Beam Element Properties

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All questions to: meshing, materials, boundary conditions and element properties

Moderatoren: ccad, mz15, auroraIco, Lehrstuhl

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Dexter22
Newbie
Beiträge: 8
Registriert: Fr 10. Okt 2014, 20:41

Beam Element Properties

Beitrag von Dexter22 »

Hi,

For the beam elements I can use Aurora's GUI for calculating the cross-section properties.

However I am a little confused.

What is Wt? - the second modulus for torsion.

all my calculations on beams before have used J - the second moment of area for torsion and G - the shear modulus (material not a section property)

Regards
-Dexter
Hyrum
Newbie
Beiträge: 4
Registriert: Do 23. Okt 2014, 05:11

Re: Beam Element Properties

Beitrag von Hyrum »

I am also stumped by this. I can't even reproduce the values that it creates automatically for the square profiles.

for a 5x5 square profile it generated these values


Second moment of area (torsion)
It: 8.812500E+001

Second modulus (torsion)
Wt: 2.600000E+001


Could someone please show how these are derived?
mk2
Import
Beiträge: 10
Registriert: Mi 22. Okt 2014, 19:46

Re: Beam Element Properties

Beitrag von mk2 »

Hello,

Wt = polar section modulus of torsion

Wt = Wp = eta * b² * h

Wt = 0.208 * 5² * 5 = 26mm³

Wt = It / R -> Wt * R = It

R = maximum Distance from the outer fiber to the neutral axis

It = Moment of inertia of torsion

It = 0,141 * 5^4 = 88.125mm^4 (formula for square profile) -> It = 0,141 * a^4

I hope i could help you :)


Kind regards,

mk2
Dexter22
Newbie
Beiträge: 8
Registriert: Fr 10. Okt 2014, 20:41

Re: Beam Element Properties

Beitrag von Dexter22 »

Ah ok, And how do I get values for a Hollow box section?

There's a formula here but it doesn't give the same answers as Aurora.

Thin walled closed tube of uniform thickness

http://en.wikipedia.org/wiki/Torsion_co ... ite_note-8
mk2
Import
Beiträge: 10
Registriert: Mi 22. Okt 2014, 19:46

Re: Beam Element Properties

Beitrag von mk2 »

Hello,

your formula from wikipedia is not so accurate...

Thin walled closed tube:

Wt = (pi / 2) * Dm² * t

Dm = middle size of bore
t = wall thickness

It = (pi / 4) * Dm³ * t
Hyrum
Newbie
Beiträge: 4
Registriert: Do 23. Okt 2014, 05:11

Re: Beam Element Properties

Beitrag von Hyrum »

Can you please point me to some references on how to calculate these for complex shapes? I am trying to model some structures made from NanoBeam.

https://www.kickstarter.com/projects/bo ... est-things

This does not seem to be covered in my book(Mechanical Engineering Design 7th, Shigley)
mk2
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Beiträge: 10
Registriert: Mi 22. Okt 2014, 19:46

Re: Beam Element Properties

Beitrag von mk2 »

Hello,

interesting Project! But are you sure you need the It = Moment of inertia of torsion?

It's difficult to solve the It for complex shapes. First you have to know the function of Torsion. (1)
Torsionsfunktion.PNG
(2.83 KiB) 2431-mal heruntergeladen
(1)

If you know this function you can solve It numerical. (2)

I found no literature, which can help you - sorry. Maybe in some Matlab/Scilab/Wolfram tools?

In Z88Aurora the It is a approximation of a function. You can only solve those functions analytical, if the shapes are easy like a bore or a square.

kind regards
mk2
mk2
Import
Beiträge: 10
Registriert: Mi 22. Okt 2014, 19:46

Re: Beam Element Properties

Beitrag von mk2 »

Torsionsträgheitsmoment.PNG
(2.13 KiB) 2429-mal heruntergeladen
(2)
Hyrum
Newbie
Beiträge: 4
Registriert: Do 23. Okt 2014, 05:11

Re: Beam Element Properties

Beitrag von Hyrum »

I am not sure I need it but Z88 requires something for it to solve and I may need it if the structures get complex. I found some info in section 2.6 of

Handbook of Mechanical Design
By Maitra, L. V. Prasad

It says that for a square τ=0 at the corners and τmax is at the sides. Since my profile is essentially a 1.85mm square with thin webs extending from the corners(which don't help much), I think I can proximate both these values for that of a 1.85 square.

http://www.thingiverse.com/thing:509373
a=1.85
Wt = 0.208 *a^3 = 1.31mm^3
It = 0.141 * a^4 = 1.65mm^4

Any thoughts?
mk2
Import
Beiträge: 10
Registriert: Mi 22. Okt 2014, 19:46

Re: Beam Element Properties

Beitrag von mk2 »

http://wandinger.userweb.mwn.de/Festigkeit/v6_2.pdf

This script is german, but on page 31 i found some profiles with correction factors from "A. Föppl".

Maybe you will become a better solution. You can solve with FEM and after you can verify your result with a phys. torsion test? After the test you can approximate a new It...

mk2
Hyrum
Newbie
Beiträge: 4
Registriert: Do 23. Okt 2014, 05:11

Re: Beam Element Properties

Beitrag von Hyrum »

I made my best attempt to measure the torsional deflection of a NanoBeam.

T=52.28N-mm
l=200mm
θ=5.0deg
G=25.8 GPa http://asm.matweb.com/search/SpecificMa ... m=MA6063T5

It=T*l/(θ*G)=5.0mm^4

This is significantly higher than my previous estimation so I'm glad did this measurement.
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