truss' moment of inertia
bjarthur
inertia of cross sections of various shapes. but there's nada for
trusses. i've got a canti-levered beam which is too heavy for the
motor i'm using to rotate it. i'm trying to avoid buying a new motor
by replacing the hollow cylindrical beam with a triangular warren
truss. but i need equations to tell me how to dimension it to retain
the same stiffness (young's modulus of elasticity). everything i've
found on the net about trusses is all about how to analyse a custom
truss for compression, tension, and displacement, but there are no
tables which parameterize the standard truss designs and give you the
formulas for things like moment of inertia. anyone know where such
things can be found?
Jim Y
"bjarthur" <bj...@cornell.edu> wrote in message
news:1143508539.4...@g10g2000cwb.googlegroups.com...
The James F. Lincoln Arc Welding Foundation, P.O. Box 3035, Cleveland, Ohio; Section 2.2 Properties
of Sections. This same text has the method of designing and calculating the properties of an
expanded beam which may suffice for your application.
One thing that bothers me is the original support is a cylinder. A cylinder offers the stiffness,
and all properties, 360 degrees about the longitudinal axis which may be a requirement. Have you
considered another cylinder - larger OD, thicker wall - to get better properties? Commercial steel
pipe can be obtained with 42 inch OD, 1.50 inch wall , 39181 in^4 Moment of Inertia, 1865.7 in^3
Section Modulus and weigh 649 lb/ft. You may not need something that big, but look up another size
of pipe to do the job.
Hope that helps,
Jim Y
Chuck
"bjarthur" <bj...@cornell.edu> wrote in message
news:1143508539.4...@g10g2000cwb.googlegroups.com...
Why don't you just analyze/design it as a regular truss? you can find the
procedure in a text book. If the truss was a flat truss you could estimate
the inertia of the truss and stiffness. You could do this by using the
center of the truss as the CG and calculate the inertia of the top and
bottom chords then multiply the chord areas times the distance to the CG
squared then add these together. The web members act as shear components
which consist of tension and compression forces (strut and tie method). For
a triangular truss you can't do this because the truss then comes a beam
with a variable moment of inertia and is more complicated and not worth the
effort.
CID...
bjarthur
but it's not. it's need's to be triangular or square so that it's
rigid in all three dimensions.
>For a triangular truss you can't do this because the truss then comes a beam
>with a variable moment of inertia and is more complicated and not worth the
>effort.
as you say, it's "complicated", which is why i was hoping to just find
a table of formulas. do they really not exist? i've made a fairly
extensive search of the web and can't find anything. all i want is a
formula for the young's modulus of elasticity for a triangular warren
truss parameterized with variables for the relevant spacings and
diameters of the members. it seems to me a table of such equations for
the various truss designs would be very handy for structural engineers
and i'm finding it difficult to understand why i can't find it
anywhere. such tables exist for beams of various cross sections, why
not trusses of various designs?
Jeff Finlayson
Don't believe trusses can always be treated as beams. They may
not have diagonal (shear) members to make it bend like a beam.
Assuming your truss behaves like a beam, you can treat it
like a sheet-stiffener design. The axial members react bending
moments and axial loads and the diagonal members react shear
loads. This should at least get you an initial sizing.
More complicated analysis or modeling will help in final sizing.
Charly Coughran
news:1143548860.1...@i40g2000cwc.googlegroups.com:
Structural beams are made to a standard, or actually one of several
standards, and thus there are a limited number sizes. There are many,
many truss designs, that can be made out of a wide variety of
different sized elements, with different truss angles and spacing. An
individual truss can be loaded in a large variety of different ways.
The number of variables is just too large for a table to be a
solution, so to speak.
Note that Young's modulus of elasticity is a material property, not a
shape property. This throws another set of variables into the list.
Space trusses are evaluated with the same tools as 2d trusses. There
are a number of relatively simple procedures to analyze them, but the
number of members and joints can quickly cause a big bookkeeping job.
In practice, most engineers rely on software of one sort or another
beyond very simple cases.
--
-------
Charly Coughran
ccou...@DELETE-TO-RESPOND-UCSD.EDU
Bob Morrison
> > as you say, it's "complicated", which is why i was hoping to just
> > find a table of formulas. do they really not exist? i've made a
> > fairly extensive search of the web and can't find anything. all i
> > want is a formula for the young's modulus of elasticity for a
> > triangular warren truss parameterized with variables for the
> > relevant spacings and diameters of the members. it seems to me a
> > table of such equations for the various truss designs would be very
> > handy for structural engineers and i'm finding it difficult to
> > understand why i can't find it anywhere. such tables exist for
> > beams of various cross sections, why not trusses of various designs?
