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پنجشنبه 5 اردیبهشت 1392 :: نویسنده : حمید میرزاعلی

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In frames with concentric diagonal bracings the dissipative zones are located in the tension diagonals only. In this case, the yielding of the tension diagonals should occur before yielding or buckling of the beams or columns and before the failure of the connections. The compressive diagonals do not contribute to the ductility of the frame because they can fail due to buckling. In this article we will present how to calculate the minimum axial force resistance requirement of beams and columns according to EN 1998-1 clause 6.7.4.

The following figure shows an idealised concentrically braced frame in which the masses are concentrated at the nodes and all the connections between the members are assumed to be pinned. The loads were calculated using the provisions of Eurocode 8 (EN 1998-1) for dissipative behaviour (q>1.50). 
 
Total gravity load: 840 kN
Total seismic lateral load: 270 kN

sinφ=3/5=0.60
cosφ=4/5=0.80

NEd,1*cosφ=270 => NEd,1=337.50 kN
NEd,2*cosφ=180 => NEd,2=225 kN

The yield strength of steel is fy=355 N/mm2.

Amin*fy>=NEd,1 => Amin>=337.50*103/355 = 950.70 mm2

Choose CHS 114.3 x 3.6

A=1250 mm2 and i=39.20 mm

The non-dimensional slenderness of the bracing should be less than 2.00 in order to limit early buckling.

λ=(L/i)/(93.9*ε)=(5000/39.20)/(93.9*(235/355)0.50)=1.66 < 2.00 OK

Ω=Npl,Rd/NEd,1=1250*355/(337.50*103)=1.314

Vertical Members - ColumnsHorizontal Members - Beams
Internal Column - 1st Level:Internal Beam - 1st Level:
NEd,G=280 kN and ΝΕd,E=337.50 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=280+1.10*1.25*1.314*337.50 =>
Npl,RdΕd)>=889.77 kN (compression)
NEd,G=0 kN and ΝΕd,E=15+225*0.80+30-337.50*0.80=-45 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*(-45) =>
Npl,RdΕd)>=-81.30 kN (tension)
Internal Column - 2nd Level:Internal Beam - 2nd Level:
NEd,G=140 kN and ΝΕd,E=135 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=140+1.10*1.25*1.314*135 =>
Npl,RdΕd)>=383.91 kN (compression)
NEd,G=0 kN and ΝΕd,E=30+60-225*0.80=-90 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*(-90) =>
Npl,RdΕd)>=-162.60 kN (tension)
External Column - 1st Level:External Beam - 1st Level:
NEd,G=140 kN and ΝΕd,E=-337.50+202.50=-135 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=140+1.10*1.25*1.314*(-135) =>
Npl,RdΕd)>=-103.91 kN (tension)

The gravity load NEd,G=140 kN is more critical!
NEd,G=0 kN and ΝΕd,E=15+225*0.80=195 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*195 =>
Npl,RdΕd)>=352.31 kN (compression) or

NEd,G=0 kN and ΝΕd,E=15 kN 

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*15 =>
Npl,RdΕd)>=27.10 kN (compression)
External Column - 2nd Level:External Beam - 2nd Level:
NEd,G=70 kN and ΝΕd,E=-135+135=0 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=70+1.10*1.25*1.314*0 =>
Npl,RdΕd)>=70 kN (compression)
NEd,G=0 kN and ΝΕd,E=30 kN

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*30 =>
Npl,RdΕd)>=54.20 kN (compression) or

NEd,G=0 kN and ΝΕd,E=-30 kN 

Npl,RdΕd)>=NEd,G+1.10*γov*Ω*ΝΕd,E =>
Npl,RdΕd)>=0+1.10*1.25*1.314*(-30) =>
Npl,RdΕd)>=-54.20 kN (tension)






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