Singularity Functions - Useful for beams with fixed ends? 2

[P1ENG]

I use singularity functions all the time for determining shear and moment diagrams for beams in MathCAD. My question is, can singularity functions be used when the beam has a fixed end(s)? I was assuming for a fixed end, that [θ]'=0 would be a boundary condition for solving for c1 and c2 in my [θ]' and [θ] equations, but I am not getting correct answers. I don't know if there is a mistake in my program somewhere, or if the mistake is my assumption of setting [θ]'=0 at the fixed ends.

Also, if anyone is familiar with both singularity functions and the moment distribution method, is there any advantage to the moment distribution method? I am not too familiar with that method, but I would think the only advantage is that the method can be applied to 2-D applications where singularity functions are limited to a continuous beam.

Juston Fluckey, E.I.
Engineering Consultant

 

[P1ENG]

Continuation of singularity function development: What if the beam doesn't have a continuous moment of inertia (e.g. a tapered beam).

I will do some thinking/research and get back to you all. Feel free to post anything you know/find.

Juston Fluckey, E.I.
Engineering Consultant

 

[ishvaaag]

Not a problem in the setup of this problem, I(x) simply enters the integral.

 

[P1ENG]

Quick response. I was planning on doing a sample calculation with the moment of inertia being a function of location and comparing it to my RISA results, but you were quicker. It seemed straight forward, but I wanted verification, which you gave me. Thanks ishvaaag!

Juston Fluckey, E.I.
Engineering Consultant

 

[P1ENG]

Additionally, it should be stated that the same could be done for varying modulus of elasticity.

Juston Fluckey, E.I.
Engineering Consultant

 

[P1ENG]

A note for Mathcad users:
Note interestingly how the Mathcad vector was able to retain in Mathcad 2000 Professional solutions in different units (moments and vertical reactions). I have seen this kind of ability disabled in later releases.

You are right. I am using Mathcad 14 and it does not handle the units.

Juston Fluckey, E.I.
Engineering Consultant

 

[x5bulldog]

I was a civil major for undergrad and graduate. My emphasis was structural. We are taught so many different methods to solve for moments and reactions for determinate and indeterminate members. I remember my sophmore year we skipped the singularity functions. Four years ago at work there was a co-worker who was a mechanical engineer student and recall that he was studying singularity functions. I usually choose moment distribution over the others since its quite simple for me. I have attached a copy of how simple moment distribution can be for beams.