Singularity Functions - Useful for beams with fixed ends?
Singularity Functions - Useful for beams with fixed ends?
(OP)
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.
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






RE: Singularity Functions - Useful for beams with fixed ends?
Taking the example given here Singularity function - Wikipedia, you would be required to add a constant of integration c when calculating M : paraphrasing the example Because the moment is not zero at x=0, a constant of integration, c, is added (and of course end reactions need be left as unknowns and determined with c from u'=0 and u=0 at the second end and from equilibrium).
Does this make sense?
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Singularity Functions - Useful for beams with fixed ends?
h
the singularity functions are used mainly in the definition of the loading. Once that is made, they should be ready to stand any of the ordinary procedures of analysis (including any boundary conditions) analytical when feasible, and numerical where not. If I find any practical reference dealing with the amtter I will post it.
RE: Singularity Functions - Useful for beams with fixed ends?
Check out "Machine Design" by Robert L. Norton, pg 116-131 discusses the use of singularity functions for beam loading including examples of beams with fixed ends. Roark also tackles beam loadings with singularity functions. As ishvaag states, once the loading function is developed and you have integrated it is a matter of proper boundary conditions.
I am a mechanical who now mainly practices structural engineering so I was exposed to singularity funtions as an ME however I have found that it is never discussed in civil, including structural engineering grad classes that I have taken.
It is a great method for programming and graphically displaying beam loadings.
Good Luck! If you have a specific case post a sketch and we can work through.
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
The previous attachment integrated the c1 term incorrectly in the δ(x) function. The attached hand calculation shows correct values. I don't know how RISA's solver handles the calculation of the reactions which are slightly different than mine, but I would think mine are 100% on.
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
My E and I are different but for constant section irrelevant to moments and shears (not vertical deflections outside nodal restraints, or slopes anywhere). Both the Mathcad and RISA 3D solutions easily changeable to your E, I values.
In this case, I have not yet stated the problem solved in Mathcad by the force method with the singularity functions. All that is needed to do so is to include a previous definition of the singularity functions required in Mathcad, then modify the statement of the moment according to such function definition, to follow the same procedure to solution.
Since I don't know about the general use of the singularity functions for structural analysis, I can't see if there is the general convenience of retaining 7 unknowns where as here we can deal the matter (mostly) with 3. Since automatical solver, scarcely relevant at this scale.
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.
For later relases it may turn necessary while solving to reduce to consistent (to be, implied) units and then recovery of the same, first by the corresponding division of the pertaining units of the component in the to be implied units and then multiplication of those corresponding after solution.
RE: Singularity Functions - Useful for beams with fixed ends?
Also, my RISA results were for a W8x10. Making it a Rigid member yields the same results as ishvaaag. I wonder if the difference is due to shear deformation.
Next thought for everyone... what would happen if the right end was also fixed? You would then loose your known BC of M(20')=0.
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Singularity Functions - Useful for beams with fixed ends?
I have not checked this time against RISA 3D.
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
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
RE: Singularity Functions - Useful for beams with fixed ends?
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?
You are right. I am using Mathcad 14 and it does not handle the units.
Juston Fluckey, E.I.
Engineering Consultant
RE: Singularity Functions - Useful for beams with fixed ends?