Three dimention beam or bending and buckling calc 3

[moranel]

Hi,
I have a three direction (bended and welded)beam that subjected to forces in two directions. these forces cause strains of bending and compression. can I add the bending strain to the compression strain and then to comer it to yield strain?
in other words, how can i calculate a cantilever that subjected to both bending moment and axial compression force at the end.
thanks!
Moran

 

[Ron]

Well, sort of. It's called a unity check.

(Compressive stress/allowable comp. stress)+(bending stress/allowable bending stress)<= 1.0

 

[moranel]

thanks,
can I add bending stress in one direction with a bending stress in other direction? meaning, if i have bending moments in two direction so sigma=sigma1+sigma2?

 

[dhengr]

Moranel:
Yes, sigma1 and sigma2 are additive algebraically, but you have to know when it’s (+s1) + (+s2) and when it’s (+s1) + (-s2). But your questions and they way you have asked them, makes me wonder how you are going to arrive at your sigmas and other stresses. And, whether you have a handle on the difference between stresses and strains. How do you get from your loads, through a number of calculation steps, to the stresses.

 

[moranel]

hi dhengr,
supposed i have M1= bending moment in x direction and
M2= bending moment in y direction:
sigma= M1*c/I + M2*c/I
and then i comper sigma to sigma yield of the beam material.
do you think it is right?

 

[rb1957]

you need to be careful, in case this is a "beam column". the lateral laods, bending the beam, reduce significantly the buckling allowable.

calculate Pcr, then P/Pcr; < 0.10 ?

 

[moranel]

it is a beam column though it is not pure axial comprssion load.

 

[rb1957]

if it's a beam column, you can't combine the stresses as oultined above. you have to analyze as a beam column, the analysis determines your MS directly.

BUT, you may be asking "how do i know if the compression flange is stable ?" then i would combine the stresses as outlined above (!!) 'cause that'll tell you the stress in the compression flange (having already done the beam column analysis so you know the structure is good, if the flange is stable) and i'd compare this with the crippling allowable.

 

[moranel]

i am not sure that i explained the problem clearly,
i will be very happy if you can look at the document attached and tell me what i did wrong.
i got very low "W" and it doesn't make sense to me.

 

[rb1957]

pls attach word2003 .doc

 

[moranel]

thanks,

 

[cloa]

I just changed moranel's file to a PDF so hopefully rb1957 you have no problems with this file.

 

[rb1957]

actually, now i'm at work i can open the original 2007 version, but ...

M1 equation is wrong, integral should be (qx)*x/2 ... M1 = ql*l/2.

M2 equation is wrong 'cause you've omitted the moment at the plane of symmetry, and you haven't included the moment due to the shear q*l1.

you haven't analyzed the leg as a beam column. google "beam column" and you'll see it's quite a different analysis. how does the leg react the moment, M2 ? most likely as a reaction moment at the base ?? this is now a column with an off-set load ... google "secant formulae" or "column with offset load" or consult a text book.

thinking about it, maybe this is a better way to approach the loading ... make a free body of a 1/2 ... zero shear at the plane of symmetry, so the leg reacts all the load ... q*(l1+l2). the moment at the base is harder to calc ... the couple from the reaction and the applied load is conservative as there is some moment reacted at the plane of symmetry ...