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help with bending stiffness

help with bending stiffness

help with bending stiffness

(OP)
hello, im trying to workout the bending stiffness of a steel L shaped bracket.  

E = 206,000 N/mm2

I = 1460.546 cm4

can snyone help with how to multiply these two??

thanks

RE: help with bending stiffness

206000x1460,546x(N/mm^2)x(10mm)^4=
206000x1460,546x10000N*mm^2=3.009x10^12 N*mm^2

the trick is to put the discordant units at one side as a function of those at the other side

RE: help with bending stiffness

(OP)
thankyou, i actually might have calculated the moment of inertia wrong, i wonder if you can go though it?  L shaped steel bracket.  100mm wide x 100mm long x 8mm thick.  thanks

RE: help with bending stiffness

i get 148cm^4 about a flange axis (parallel with one of the angle flanges), 236cm^4 about the strong axis and 59cm^4 about the weak axis ... i assumed it was a square (90deg) angle

RE: help with bending stiffness

(OP)
thanks very much, so can you also show me how to multiply 148 cm4 x 206,000 N/mm2 to get the bending stiffness in kN/m2 ??   

RE: help with bending stiffness

bending stiffness = EI = N*mm^2, like ish showed above, no ?    

RE: help with bending stiffness

If you find repeteadly this problem you may need either take the things slowly or using systematically Mathcad. Mathcad eats whatever units you throw to it, and produces the answer in the units you want. There may be out there even old free Mathcads (2.4?) I am not sure about.

RE: help with bending stiffness

(OP)
ok so by ish's reckoning above do i now have 146000mm4 x 206000 N/mm2 = 3.0076x10^10 N/mm2  ???

this then gives 3.0076x10^13 kN/m2...i feel i must have something wrong as this is a rather large figure?!?

RE: help with bending stiffness

(OP)
thanks ishvaaag i shall search for this mathcad

RE: help with bending stiffness

Guys,

Is Mathcad really necessary for multiplication?  

FYI, 1kN = 1000N, and 1m = 1000mm = 100cm

There's all the info you need wo proceed with this conversion.

tg

RE: help with bending stiffness

rudigger,

   You are making me nervous.  Moment of inertia and unit conversion are very basic engineering.  You ought to be good at this.  You should have some sort of textbook lying around.

   Unit conversions are simple if you do unit balances.

   148cm4 x (0.01m/cm)4 x 206,000 N/mm2 x (1000 mm/m)2 = 305x103N.m2

               JHG

RE: help with bending stiffness

Do a web search on "units conversion table", it is cheaper than MathCad, unless you need to draw the exact shape of MATH.

RE: help with bending stiffness

(OP)
lol, i am a very basic engineer!! thanks for all your help

RE: help with bending stiffness

So...  You're a BE?

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

RE: help with bending stiffness

If you are talking about a shelf angle with the horizontal leg loaded, then I = bd3/12.

That is, I = 100*83/12 = 4,267 mm4.  In the SI system, do not use cm.  Use mm or m.

EI = 206,000 * 4,267 = 879e6 N mm2

BA

RE: help with bending stiffness

(OP)
hi another query if anyone doesnt mind...

i was indeed talking about a shelf angle with the horizontal leg loaded, so as above

I = bd³/12  =  100 x 8³/12 = 4,267mm­4

how do i then calculate the maximum bending moment capacity of the bracket in kN.m??  thanks

 

RE: help with bending stiffness

sorry ru, but do you know how to calculate a bending stress ?  if not, as suggested by your last post, you Need to learn this from a book and not a forum (sort of like the difference between giving a person a fish or teaching them how to fish)

RE: help with bending stiffness

(OP)
if i have a load of 21kN acting @ mid-span of 100mm horizontal leg of bracket:-

f  =  M.y/I     M  = 21kN x 0.050m = 1.05 kN.m  y = 0.004m
        
                I  =  4,267mm4  =  0.4267m4

f  =  1.05 x 0.004 / 0.4267  = 0.01 kN/m²

please correct me if im wrong.  if not, again how do i calculate the maximum moment capacity of the bracket?  thanks

 

RE: help with bending stiffness

You have used the correct equation for applied stress, now go to the other side of the equation - regional/countrywide Steel Design Code to figure out the capacity. Good luck.
By the way, is this a personal practice, or a real world design problem? If the latter, I strongly urge you to have someone, who is seasoned professional, to review and comment on your work.

RE: help with bending stiffness

(OP)
thanks, i have the use of the steel designers manual, with all the relevant extracts from British Standard 5950.  I am still unsure of how to derive the maximum moment capacity using it??

it is actually a real problem but already solved by a structural engineer(the thickness of the bracket was increased to carry the load).  Im just trying to figure out, for my own future reference, how it was arrived that the 8mm thick bracket had a maximum moment of 0.66 kN.m

  

RE: help with bending stiffness

rud:

Provide a sketch with loads indicated. Here are some fellows seem work from England that may help, once they understand the problem better (graphically).

