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Mcr greater than Mp

 
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vivekks
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Joined: 28 Oct 2014
Posts: 17

PostPosted: Tue May 24, 2016 4:52 am    Post subject: Mcr greater than Mp Reply with quote

If Mcr is greater than My, it is inelastic buckling.

But for some problems in all steel text books, Mcr is greater than Mp for beams and beam columns. What does this mean? (Mp = Zpz fy)
(From  a text book, beam columns chapter, The Mcr is  16866 kN-m but the Mp is aound  987.20 kN-m (given Zpz = 3948812 mm3 and fy=250n/mm2) )
Are they behaving as stocky beams and stocky beam columns?

But slenderness ratio λ is greater than 0.4 (means either they are intermediate or slender)


Even they do so, how can Mcr be greater than maximum moment capacity Mp...?


Even fcrb is greater than fu. What does this imply..? because exceeding ultimate stress is failure!!!!!


In is 800 -2007, table 14, fcrb are like 22551.2 n/mm2. They are higher than fu = 410 n/mm2.


what does these mean???


Pls clear my doubts.............Thank you in advance
  
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vegad
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Joined: 25 Dec 2013
Posts: 138

PostPosted: Tue Aug 16, 2016 9:04 am    Post subject: Reply with quote

Dear Er. Vivek,

I hope you also have come across:

http://www.steel-insdag.org/TeachingMaterial/Chapter11.pdf

First of all, Mcr is a function of torsional and warping resistance which is further used to calculate the actual design capacity in case of unrestrained beams. Keep the above PDF open for quick shuffle reference.

So Mcr itself serves as representative function to calculate fbd, and not compared directly as you use Mp due to pure in plane bending in Plastic sections. Note that for Mp is not the function of length of the section, where as the MCr or fcr,b is. Hence the vary as per length.

Here we are comparing results of two different scenarios and that too at different stages.

1) fcr,b is extreme fiber stress which may cause failure of the section - what kind of failure? Its the failure owing to the stiffness - which stiffness? Stiffness which resist torsion and warping? So the fcr,b indicates the maximum limit due to the 'form' of the section. There are no limitations on it, because it is not used for design directly. It is used for assessment of the criticality of the form which may affect the strength.

2) Now after computation of fcr,b; we further use it for strength computation by using the actual fy and discount it by the Chi LT - the bending stress reduction factor based on fcr,b. Note that the Chi LT is capped to 1, this automatically renders capping of the fcr,b value no matter how large it is  . .say . . for rolled section by 1.66 times the fy value.

Let me know what do you think.

Thank you.
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