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Beam / structure Calculations

Beam / structure Calculations

Beam / structure Calculations

(OP)
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

RE: Beam / structure Calculations

Yes.

Mike McCann, PE, SE (WA)


RE: Beam / structure Calculations

What are the acronyms SFD and BMD?

A confused student is a good student.

RE: Beam / structure Calculations

Steel or wood?

A confused student is a good student.

RE: Beam / structure Calculations

For TJI floor joists I like to use an application called FORTE by Weyerhaeuser:

http://www.woodbywy.com/software/forte-software/

The learning curve is essentially zero and its nice for quickly sizing floor joists for about any application.

A confused student is a good student.

RE: Beam / structure Calculations

(OP)
Hi,

Sorry, SFD = shear force diagram, BMD = bending moment diagram

I'm was thinking of calculating a steel main structure with timber joists, but I guess it doesn't matter as its just a learning exercise at the moment.

A program would definitely be useful, but I want to try and learn and understand the theory / fundamentals first

One questions, I notice there a certain regs that give KN/m2 values for minimum floor loads, but how do you apply this as a UDL when UDL's are KN/m

RE: Beam / structure Calculations

RustyH,
Your process is logical.
Multiply the specified loads/area by the spacing of your structural load carrying members to get uniform loads per unit length for your design. Google "tributary width" & "tributary area".

RE: Beam / structure Calculations

(OP)
Thanks mate,

So say you had 400mm joist widths, would you base calculations for a joist on the 400mm area that could act up on it

RE: Beam / structure Calculations

(OP)
Tributary width / area - just looked it up, I got ya, so I was on the right path with what I just said.

So as toy said, just just multiply out the KN/m2 value by the Tributary area acting on the beam.

Definitely something new I've learnt here. Thank you

RE: Beam / structure Calculations

Using inches feet & pounds (sorry), if your joists are spaced at 16" on center, and the specified load is 40 pounds per square foot live load and 20 pounds per square foot dead load, then your joists must support (40+20) x 16/12 = 80 pounds per lineal foot.

RE: Beam / structure Calculations

(OP)
Got you, that makes sense

I am right in thinking dead loads are loads permanently in place, such as weight of beams, weight of walls or structures built on top of the beams, etc

And live loads are every day usage loads, such as people, storage, etc

RE: Beam / structure Calculations

You are correct in that assessment as well. Think of it as your dead loads being the stuff you can accurately measure and be reasonably confident in the magnitude. The live loads are the uncertain loads, might be there or might not, could be in excess of your design load or you could never have your actual live load even come close to your design.

It's more a question of confidence when choosing what is a dead load and what is a live load. But your thinking is the general consensus.

RE: Beam / structure Calculations

(OP)
Thanks for all your help so far everyone.

As already discussed, Im starting with a Joist calculation, and made it with a UDL and single point load, with two supports (one offset from end)

I've had my head in the books and think Ive figured out how to do the BM and SF diagrams and the equations to go with it. Please see the attached for any comments

I am a little stuck now mind,. Where do I take it from here to work out if a specific beam profile and material can with stand this loading with out failure.
Do I work out the aera of moment of inetia and calculate the maximum Tensile and Shear stresses?
Do I need to work out the beam deflection as well, or providing the beam is not in a faulure mode then all is ok and deflection is not needed?

RE: Beam / structure Calculations

(OP)
Right, I've tried to take a step further and do the stress calculations (see below)

I've based this on formulas from Roark's

Am I in the right ball park here??

RE: Beam / structure Calculations

You are in the right ballpark (though I'll caveat that by saying I've only glanced at your calculations) for the old fashioned working stress design.

Modern design for the vast majority of the world is now limit states. For a fundamental understanding of what is going on, you should jiay keep going with working stress as you have done so far.

RE: Beam / structure Calculations

(OP)
Thanks for the input

Can you elaborate on what Limit State disign is?

