline should guide you to a solution. As with the other contests that will follow this one, the point is not the answer to the problem, but your execution of the solution.

Some ideas you may consider including in your worksheet:

• Allowing the user to change the material via a Combo Box Input Controls.
• Depicting the results with a Chart Component, such as the truss in the deformed shape, or the deflection at D due to changing input loads.
• Making the problem more open-ended, such as using matrices and programming for different geometry and loading.

Note that these are just ideas; I have not tried any of these. Maybe you can explore different approaches. The problem is simply a starting point.

This is an excellent problem for a team to solve, especially for civil and mechanical engineering students. How would you tackle this problem in Mathcad?

Find the Mathcad Community Challenge Guidelines here!

[terryhendicott]

Hi,

I'll accept the challenge and get the ball rolling.

Cheers

Terry

220105-TrussChallenge.mcdx

[DaveMartin]

Holy cow, that was fast!

[VladimirN]

 Terry,

You can also add a selection list ("Combo Box") of different materials (with the corresponding modulus of elasticity) to your calculation: steel, titanium, aluminum, magnesium alloy, wood. Thus making your program more versatile.

[terryhendicott]

Hi Vladimir

Done on my sheet.

Not sure if it worth resubmitting the file with the combo box

Cheers

Terry

[VladimirN]

Well done!

[DJNewman]

If anyone has other variations on the solution to the problem, or a different approach they'd like to contribute using PTC Mathcad Prime, you have ten days left!

[DF_5185570]

Here is another solution to the truss problem. The objective of this solution is to provide a teaching tool to be used in a statics of strength of material course at the sophomore level.

Truss example uisng Mathcad solution.mcdx

[terryhendicott]

Hi.

Interesting.

The same force in the members is arrived at in each approach.

The downwards deflection of the middle point D is different in each approach?

0.163" by stiffness method 0.05" by virtual work?

I have looked closely and the E used in virtual work method is Steel, and in stiffness method Aluminum.

Cheers

Terry Hendicott

[DF_5185570]

Terry

Thanks for picking this up.  I changed E to aluminum and got an answer of 0.165 inches.

Regards, Dennis Fallon

[DJNewman]

Thanks to those that participated!

Stay tuned for Dave Martin's write-up of the solutions and his own spin coming within a couple of weeks. We're also distributing badges to those that participated now.

[DJNewman]

@DaveMartinhas published his discussion blog on the first Mathcad Community Challenge!

Take a read for his thoughts on the truss problem:

https://www.mathcad.com/en/blogs/community-challenge-truss-problem

Features big shout-outs to @terryhendicott  and @DF_5185570 !

Please look forward to the next challenge starting in March.

[BertBeirinckx]

Hello,

I stumbled upon this page and was blown away by this excellent solution!  I really hope you don't mind but I modified your solution a little bit to show the power of the unit awareness of Mathcad.

The solution remains the same, but in Mathcad there is no need to make all values unitless.  Please review the solution I sent along, if I got something wrong, please let me know.  In the modified sheet you can now express all inputs and results in whichever unit you feel comfortable with.  Formulations are also a bit cleaner.

Kind regards,

Bert

220105-TrussChallenge_mod_units.mcdx

[DaveMartin]

Thanks, Bert!

Your contribution is a great reminder that this is a community challenge and we hope that people build on previous submissions. The next challenge is a bit more open-ended so I hope we see even more people taking what's been posted before and adding to it. It's a great way for people to build their skills. I definitely learned from this challenge's submissions.

Dave

[terryhendicott]

Hi Bert,

Thanks for improving the solution.

Enclosed is an extra section that now calculates the reactions

Cheers

Terry

220217-TrussChallenge_mod_units_reactions.mcdx