Beam Element Properties
Moderatoren: ccad, mz15, auroraIco, Lehrstuhl
Beam Element Properties
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
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
Re: Beam Element Properties
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?
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?
Re: Beam Element Properties
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
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
Re: Beam Element Properties
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
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
Re: Beam Element Properties
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
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
Re: Beam Element Properties
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)
https://www.kickstarter.com/projects/bo ... est-things
This does not seem to be covered in my book(Mechanical Engineering Design 7th, Shigley)
Re: Beam Element Properties
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)
(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
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)
(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
Re: Beam Element Properties
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?
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?
Re: Beam Element Properties
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
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
Re: Beam Element Properties
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.
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.