Plastic bending -using FTU

[40818]

Hi all,
Does anyone have any knowledge of using plastic bending factors on FTU rather than FT2 (FTY) to calculate an allowable stress?
Rectangular section with K=1.5 (or esdu 01.06.01 which comes to 1.4).
I always thought it was the yield moment multiplied by the shapefactor (i.e 1.5).

 

[rb1957]

i thought it was based on ftu ... i've usually applied it as, down your usual linear bending calc, then factor ftu by the Form factor to get an equivalent linear peak stress allowable ...

clear as mud ?

 

[YoungTurk]

I agree with rb, the shape factor is applied to Ftu. Although plastic yielding causes the load to spread across the cross section after yield is reached at the extreme fibers, rupture doesn't occur until the ultimate stress is achieved. Niu has a good section on plastic bending, but don't have the book handy to point you to it.

 

[edbgtr]

40818

Go to thread thread2-256804 earlier in this forum to see the difference between shape factor and form factor.

Ed

 

[Allanon81]

The simple (and most conservative way) to calculate FTB is to use the following formula:

FTB = FTU + (1-k)*FTY

There is, however, another way to calculate FTB using a longer method out of the Boeing Design Manual (1967). I've attached an image using from a MathCAD document showing this method.

 

[YoungTurk]

The Niu reference I was thinking of comes from section 6.4 of "the red book", Airframe Stress Analysis & Sizing. His method is not in perfect agreement with the formula i'm familiar with, which is Fbu = (1+4k)/5 Ftu, but close. I am guessing that the curves he uses to get from Ftu to Fbu include analysis similar to the Boeing method.

Given that the "shape factor" I'm familiar with, as well as the "section factor" Niu presents are both always >1, the (1-k) factor in Al's formula is probably supposed to be (k-1). The inclusion of the yield makes intuitive sense, but does not match any of my available references.

 

[rb1957]

the error of my ways was pointed out today (well one of them) ...
K = 1.5 (for a rectangular section),
(1+4K)/5 = 1.4 (the factor you noted from ESDU)

as someone else posted out above, form factor and shape factor ...

 

[40818]

Thanks for that, i always used yielding as the criteria for plasticity. However, how does the use of FTU as the basis for plastic bending go with the development of a plastic hinge on a simple beam. I understood that upon a full depth hinge developing a mechansim essentially is created and would lead to failure. Would it therefore be fair to assume that this would also be based on Fb=FTU+Fo(K-1) instead of FTY+Fo(K-1)

 

[dodger10]

The Cozzone method requires two calculations of the energy to form a plastic hinge; one for the section above the centroid and one below. For an unsymmetrical section one of these sections will not use Ftu as the maximum stress. The extreme fiber stress closer to the centroid will be calculated from that extreme fiber strain. Fb = Fm + Fo (K-1) will therefore be different for each section except for a symmetrical section (like a rectangle) where Fm above and below the centroid will both be Ftu for an ultimate plastic analysis. Remember that plastic bending is non linear and must not be factored. It must therefore be checked also at limit where Fm = Fty. The calculation for Fo, the stress at zero strain is much more complicated.