>
It sort of depends on why you need the information. For a quick
deflection check, Chuck's method of treating the truss as a deep beam with
top and bottom flanges only (the top and bottom chords) should be
conservative. Formula for Moment of Inertia (I) = A*(d^2), where A is the
area of the chord and d is the distance between the centroids of the top
and bottom chord. Of course this assumes that the top and chords are the
same size.
Anything else will require an FEM model with member sizes in order to
compute more exact deflections and member forces.
--
Bob Morrison, PE, SE
R L Morrison Engineering Co
Structural & Civil Engineering
Poulsbo WA
bob at rlmorrisonengr dot com
Spaceman
"bjarthur" <bj...@cornell.edu> wrote in message
news:1143508539.4...@g10g2000cwb.googlegroups.com...
> inertia of cross sections of various shapes. but there's nada for
> trusses. i've got a canti-levered beam which is too heavy for the
How about gearing the motor?
bjarthur
privately) and chuck's idea of computing the inertia of the cross
section of the longitudinal beams and did some strength-to-weight
calculation's comparing trusses to thin-walled tubing (which i'm
currently using and which jim y suggested), and surprisingly, at least
initially to me, the two are roughly equivalent. (keep in mind i'm a
neurobiologist trained as a computer scientist.) so for example,
unless i'm doing something wrong, a 0.5" cylinder with 0.01" walls is
about as strong and weighs about as much as a truss with three 0.08"
diameter longitudinal members forming a triangle circumscribed by a
0.5" circle. and this neglects the diagonal supporting members, so the
truss actually has a *worse* strength-to-weight ratio for similar outer
dimensions. same is true when everything is scaled up 100x. i guess
looking at the equations this all makes sense b/c the dominant term is
the outer dimension. but now i'm confused b/c i had always thought
that trusses had superior strength-to-weight ratios compared to beams.
so am i doing something wrong? the only advantage i can see to trusses
is windage, which in some apps, mine being one of them, is certainly a
consideration. just seems to me i'm missing something here. thanks
again for the help.
Bob Morrison
> so for example,
> unless i'm doing something wrong, a 0.5" cylinder with 0.01" walls is
> about as strong and weighs about as much as a truss with three 0.08"
> diameter longitudinal members forming a triangle circumscribed by a
> 0.5" circle
>
I'm actually not surprised by this. The tube section has about 50% more
material located away from the neutral axis than the two much smaller
tubes in the truss chords. A simple drawing (cadd helps) will confirm
this, although you could calculate the difference.
roleic
When comparing the strength-to-mass ratio (aka specific strength) of
different structures you have to consider all failure modes limiting their
strengths not just global bending. E.g. Don't forget buckling (global
instability) under compressive, shear and bending loads.
Beams made of very thin walled cross sections are limited by cylinder
buckling under bending or shear load. Trusses can of course also be limited
by instabilities. Their instability type is beam buckling under compressive
load of the truss members where the buckling length of the members is the
free truss length btw. the truss nodes.
Buckling strength is a bit more complicated to calculate than bending
strength. Where as the formulas for compressive beam buckling are still
rather simple and easy to find in lit., for cylinder buckling under
compression or shear or bending load you need special charts from reference
literature for standard geometries like cylinders, cones, cyl. shell panels
(e.g. Bruhn,1973, Analysis and Design of Flight Vehicle Structures or
ESDU-sheets) or a finite element model for non-standard geometries.
So don't jump to conclusions before you have considered all relevant
physics:-)
Tom Sanderson
> but now i'm confused b/c i had always thought
> that trusses had superior strength-to-weight ratios compared to beams.
This isn't generally true. A truss is statically determinate which, under
some loading conditions, means you can use the material more efficiently
than a statically indetermiante structure (which most beam structures are).
However, there are many types of loading where a beam or shell is more
efficient.
> the only advantage i can see to trusses is windage
This is can be an advantage, but there's also ease of pass-through (same
roots as low windage, but different design considerations), ease of
manufacture, ease of transport (trusses are generally easy to break up), and
ease of analysis (static determinacy). Ease of manufacture is a huge reason
for seeing trusses in large structures...a 10' deep solid beam would be a
nightmare to build, a 10' deep truss is trivial.
Tom.