Also, from the above stress, is it possible to determine if a beam would fail or not, do you just compare the calculated stresses against the ultimate tensile stress of the material

RE: Beam / structure Calculations

You're asking me to lay out two years of Uni... Pretty tough. Limit States and split factor LRFD (not the same thing) have been discussed here at length. Not to be flippant, but a search will give you plenty to read...

RE: Beam / structure Calculations

(OP)
Thanks mate, will do some googling

RE: Beam / structure Calculations

(OP)
by the way, am I right in assuming that the stresses calculated above are enough to determine if a beam will fail or not by comparing with the Ultimate Tensile Strength of the material?

RE: Beam / structure Calculations

That's what CEL was alluding to... Limit states design factors your applied loads up, and your material resistance down, and then you check the calculated stresses versus the reduced resistance.

The old days, you took the applied loading and analyzed for that directly, then compared to an Allowable (or working) stress that was a reduced value from the ultimate stress.

Your analysis appears correct (at a brief glance) however actually determining whether it passes the design codes requires a bit more digging into the codes. For wood in the USA you'll want to be looking at the NDS, in Canada it's CSA O86. Other materials have their own governing codes.

RE: Beam / structure Calculations

(OP)
Thanks Gents,

I will do some more digging, but glad Im on the right path

RE: Beam / structure Calculations

Just for the sake of safety..... No you don't compare the stresses caused by applied loads to the ultimate tensile strength. Instead it's compared to the allowable tensile stress, which is the yield strength * Factor of safety. As I'm sure you have or will read. This is the older method, Allowable stress design or ASD. My terms may not be 100% because I myself don't use this method, but that's the idea behind it.

RE: Beam / structure Calculations

(OP)
Thanks ajc,

I guess what Ive done so far has not been wasted, but will do some reading on the more modern approaches

RE: Beam / structure Calculations

Also, depending on how it is set up, the allowable stress is the Fy DIVIDED by a F.O.S..... IE: 350MPa/4, with four being the "Omega", or Safety Factor (aka Factor of Safety)

RE: Beam / structure Calculations

Just wanted to add my support in this thread, think you've set yourself a really cool goal here rooting for ya buddy. In a (extemely small) nut shell yes, work your way down from the top. First work out what the structure needs to be designed for, get your loads first after doing the conceptual design. A knowledge of structural behaviour will come, eventually!

I recommend grabbing a good designers manual for the relevant codes and working your way through that, you'll learn how calcs are done in practice and all the various checks that are done. It won't cover everything but will get you off to a good start. Best of luck! Pete

RE: Beam / structure Calculations

(OP)
Thanks for the positive words everyone, I'm certainly trying, typical I was taught old school solid mechanics!! Haha. Themis new system is mind boggling!!

Can I ask,
What is meant by Characteristic Load Capacity?
What is meant by the term 'design'. I.E: 'design shear stress' or 'design bending stress'. Is it just referring to the design in question, or does it refer to predetermined design constraints??

RE: Beam / structure Calculations

The "design" in most terminology indicates that something has been factored. "Ultimate" is typically the corollary term.

Characteristic stresses and strengths are normally a material property point or somewhat arbitrary issue. Be warned this does tend to change between traditions and eras (read: countries and code generations), and should be read co textually. The most common characteristic stresses or strengths are found in offset materials (such as those which are brittle or have no distinct yield plateau) and large sampling groups on existing structures, where the 5% value is taken to be characteristic. The same is done with all wood/timber grades as well.

RE: Beam / structure Calculations

(OP)
Apologies......whats the 5% value mean (I did try a google search but not alot came up)

RE: Beam / structure Calculations

Quote (RustyH)

whats the 5% value mean

I think CELinOttawa is referring to the statistical approach, like 95% confidence level.

RE: Beam / structure Calculations

Yup... Effectively in that CONTEXT (damn autocorrect!) The "characteristic" should be seen as indicating the value used in design. It is a practical thing when the material is brittle or highly variable, such as aluminium and timber, respectively...

