Maxwell's reciprocal theorem 4

According to Maxwell's reciprocal theorem the displacement at coordinate i due to a force at a coordinate j is equal to the displacement at coordinate j due to a force at a coordinate i.
What if the dispacement at coordinate i is a rotation and at j is a translation?
How can a translation and a rotation be equated?

 

[satee]

Trilinga,
Can we say that the spring deflects because it has to reach from the state of unstable equilbrium to stable equilbrium?
The load gets teransferred gradually in increments.During each increment the spring has to reach from the state of unstable to stable equilbrium.Suppose the deflection in the spring at an increment is Dt, work done is (K*Dt)
Finally it is K*D.
The reason for division for 2 is load getting transferred in increments, the theorem for minimum potential energy is merely an expalnation for unstable/stable equilbrium but provides some insight to work done.
Stable equilbrium is raeched when spring stops deflecting.

 

[trilinga]

Satee

It is NOT unstable equillibrium since the stability is NOT lost during the motion of the spring.

The fact that there is motion in the system does not mean instability.

It is only a change from a state of dynamic equilibrium to a state of static equilibrium.

Througout the process of load transfer the equilibrium is not affected. An unstable system such as a three hinged beam has no capacity to transfer load to the support and hence it collapses, whereas the spring at any moment is transfering the load to the support.

Mathematically an unstable system will have a singular stiffness matrix. The spring we talk about along with its support has a finite non-zero stiffness and hence the whole system (spring along with its support)is stable.

The system comes to rest by keeping only the minimum energy and dissipating the excess energy during the oscillatory motion.

Trilinga

 

Is this energy that is dessipated "complimentary Energy"?
Can we say for a completely rigid system that will not deflect during loading(just imaginary) the entire energy would be strain energy (not divided by 2)?

 

--- that is for a completely rigid system complementary energy would be zero?

 

[trilinga]

Setee

Forgive me if I sound a little curt but I mean absolutely no offence.

I sincerely feel that you have been using different terms without fully understanding what they mean. My friendly advice to you is to brush up your fundamental concepts by reading a standard text book on structural analysis.

 

Trilinga,
Thanks for your suggestion!!May be, i am not as intellectual as you are, also i would not have been fortunate enough to have a set of faculties in school as i think you would have had.Also, i know my thoughts are not as clear as they should be in structural anlysis but still i aim to make the best possible.I am currently reading books, and try to involve in discussion groups like these to get an insight into how others think of a physical phenomenon to shape myself into coorect thinking.I sincerely feel that no doubt is stupid once asked .
I am extremely grateful to you for having bring patient enough to answer my queries and having dealt with a person who probably may be having 1/1000000 intellect of yours.

 

[trilinga]

Setee

My intention was never to discourage you from asking questions since I developed my understanding only by asking a million questions when I was young. It might be true that the masters of yester years were extremely patient with us in answering our questions which people like me have to learn yet.

I strongly believe that the term intellect is an invariable entity residing in every individual which has no relative measurement. What we require is the faith in it and start applying in the right direction. I learn a bit more everyday from evryone I come across and at times get astonished by the excellent ideas and explanations on structural behaviour from my juniors.

Believe it, knowledge is a sweet ocean and we are fed with drops of it every now and then by nature.

My post was not born out of frustration on the stupidity - you said so and I never thought it was - of your last question, but on the lack of clarity and direction in it. It may be just my feeling and I may be wrong. Hence I felt it would be better for you to get the direction by refering to some good authors who have explained these concepts with clarity. (Do not ask me who the best author is but find out)

Good luck!

 

Trilinga,
You mentioned:
"I developed my understanding only by asking a million questions when I was young."
I am still young , having finished my courses last year.But then i lack clear ideas anh hence my questions do lack clearity.
Then you said:

"It might be true that the masters of yester years were extremely patient with us in answering our questions "
Well, to be frank(not exagerating) when i asked questions to my teachers in school few times i got excellent replies but most of times i was turned down in a way not to ask .
questions again(God only these reasons, perhaps my teachers lacked the ability).In this case you were not as unlucky as i have been, i suppose.

Then you said:
"I strongly believe that the term intellect is an invariable entity residing in every individual which has no relative measurement. What we require is the faith in it and start applying in the right direction. "

This is what i have been trying to do but i am yet to find the right direction!!!!

"I learn a bit more everyday from evryone I come across and at times get astonished by the excellent ideas and explanations on structural behaviour from my juniors."
This is what i feel when i get replies to my questions from this site . It makes me happy at times to get my answers at the same time makes me feel down too when i look at my thoughts.

"My post was not born out of frustration on the stupidity - you said so and I never thought it was - of your last question, but on the lack of clarity and direction in it. "
I fully agree here."
Appologies!!!

"Hence I felt it would be better for you to get the direction by refering to some good authors who have explained these concepts with clarity. "
I am currently reading books, in whatever time i get from my work.These are
1)Elements of Strength of MAterials(Timoshenko and Young)
2)Intermediate Structural Analysis(Wang)
3)Theory Of Structures(Timoshenko and Young)
Few indian authors which probably you might not know:
3)Structural Analysis(Pandit and Gupta)

Thanks , Sir.

 

[trilinga]

Setee

Glad that you have been reading real good books. I was reading other Indian authors like Ramamrutham and Vazirani for analysis.

Remember, whoever be the author you are reading, try to visualise and try to link the associated mathematics with the physical phenomenon and do not give up until you get convinced of the behaviour.