help with bending stiffness

[rudigger]

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

 

[ishvaaag]

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

 

[rudigger]

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

 

[rb1957]

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

 

[rudigger]

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 ??

 

[rb1957]

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

 

[ishvaaag]

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.

 

[rudigger]

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?!?

 

[rudigger]

thanks ishvaaag i shall search for this mathcad

 

[trainguy]

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

 

[drawoh]

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

 

[cntw1953]

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

 

[rudigger]

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

 

[msquared48]

So... You're a BE?

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

 

[BAretired]

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

 

[rudigger]

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

 

[rb1957]

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)

 

[rudigger]

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

 

[cntw1953]

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.

 

[rudigger]

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