RE: Beam / structure Calculations

RustyH,
I have a different take as to 'characteristic' and 'design'. I am older than some of these folks, but I was taught that characteristic loads are unfactored. When you factor the loads, they become design loads. You use characteristic loads in serviceability assessment, and design loads for strength.

RE: Beam / structure Calculations

(OP)
So, am I right in thinking that the characteristic value is the value from the material datasheet / properties, and the design value is the end value after applying safety factors, etc

If so, if the design value calculated merely by the characteristic value * Safety Factor

RE: Beam / structure Calculations

(OP)
I found this about "design" strength values (which Im reading over and over to try and understand!)

Design Strength values
The characteristic strengths, Xk, are converted to design values, Xd, by dividing by a partial factor, γM and multiplying by a factor kmod.

Xd = Kmod(Xk / yM)

Values for these factors are included in the tables below.

Note: γM is not simply a partial factor for materials but also takes account of modelling and geometric uncertainties.

kmod = modification factor to strength values, allowing for load duration and moisture content

The eurocode , like BS 5268, allows the design strength determined using equation this be multiplied by a number of other factors as appropriate such as kcrit , kv , kc,90 and the loading sharing factor, ksys,where several equally spaced similar members are able to resist a common load. Typical members which fall into this category may include joists in flat roofs or floors with a maximum span of 6m and wall studs with a maximum height of 4m

The design values for the stiffness are obtained as follows

Ed = Emean / γM
Gd = Gmean / γM



Table for partial factor γM

Design situation Partial factor γM
Fundamental combinations ...
Solid timber 1.3
Glued laminated timber 1.25
Laminated veneer lumber (LVL),plywood, OSB 1.2
Particle board 1.3
Fibreboard hard 1.3
Fibreboard medium 1.3
Fibreboard, MDF 1.3
Fibreboard , soft 1.3
Connections 1.3
Punched metal plate fasteners 1.25
Accidental combinations 1.0
Serviceability limit states 1.0

RE: Beam / structure Calculations

(OP)
Good Evening All,

I have another quick question.

I'm starting to understand alot more the design limits concept of analysis, and found some great examples on gooooooogle.

In addition, I've downloaded a decent beam analysis spreadsheet that is based on this design limit approach. The spreadsheet is specifically for timber as thats what I will be doing an analysis on first and based on EN-1995.

The thing Im really struggling with is as follows

The spreadsheet give you an option to analyse based on a timber beam or a timber joist. If I set it to a timber beam, I have no issue in understanding how it works out the deflection (which is by the standard form in Roark). BUT, if I select it as a joist, the deflection is completely different (its less that half of as a beam). I cant for the life of me work out or understand why that would be (and if it should)

RE: Beam / structure Calculations

(OP)
Scrap that last post, Ive just figured it out.

For a Joist, it was taking the UDL as a per square value and then multiplying it by the joist spacing to get the direct UDL acting on 1 joist.

I'd already accounted for this and was entering the my calculated per unit UDL (which was instead being treated as a per square force)

RE: Beam / structure Calculations

Hmmm.... Of course don't know what software you downloaded, so a wild guess.,,, some of the engineered wood spreadsheets took deflection credit for the joist by assuming some composite action with a wood diaphragm. If that's your case, you should be able to toggle that feature off and get a deflection linearly related to your moment if inertia, and also relatable to your weed beam calc.

RE: Beam / structure Calculations

I'm impressed Rusty... Keep it up!

RE: Beam / structure Calculations

ahhhhhhhh......, seeing your scrap that last post.... Then also scrap my last post!! Good luck!

RE: Beam / structure Calculations

(OP)
I know I said 1 question, but just want to swing back round to Deflection again

I can calculate deflection by using roark's tables. (Which I assume is classed at instantaneous deflection)

But Ive noticed some examples work out the deflections individually (Dead Load Deflection, Live Load Deflection, Dead Load Shear only Deflection, Live Load Shear only Deflection) then sum them up at the end to give a final deflection.

Is there a need / advantage for this?


