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Steel Portal Frame EC3 RUNET software
γ
Μ1
= 1.00
γ
Μ2
= 1.25
Usual values for concrete structures (EN1992-1-1 Tab. 2.1N)
γ c
γ s
= 1.50 (concrete)
= 1.15 (reinforcing steel)
16.6 Second order effects EN1993-1-1 §5.2.1
The material behaviour is considered linear elastic. The second order effects are geometrical
(P-Δ and P-δ) effects. The practical consequence of (P-Δ) effects is to reduce the stiffness of the frame, with a result the increase of the deflections and the internal forces beyond the ones calculated from first-order analysis.
The effects of the deformed geometry are quantified using the factor a cr
EN1993-1-1 §5.2.1 acr=Fcr/Fed EN1993-1-1 Eq. (5.1)
Fed: is the design loading of the structure
Fcr : is the elastic critical buckling load for global instability mode based on initial elastic stiffness.
The frame is considered sufficiently stiff and second order effects may be ignored in a first order analysis if a ≥ 10 cr
For portal frames with shallow slopes according to EN1993-1-1 §5.2.1 (4) a as cr
can be estimated
α cr
=
H
Ed
V
Ed
h
H
,
Ed
EN1993-1-1 Eq (5.2)
Hed : total design the total design horizontal load
Ved : total design vertical load
δ hed
: is the horizontal displacement at the top of the columns h : is the column height
Axial force in the rafters may be assumed to be significant if
0 .
5
Af y
EN1993-1-1 Eq (5.3)
N
Ed
According to EN1993-1-1 §5.2.2 (5), single story portal frames designed based on elastic analysis the global analysis second order effects due to vertical load may be calculated by increasing the horizontal loads Hed by equivalent loads φ Ved due to imperfections and other possible sway effects according to the first order theory by an amplification factor
1
1
provided that a cr
≥ 3 EN1993-1-1 Eq (5.4)
1
cr
If α cr
< 3, second order analysis is necessary
16.7 Imperfections EN1993-1-1 §5.3.1
Global initial sway imperfection: φ = φ
0
: Initial value =1/200
α h
φ m
φ
0
α h
: Reduction factor for column height = 2/√h (2/3 ≤ α h
≤ 1) (h: structure height)
φ m
: Reduction factor for number of columns in a row α m
=
0 .
5
1
1
m
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RUNET Software www.runet-software.com 31
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