Castigliano's Second Theorem - Solving Deflection in x and y - Truss Example and Formula Derivation

In this video, we solve for the vertical and horizontal deflections of a determinate truss simultaneously using castigation's second theorem. As also go over where the formula comes from, which is derived from the strain energy of a truss.
More introductory video on applying load P to a beam: • Castigliano's Theorem ...
Another beam example: • Castigliano's Second T...
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[@AFMathandEngineering]

More introductory video on applying load P to a beam: kzbin.info/www/bejne/inecnaGdoZlroaM Another beam example: kzbin.info/www/bejne/pnLLoWVmjNiBhMU

[@blinkkawin18]

To anybody who is wondering how does the (∂F/∂P2)FL in member AB equals -640 if you follow his solution you will find that it's all 0 on all members. It's because he forgot to put horizontal force of 120 kN on the truss at point B. Once you put 120 kN on point B and find the reaction you will find that Cy = 0 and Ay = 160 - P and that's it you can go on from here and it equals to -640 kN if you put P force downward on point B (and positive if you assume P is upward)

[@perasenmosespaul416]

God.... you explain 10x better than my lecturers.

[@AFMathandEngineering]

Perasen mosespaul thank you very much for the compliment, sorry to hear you're having trouble with lecturers at your school!

[@jmmifsud1]

Not surprised that this is 10x better than lectures - lets face it lecturers are morons when it comes to teaching and making you learn anything. That's why they should stick to doing research. That way they would only confuse their colleagues.

[@betty.4585]

Thankss you made me realize what I did wrong. I was absent went our Prof taught this method. I was was able to solve it using virtual but in castiglano's. I derived it in terms of x not P that's why my answer weren't the same. Our plate were frames though. Thanks again.

[@sencegame8685]

how did u get -640. when P2=0??

[@vhk26]

Makes complete sense. Great video!

[@AFMathandEngineering]

Thanks!

[@JOKERMANCH]

If you confuse with why P=160. You must find AY CY at first. So it is 4/3p p=120 now Ay and CY 120x4/3 ====== 160

[@betty.4585]

Can i ask a question. How can I solve castiglano's when I have a beam with roller and hinge at 2m and 5m but deflection is needed at the free end of the beam which is at 0 and 7m I assigned P1 and P2 got the moments at the cut sections and derived it in terms of P1 and another for P2. But how do I integrate to get the deflection due to flexure with the P1 and P2 still present

[@AFMathandEngineering]

P1 and P2 either have values or are 0 depending if there are forces located at those points. You have to plug in these values before integrating. We do this in this video, also watch our other two videos where we solve a beam using castiglianos.

[@izharsulaiman4595]

hey do you have the video of the steps to find the member bc (that 1.667P) ?

[@AFMathandEngineering]

If you're talking about the steps for solving a truss using the method of joints (which was done here) yes, we do. Here's the link for an example: kzbin.info/www/bejne/rpnSkGtobbNpoK8

[@izharsulaiman4595]

tq very much. :)

[@redouanhasnaoui4306]

Manabrea ?

[@perasenmosespaul416]

but those written are small to view. maybe u make it more bigger and clearer.

[@AFMathandEngineering]

Perasen mosespaul thanks for the feedback and letting us know!

[@kgobudimokgopi2091]

How dd u come up with -640?

[@bouchrameddahi7713]

Me too i did'nt undersatand !

[@manosxa]

please use SI all the time

[@AFMathandEngineering]

No, there are lots of viewers from the states that use non SI units.