The number you calculated is the yield strain. For all materials it's Fy/E, by definition. Beyond that point, steel becomes plastic and E goes to zero in our lovely all-too-simple models (or concrete crushes, masonry breaks, etc). If you go back to first principals, E is frequently determined using the a strain 2% offset. Basically you load a material, measure stress and strain and numerous points and draw a pretty picture. I imagine you remember most of this.
For your model, I wonder if the old working stress masonry model might be better. You have heterogeneous materials. One takes compression (base plate to wood interface) and the other takes tension (steel). There are numerous charts that predict stress (see Amrhien) based on this model and the modular ratio (E1/E2). Basically use the wood E for the compression element and steel E for the tension element.
If this is too rambling (or I missed your point), send me an email back and I will try and elaborate a little more. Most small problems are more interesting than the big ones.
Jake Watson, SE
Salt Lake City, UT
On Mon, Sep 14, 2009 at 9:53 AM, Thor Tandy <vicpeng@telus.net> wrote:
Hi Jeff.
I was doing an exercise over the weekend on base plates that are connected
to timber elements. (Yeah, I'm still looking for my life) E.g. guard rail
side-mounted onto a deck edge beam. This is a typical base-plate problem
but the material is timber instead of concrete.
I used first principals to determine a pressure distribution across the
plate (in this case assumed very stiff but that might not be a problem on
timber), looked at using concrete section concepts and then at strain
compatibility methods. For concrete, there are factors that are not
applicable to timber and the yield behaviour of timber in bearing is
different from concrete. That said, by (wise??) juggling of the factors etc
I arrived at section properties in all 3 methods that produced anchor
requirements and restraining loads within 10% of each other. I'm not
claiming the results are correct. Timber in bearing squashes the fibre
(X-grain) and as deformation occurs the sides of the plate are also
supported by shear across the fibers. So the pressure bulb has to be
different from concrete. But it's probably simpler than concrete being
either triangular or possibly reverse parabola (I'm just guessing). The
deformation is very MC, and species, dependent but I figure there had to be
an average equivalent strain modulus that I could use to do the
calculations. From Borg Madsen's book on timber testing and behaviour I
extracted a strain of about .02 at a stress of about 2.5MPa.
So I was seeking an opinion on what strain to use to determine the stress
distribution across the plate-timber section.
Thanks
Thor
-----Original Message-----
From: Jeff Linville [mailto:linville@aitc-glulam.org]
Sent: Monday, September 14, 2009 8:06 AM
To: seaint@seaint.org
Subject: RE: Cross-grain Compressive Strain in Timber
I might be able to help you with a number, but I am not clear on what
the number means. How are your example numbers determined?
I'm also not clear on the application.
What species of wood are you talking about?
Jeffrey D. Linville
Director, Technical Services
American Institute of Timber Construction
(303)792-9559
linville@aitc-glulam.org
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-----Original Message-----
From: Thor Tandy [mailto:vicpeng@telus.net]
Sent: Friday, September 11, 2009 6:36 PM
To: SEAInt
Subject: Cross-grain Compressive Strain in Timber
I'm doing some casual analysis of metal support plates bolted to the
side of, say, a built-up 2x10 beam. If I try to use, eg, concrete
section analogy, I need to know a strain modulus for the timber (yeah, I
know timber doesn't behave like concrete). What cross grain modulus
might I use?
Eg: conc = .0035, masonry = .003, steel = .002 I could see a virtual SE
= .007? I know that ASTM tests to develop bearing stresses and lengths
invoke the concept of strain = del L/L and I also am aware that the
value must be very variable espec with MC.
Again, if I use strain compatibility analysis, I have to know what value
to use for the strain modulus .
Thanks
Thor A. Tandy P.Eng, C.Eng, Struct.Eng, MIStructE Victoria, BC
Tel: (250) 382-9115
hst_ngc4414_9925Please consider the environment before printing out this
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