Beam / structure Calculations

[RustyH]

Good Afternoon,

Over the years since qualifying as a mechanical engineer, Ive wanted to learn more about structural mechanics. We learnt a fair bit about about beam analysis when I done my degree 15 years ago, and the fact I went down a thermal engineering route means Ive had to dig out all the old structural mechanics books.

I've decided to set myself a challenge of designing a mezzanine floor, nothing more than a learning exercise and not to actually be assembled and used!

Ignoring all the requirements for seismic assessment, floor loading assessment etc. I just wanted to check if I was going about things the right way. Do you start from the tops, working down. So knowing your dead weights (structure weight) and live loads, then first carry out SFD and BMD on the joists, then on the main beams, then the pillars?

Thanks in advance for any help

 

[RustyH]

Thanks CEL

On the safety factor, is the consensus to apply this to the calculated value or the allowable value?

 

[CELinOttawa]

Now you're back to working stress, so not my forte, but as best as I understand that type of design it is the application of the safety factor that gives you the allowable stress.

 

[RustyH]

Been trying to work on deflection today, based on macaulay method

Got to admit, absolutely pulling my hair out!!

 

[CELinOttawa]

Commendable... But practicing engineers typically used canned solutions for reflection. That or software.

 

[RustyH]

Thanks CEL

Is it recommended I keep trying to learn this (struggling with the integral constants), or don't sweat it and learn it to a software?

 

[PEinc]

Look in the AISC, 14th Edition (or earlier) of the Steel Construction Manual for Table 3-23. It has diagrams for various beams, including yours, with equations for deflections. You can use the example for a distributed load and the example for a concentrated load. Add the two deflections together at any point along the beam.

http://www.PeirceEngineering.com

 

[RustyH]

Will take a wee look at that, thank you

 

[CELinOttawa]

PEinc is referring to one source of the canned solutions I was talking about...

Just get a series of tables for examples from which you can use superposition to determine the total reflection from the sum of the little partial causes of deflection.

 

[CELinOttawa]

Damn autocorrect.. Deflection!

 

[RustyH]

Thanks CEL, are you refering to the deflection formula tables in roark, so you take the UDL only formula and calculate, then the point load formula and calculate, then the reaction formula and calculate, and sum together

 

[CELinOttawa]

Yes. Only the reaction formula should be the shear deflection formula... Otherwise I'm confused and missing something.

 

[PEinc]

The AISC diagrams and formulas are much simpler and easier to use than the Roark formulas.

http://www.PeirceEngineering.com

 

[RustyH]

Managed to get the AISC tables and used the beam that is similar to mine. It did seem alot easier to follow for me personally.

So, Im not getting somewhere on the deflection side of things which is great.

I'm struggling understanding one thing now. The Eurocode call for a modification to be made to the Modulus of Elasticity, for which the modifications take in to account the load durations and moisture influences.

There is a formula for the "Serviceability Limit State Design" = E / (1 + Kdef)
and there is a formula for the "Ultimate Limit State Design" = E / (1 + w2*Kdef)
where kdef = factor related to calculation of creep deformation, and w2 = factor for quasi-permanent value for the action causing largest stress (for permanent action = 1)

What I dont understand, is at what stage are these applied

My current thinking is that you apply the "Serviceability Limit State Design" to the deflection calculations, and the "Ultimate Limit State Design" to the maximum allow limit of deflection. But I also think that my thinking is wrong!!
Especially as I found an example where they applied the "Serviceability Limit State Design" formula to the Dead Load deflection calculation and the "Ultimate Limit State Design" formula to the Live load deflection calculations - which I cant make sense of

 

[CELinOttawa]

I don't use Eurocodes, so take this with a grain of salt and hope for a EC user to chime in, BUT:

Deflections are an SLS condition. Strength and Stability are ULS. You should apply ULS formulae to strength calcs, and the SLS formulae to deflection.

 

[RustyH]

I think Im following you, so the "Serviceability Limit State Design" is SLS and is for deflections etc, and the "Ultimate Limit State Design" is ULS for stresses etc.
I guess the ULS looks at if the design will have a catastrophic failure, where as SLS allows certain characteristics but they have to be with in a defined limit.

Not sure why the example excel sheet I have takes the "Serviceability Limit State Design" formula for the Dead Load deflection calculation and the "Ultimate Limit State Design" formula to the Live load deflection calculations.

 

[RustyH]

One other question on deflection, sorry about this, the deflection thing really did have me stumped, but getting there.

The regulation suggest a deflection (Wnet.fin) of L/250 to L/350
Is this open to the designer to choose what value to limit to between this range?

 

[jayrod12]

Yes, there are code recommended minimums however deflection criteria can be modified by the designer to suite a specific case.

 

[RustyH]

I guess choosing one really comes down to experience then, and if just out learning then I'd be better selection the minimal value of that range

 

[jayrod12]

At this point since you're just learning you don't necessarily care what you are designing to in terms of criteria but rather care to learn the process of determining the deflection. The criteria varies depending on materials being supported and the type of structural material used.

 

[RustyH]

Well, I've given a damn good go and learnt so much over the last week or so, thanks for everyone help so far, hugely grateful.

The attached document is my work / report so far. Obviously not expecting people to have time to read this, but its there is anyone is interested, and I would be hugely grateful for any feedback from people who do read it