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Wood Design - Deflection

Wood Design - Deflection

Wood Design - Deflection

(OP)
In calculating deflection of a beam, is the adjusted Elasticity of the member, E', used?

RE: Wood Design - Deflection

No, not normally, just E.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: Wood Design - Deflection

Make sure you have accounted for shear deformations.

RE: Wood Design - Deflection

I think E' is supposed to be used. I'll Check when I get into the office, but I know that moisture content affects the stiffness and if you use E there is no way to account for that.

Asixth-
Do you typically account for shear deformations in wood beams/joists? I don't unless it's a very short, deep beam.

RE: Wood Design - Deflection

E' should be used.   

RE: Wood Design - Deflection

I am putting together a spreadsheet that enables shear deformations to be calculated along with flexural deformations. The timber code I use which is AS1720 (Australian) gives a characteristic modulus of Elasticity and says 'The average modulus of elasticity includes and allowance of about 5% for shear deformation.' I generally take this to mean that the designer is to multiply the short-term deflection by 1.05 and by doing so shear deformations have been accounted for.

Even if the shear deformations only account for 2% of the overall deflection, I still think it should be considered during the calculations.

There is also the statistical aspect which comes with estimating the E-modulus of a particular wood sample.

RE: Wood Design - Deflection

asixth
I take it to mean that shear deflection doesn't have to be calculated separately, as the given E is already factored by 1.05 to allow for it.

RE: Wood Design - Deflection

I agree with apsix, that the wording you used means that the E value has been adjusted to account for the shear deformations so that you don't need to do anything to account for it.

RE: Wood Design - Deflection

What does Clause 2.1.3 say?  Does that give a method to calc Ebar or is Ebar what is given in the table?  It looks like E is given in the table and 2.1.3 gives a formula for Ebar to account for shear deformations.  

This is just my opinion, but the shear deformations for the typical span/depth ratios associated with wood construction would easily be less than the statistical differences between the actual E and the prescribed E.  Even for a shear deflection that is 4% of the flexural deflection, you're talking about L/360 for LL compared to L/346.  That's not a big deal, IMO, and if E is 4% higher than listed than the whole thing goes away.

RE: Wood Design - Deflection

Clause 2.1.3 just says to use the section property, average E and various modification factors when determining member stiffness. It doesn't mention shear deformation.

I think Ebar is a typo, it should be just E; both are defined as 'average modulus of elasticity'.

Paraphrasing the note from Table 2.4; 'E includes an allowance for shear deformation' and from Table H2.1; 'E contains the effects of shear'.

They basically say the same thing; shear deformation is already accounted for.

RE: Wood Design - Deflection

I agree.

RE: Wood Design - Deflection

How is E' or Ebar defined in your code?  I cannot see how it could take into account shearing deformation except in a very approximate way.

Deflection of a wood beam is affected by service conditions (wet or dry), duration of load (creep effects) and treatment factor (preservative treated incised lumber).  Shear deformation is not normally considered.

BA

RE: Wood Design - Deflection

Only E is defined, E' & Ebar are not used, except that E bar just appears in the notes of Table 2.4, as discussed above. As you say, shear deformation is allowed for in an approximate way.
There are also the factors to account for moisture content and load duration.

RE: Wood Design - Deflection

Clause 2.1.3 Member Stiffness: In determining member stiffness the design rigidity is the product of the relevant section property, the average modulus of elasticity and various modification factors denoted by 'j' that account for service conditions as given in Clause 2.4.1.2.

Clause 2.4.1.2 goes on to give modification factors that increase the deflection of the wood from creep for sustained loads. There are no modifications to the E-modulus that account for items which BAretired mentioned. The modification factors other than a load duration-creep factor are only accounted for in strength and joint design. I assume this differs to the NDS approach to E-modulus which the original post was questioning (E' opposed to E).

I will accept that shear deformations of wood is accounted for in the average E-modulus.