RE: help with bending stiffness

rud:

Nothing on the attached sketch. Looks like you didn't upload correctly. Try again.

RE: help with bending stiffness

Moment capacity in BS 5950 is determined Mc=py x S, for the low shear case (cl 4.2.5.2).  There are other limits also.

From what you have said above.  You have a flat plate 100mm wide and 8mm deep.  It is loaded with a 21kN point load at a distance 100mm along so as to load your plate in the minor axis (I assume you have a cantilever based on the way you calculated the moment).  Is this correct?

You need to calculate the ULS load, i.e. factored, and compare it against the capacity.

According to your posts above, the structural engineer determined the moment capacity as 0.66kNm.  You have calculated the applied moment as 1.05 kNm.  This means it doesn't work.  Either you have determined the moment incorrectly, or the your colleague determined the capacity incorrectly.

 

RE: help with bending stiffness

I gave up. HELP, someone!

RE: help with bending stiffness

still nuthin

RE: help with bending stiffness

(OP)
sketch is uploaded this time

thanks ussuri, yes the bracket failed but in practice the thickness was increased to make it work.  im actually just trying to determine how the moment capacity of 0.66 kN.m is calculated, for future reference

i made a slight error, as you can see from the sketch the moment applied is 21 x 0.046 = 0.97 kN.m   

RE: help with bending stiffness

In simple terms:

Moment Capacity  Mc = py x S = py x b x d^2 x (1/4)

You need to know the yield strength of the material and the width, b.


  

RE: help with bending stiffness

IMHO, this problem has nothing to do with the capacity of the angle.  we're not bending the angle, only a flange.

with respect to ussuri, (1/4) should be (1/6) no ? ... bending stress = 6M/(b*t^2)

RE: help with bending stiffness

rb1957,

BS5950 typically states the moment capacity is the yield strength multiplied by the plastic section modulus (S, in the UK, Z in the US).  This reduces depending on the section classification (b/T ratios) so that it may be the elastic section modulus (Z in the UK, S in the US) that should be used, so you may indeed be correct.  In the case of particularly slender sections is will be less than Z (or S).

RE: help with bending stiffness

In Canada, we use Z for plastic modulus and S for section modulus.  So Z = bd2/4 and S = bd2/6.

The resisting moment, Mr = φFy*Z

Resistance Factor,φ = 0.90

Z = 100*82/4 = 1600 mm3

For a yield of 350 MPa, Mr = 0.9*350*1600 = 504,000N-mm or 0.504kN-m (Note that this is the factored capacity)

M = 21*50/1000 = 1.05 kN-m. > 0.504 [NO Good]

Maximum factored load Pf = 0.504/0.05 = 10 kN

Maximum allowable load (assuming live load) = 10/1.5 = 6.7 kN.
 

BA

RE: help with bending stiffness

rudigger:

I commend you for wanting to learn, and for taking on a problem like this for your own edification, even though it wasn't your problem to solve.  This shows some real initiative on your part.  At the moment you may only be a vBE ("very basic engineer", Mike never could get his degrees straight), but you could very quickly graduate to a lbvBE (less bashful very basic engineer) if you would get with that other structural engineer you mentioned.  Hopefully he is in the same office as you are. Ask him to be your mentor, you will find that most engineers are glad to help a beginner learn the ropes, as is evidenced by the many responses you got on this thread,  as long as you show the initiative.

As someone else said 'you need a few text books, not this forum' to do what you are trying to do.
You need a basic strength of materials book and a steel design text, and your own time to study them.  Then develop that relationship with a smart engineer who will spend some time with you.  He can see the problem with you and send you off in the right direction, or tell you where to look for the answer or what to study.  And he can correct you, immediately, when you are going off track, more efficiently than we can on this forum, i.e. it took us 20 posts to get a picture of the problem.

If you can find that mentor in your own company, and really show that initiative, that can lead to promotion.  If you go outside for that mentor, hard work could lead to a new job.  Don't be bashful, none of us objects to an honest question, and we all admire honest initiative.
Good Luck

RE: help with bending stiffness

I hope that we've not assisted yet another student with a homework problem.....it's getting to be the end of term these days ya know.

Regards,
Qshake
pipe
Eng-Tips Forums:Real Solutions for Real Problems Really Quick.
 

RE: help with bending stiffness

(OP)
thanks all for the help, and dhengr for the encouraging advice. i am infact, Qshake, a part-time civils student but this wasnt homework.  i have plenty of that though if anyone knows their water infrastructure and retaining walls ;0)      

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