Moment/Shear/Deflection/Rotation Diagrams
Moment/Shear/Deflection/Rotation Diagrams
(OP)
Greetings:
I am trying to put together a program that will work in many many instances. I've worked it out so that for a given "element" (a given section of a continuous beam) I know the Moment, Shear, deflection, and rotation of both end points AND all loads applied onto the element.
How do I calculate the Moment, Shear, Deflection, and rotation for any point within my element? I seem to have all the information I could possibly need to produce these 4 diagrams. I cannot seem to find the answer I am looking for.
If you are somewhat confused as to what I am calling an element: it's basically a section of a beam. Say I have a 30' long simply supported beam with a uniform load throughout. My element dilemma is that: I know the M,V,Δ, and θ at both the 1/3 and 2/3 points of the beam, but cannot find these values within the element (between the 1/3 and 2/3 points).
I am trying to put together a program that will work in many many instances. I've worked it out so that for a given "element" (a given section of a continuous beam) I know the Moment, Shear, deflection, and rotation of both end points AND all loads applied onto the element.
How do I calculate the Moment, Shear, Deflection, and rotation for any point within my element? I seem to have all the information I could possibly need to produce these 4 diagrams. I cannot seem to find the answer I am looking for.
If you are somewhat confused as to what I am calling an element: it's basically a section of a beam. Say I have a 30' long simply supported beam with a uniform load throughout. My element dilemma is that: I know the M,V,Δ, and θ at both the 1/3 and 2/3 points of the beam, but cannot find these values within the element (between the 1/3 and 2/3 points).





RE: Moment/Shear/Deflection/Rotation Diagrams
Ed.R.
RE: Moment/Shear/Deflection/Rotation Diagrams
i've done this (not the achievement of my life) in excel to help solve redundant beams ... yeah, i know i can download it from several places, but it was slow and a minor challenge!
RE: Moment/Shear/Deflection/Rotation Diagrams
Eg. Take an element of length [l] loaded by [w]
For Shear:
Vintermediate=Va+w*x
where Va is shear at node A
For Moment
Mintermediate=Ma+Va*x+w*x/2
For Rotation
Sigmaintermediate=sigmaa+Ma/E/I*x+Va/E/I*x^2/2+w/E/I*x^3/6
And likewise for displacement however I am not going to write it out.
How are you writing your program and what elements are you programming and what codes do you intend to include. I have only put together a Matlab routine, I can upload my code if you need any help. Let us know how it goes.
Don't forget axial forces if you are programming 3d beam elements.
RE: Moment/Shear/Deflection/Rotation Diagrams
RE: Moment/Shear/Deflection/Rotation Diagrams
As most suggest using a free body diagram and an integration scheme to fet forces/displacements within the element.
However, once we use an integration scheme we are doing essentially conventional mechanics.
What am trying to question is,whether is there any procedure that one could get exact solutions within the leemnt using the interpolation/shape functions for the corresponding element (beam element here)?
I know the solution using interpolation/shape functions would not be exact-is there any scheme to obtain an exact solution using Finite element procedures than the free body diagram?
RE: Moment/Shear/Deflection/Rotation Diagrams
if you're saying you know the free body diagram of the "element" (in the real world), then applying the equations of equilibrium (integrating shears to moments, etc) will give you the exact solution. equations of equilibrium will also work with the free body from the FE (though of course this is an approximation of the real world).
RE: Moment/Shear/Deflection/Rotation Diagrams
Of course integration is only exact if you truely integrate it which is difficult to program so you'll probably have to use Newtonian integration (Take it piece by piece). The spreadsheet I made could go up to 1000 pieces and that was more than suffice.
I would also recommend for a truely exact solution to use the equations given in the AISC manual and super impose each case (Point load, distributed load, point moment). It all depends on how your loads are defined for this to be feasable, plus the AISC manual doesn't provide equations for theta and point moments so further research is required for that.
RE: Moment/Shear/Deflection/Rotation Diagrams
RE: Moment/Shear/Deflection/Rotation Diagrams
RE: Moment/Shear/Deflection/Rotation Diagrams
RE: Moment/Shear/Deflection/Rotation Diagrams
no wonder why you're extinct
RE: Moment/Shear/Deflection/Rotation Diagrams
I suffer from "Fat finger syndrome" and often what I mean to type is not what makes it onto the page. However, I don't recall which word I wanted to use.
But the point remains the same, in the last step you have to superimpose the interior loading onto a fixed-fixed beam element to maintain compatability between elements.
RE: Moment/Shear/Deflection/Rotation Diagrams
I think these 2 methods are exactly the same. I'll have to do an exeriment.
RE: Moment/Shear/Deflection/Rotation Diagrams