I was back-checking deflection calculations today of a widely used timber design program in Australia and was finding it to underestimate the deflection of common studs. Along with ignoring internal pressures and local pressure co-efficients IMO.

RE: Wood Design - Deflection

Shearing deformation does not follow the same curve as bending deformation.  For a simple span beam with uniform load, shear is maximum at the supports and zero at the center whereas bending is zero at the supports and maximum at the center.

To account for shearing deformation by merely changing the E value would imply that shearing deformation is some constant fraction of bending deformation, which is not the case.  

If the modified E value is intended to take into account shearing deformation, it must do so in a very approximate way.  I do not know how the E' or Ebar value is defined, but I doubt that it is intended to take into account shearing deformation.  

BA

RE: Wood Design - Deflection

Quote:

If the modified E value is intended to take into account shearing deformation, it must do so in a very approximate way.

BAretired...I think you are correct about shear deformation being intrinsically different - and I would agree with your quoted statement above that with wood...it's all very approximate.  Keep in mind the wood design values are generally developed through visual grading rules....a very approximate thing indeed.

 

RE: Wood Design - Deflection

asixth
The duration factor in Cl.2.4.1.2 is determined using both load duration and moisture content.

All my comments are valid only for the Australian code AS1720 and do not directly address the original question.

RE: Wood Design - Deflection


Apologies for further hijacking the thread, but in response to the comments about the statistical variance of E - AS1720 has a recommendation stashed away in the notes of appendix B (note 3) that recommends adopting a lower 5th percentile value which corresponds to 0.5 E (hardwoods) for deflection sensitive elements. First time i have come across it...

RE: Wood Design - Deflection

Where would it be applicable other than lintel or header design? 50% reduction in E results in a large increase in deflection.

RE: Wood Design - Deflection

OzEng80,

I think you are misinterpreting the value of E in the reference you cited.  I suspect that E0.05 in the Australian Code corresponds to E05 in the Canadian Code.  It is the Modulus of Elasticity for design of compression members and is substantially less than E used for deflection calculations of flexural members.

BA

RE: Wood Design - Deflection

BA

Unfortunately the E value cited relates to flexural members – I have attached the rest of the Appendix for your consideration. Note that the appendix is only an informative 'guideline' which (it is my understanding) the industry ignores – first time I have come across it.
Given that this has become pretty much an AS1720 thread and the magnitude of the reduction I thought it would be worthwhile throwing some more wood on the fire...
 

RE: Wood Design - Deflection

This seems to be a good reference on wood.

"Wood Handbook - Wood as an Engineering Material"

http://www.fpl.fs.fed.us/products/publications/several_pubs.php?grouping_id=100&header_id=p

Chapter 4 on mechanical properties also suggests that E measured from bending tests includes the effect of shear deformation and can/should be adjusted to correct for this.  I think the point is that say for instance if you measured using a simply supported beam with a point load in the center you would have something like

w=PL^3/48EI -> E=PL^3/48wI

The deflection w at load P inherently includes some deflection due to shear and will make E too small.

RE: Wood Design - Deflection

OzEng80,

E0.05 in your code is the lower fifth percentile estimate of Modulus of Elasticity.  It varies from 0.5E to 0.85E, depending on the grade of lumber used.

It should be used in calculating an upper bound on deflection where clearances must be maintained, such as doors or windows jamming, but it is not used for routine deflection calculations.

BA

RE: Wood Design - Deflection

Is this common for wood design to look at upper bound solutions for deflection sensitive designs?

I am thinking of the application of this principle to other building materials such as concrete. I am unsure on ACI209 or Eurocode creep models but AS3600 (Australian Concrete Code) has a clause stating that the actual creep models may vary by +/-20%. Would a similar principle of calculating an upper bound solution be applicable to deflection sensitive concrete designs such as a slab supporting brittle finishes or a floor which is housing sensitive equipment?

Of course this application to concrete design is only a thought. I am in the process of writing a complete timber design spreadsheet to AS1720 and will be included the above modifications based on service sensitivity.

 

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