Also, I notice in the Standards, they mention deflection by creep. With it being timber in the first instance, I would imagine creep is quite important, but I can’t seem to find any reference to working this out properly.

RE: Beam / structure Calculations

Okay, so knowing specific components of the total defection will allow us to address them. A good example is cambering of steel beams, as well as some glulam "cambers", which are created during manufacturing.

As for the calculation, in many materials this is as straightforward as the elastic formulae you find in Roarke's, but not in timber and a few others (eventually you should look into th e plethora of methods in reinforced concrete!). Timber has now a number of factors applied to the elastic defection to increase this to a more realistic estimate.

Keep reading; You're doing great!

RE: Beam / structure Calculations

(OP)
Thanks CEL

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

RE: Beam / structure Calculations

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.

RE: Beam / structure Calculations

(OP)
Been trying to work on deflection today, based on macaulay method

Got to admit, absolutely pulling my hair out!!

RE: Beam / structure Calculations

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

RE: Beam / structure Calculations

(OP)
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?

RE: Beam / structure Calculations

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.

www.PeirceEngineering.com

RE: Beam / structure Calculations

(OP)
Will take a wee look at that, thank you

RE: Beam / structure Calculations

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.

RE: Beam / structure Calculations

Damn autocorrect.. Deflection!

RE: Beam / structure Calculations

(OP)
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

RE: Beam / structure Calculations

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

RE: Beam / structure Calculations

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

www.PeirceEngineering.com

RE: Beam / structure Calculations

(OP)
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

RE: Beam / structure Calculations

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.

RE: Beam / structure Calculations

(OP)
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.

RE: Beam / structure Calculations

(OP)
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?

RE: Beam / structure Calculations

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

RE: Beam / structure Calculations

(OP)
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

RE: Beam / structure Calculations

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.

RE: Beam / structure Calculations

(OP)
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

RE: Beam / structure Calculations

Matlab? What did you do this in? If this is Word or anything of the like, I'd love to have the original file!

RE: Beam / structure Calculations

(OP)
Hi CEL,

What part are you referring too the report was constructed in Word

RE: Beam / structure Calculations

Okay, so you stuck output results / graphics into a word file... Fair enough. Matlab and a few others will produce documents that look like this AND do the calcs. Thought you might have done something similar...

RE: Beam / structure Calculations

(OP)
Oh ok, no done it all in word and pasted the output results. Can ping you across a copy of the word doc if you want.

How do you think it all looks?

RE: Beam / structure Calculations

(OP)
When I was doing the calculations for the timber joists, the Modules of Elasticity was down graded by use of a formula (E = Ematerial / 1 + Kdef) where the Kdef value compensated for things like load duration and moisture content.

Im not looking at steel I beams, is the same downgrade of E occur during calculations

RE: Beam / structure Calculations

No downgrading of the modulus of elasticity for steel... The reduction is to compensate for the loss of stiffness due to moisture, etc... That doesn't happen with steel.

RE: Beam / structure Calculations

Hello Rusty, very nice presentation with the calcs.

My only comment is that it appears you only ran 1 scenario for the live load on the cantilever joist. With live load on the cantilever portion, you're reducing the deflection and bending moment on the interior span...with live load on the interior span you're countering the deflection at the tip of the cantilever. So you should check 3 cases in total a)live load over entire joist b) live load on interior portion only c) live load on cantilever portion only.

RE: Beam / structure Calculations

(OP)
Got you, had a feeling I was going wrong downgrading it

So you jusrt leave it as 200000 MPa

Can you also be a little more lenient on your factor of safety with steel as its a more controlled manufacturing process, whereas timber is left to nature

RE: Beam / structure Calculations

(OP)
Just been reading up a little on Tata Steel technical reference pages, and they mention that typical safety factors of 1.4 for dead loads and 1.6 for imposed loads are typical. That seems quite a low factor of safety if designing large steel structure. Is that really the norm?

RE: Beam / structure Calculations

That is the loading factors only. That is using LRFD which would also apply factors to the material resistance. For steel it is typically 0.9 in bending.

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