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
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
Mike McCann, PE, SE (WA)
RE: Beam / structure Calculations
A confused student is a good student.
RE: Beam / structure Calculations
A confused student is a good student.
RE: Beam / structure Calculations
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
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
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
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
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
RE: Beam / structure Calculations
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
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
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
I've based this on formulas from Roark's
Am I in the right ball park here??
RE: Beam / structure Calculations
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
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
RE: Beam / structure Calculations
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
I will do some more digging, but glad Im on the right path
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
RE: Beam / structure Calculations
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
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
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
RE: Beam / structure Calculations
I think CELinOttawa is referring to the statistical approach, like 95% confidence level.
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
If so, if the design value calculated merely by the characteristic value * Safety Factor
RE: Beam / structure Calculations
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
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
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
RE: Beam / structure Calculations
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
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
On the safety factor, is the consensus to apply this to the calculated value or the allowable value?
RE: Beam / structure Calculations
RE: Beam / structure Calculations
Got to admit, absolutely pulling my hair out!!
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
www.PeirceEngineering.com
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
RE: Beam / structure Calculations
RE: Beam / structure Calculations
RE: Beam / structure Calculations
www.PeirceEngineering.com
RE: Beam / structure Calculations
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
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
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
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
RE: Beam / structure Calculations
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
RE: Beam / structure Calculations
RE: Beam / structure Calculations
What part are you referring too the report was constructed in Word
RE: Beam / structure Calculations
RE: Beam / structure Calculations
How do you think it all looks?
RE: Beam / structure Calculations
Im not looking at steel I beams, is the same downgrade of E occur during calculations
RE: Beam / structure Calculations
RE: Beam / structure Calculations
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
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
RE: Beam / structure Calculations