skills m08 e_portalframes_singlestoreybuildings
TRANSCRIPT
SKILLS Project
October 2013
PORTAL FRAMES IN SINGLE STOREY BUILDINGS
Structural elastic analysis including second order effects and imperfections
Design procedure of portal frames
Design procedure of roof bracing and vertical bracing
3
LEARNING OUTCOMES
Introduction
Presentation of industrial steel buildings
Examples
Global Analysis
General
Second order effects
Frame imperfection
Rigidity of joints
Design Procedure of portal frames
Structural stability of frames
Stability of columns and rafters
Vertical Bracing
Roof Bracing
Conclusion 4
LIST OF CONTENTS
INTRODUCTION
6
INTRODUCTION
Typical design of single storey
steel buildings
7
INTRODUCTION
Purlins
8
INTRODUCTION
Haunched portal frames
9
INTRODUCTION
Roof bracing
Photo APK
10
INTRODUCTION
Vertical bracing
Photo APK
11
INTRODUCTION
Photo APK – JP Muzeau
12
INTRODUCTION
GLOBAL ANALYSIS
Methods of structural analysis
Elastic analysis
Material is supposed to behave perfectly linear elastic
Plastic analysis
Material non linearity is taken into account
Redistribution of internal forces and moments
14
GLOBAL ANALYSIS
EN 1993-1-1 § 5.4
Effects to be taken into account when significant
Effects of deformed geometry (2nd order effects)
Imperfections
Stiffness of joints
Ground-structure interaction
15
GLOBAL ANALYSIS
EN 1993-1-1 § 5.1
16
GLOBAL ANALYSIS
First order and second order analysis
First order analysis: performed on the non deformed structure
Second order analysis: performed including effects of deformed geometry
Effects of deformed geometry/Second order effects
17
GLOBAL ANALYSIS
V
H
MI
h
First order analysis of the structure gives:
hHM I
EI
hHI
3
3
I
Effects of deformed geometry/Second order effects
18
GLOBAL ANALYSIS
Second order analysis of the structure gives:
iterative calculation of II necessary
IIII VhHM
EI
hVhH
IIII
3
2
n1n
V H
MII
II
Effects of deformed geometry/Second order effects
19
GLOBAL ANALYSIS
Supposing: And:
With:
cr
2
2
1
1
31
1
3
V
V
EI
VhEI
hhH III
IIIIn1n I
EI
hhH
3
2
2cr
3
h
EIV
V H
MII
II
EI
hVhH
IIII
3
2
n1n
20
GLOBAL ANALYSIS
Effects of deformed geometry/Second order effects
Substituting:
cr
III
V
V
1
1
crcr
V
V
cr
11
1
III
cr
11
1
III MM
V H
MII
II
21
GLOBAL ANALYSIS
Global and local second order effects
Global 2nd order effects – P-D-effects
Concerns the deformation
of the whole structure
Local 2nd order effects – P--effects
Concerns the deformation between member ends
Generally covered by member checks EN 1993-1-1 § 6.3
D P
P
Summarizing the effects of deformed geometry
Taking the deformation of the structure into account generally leads to higher internal forces (shear force) and moments for portal frames.
The lesser the rigidity of the structure is, the higher are the deformation and therefore the 2nd order effects.
cr is representative for the influence of 2nd order effects (high values of cr stand for little influence of 2nd order effects )
22
GLOBAL ANALYSIS
Second order effects in EN-1993-1-1
First order analysis is permitted if:
for elastic analysis
for plastic analysis
23
GLOBAL ANALYSIS
10cr
15cr
EN 1993-1-1 § 5.2.1
If criterion is not respected 2nd order effects have to be accounted for
Accounting for second order effects in EN-1993-1-1
2nd order analysis (buckling length = member length) or
1st order analysis followed by amplification of sway effects (buckling length = member length) or
1st order analysis (buckling length according to sway buckling mode)
2nd order analysis (buckling length = member length)
24
GLOBAL ANALYSIS
103 cr
3cr
Amplification of sway effects
Amplification factor:
Sway effects: Horizontal loads (e.g. wind)
Effects due to imperfection
Effects due to geometry of the structure
25
GLOBAL ANALYSIS
cr
11
1
Calculation of cr
Simplified formula:
if roof slop is swallow: < 26°
if axial force in the rafter is small: or
26
GLOBAL ANALYSIS
EdH,Ed
Edcr
h
V
H
Ed
y3,0
N
Af crEd 09,0 NN
EN 1993-1-1 § 5.2.1 (4)
h
H,Ed
VEd
HEd
Practical calulation of cr for portal frames
27
GLOBAL ANALYSIS
VEd Hunit
unit
unitEd
unitcr
h
V
H
VEd
0,5 Hunit 0,5 Hunit 0,25 Hunit 0,5 Hunit 0,25 Hunit
VEd
column.meanunit column.meanunit
h
IMPERFECTIONS
Structural imperfections
Due to: lack of verticality
lack of straightness
eccentricities in joints
residual stresses
inhomogeneity of material
Physical imperfection are replaced by equivalent geometric imperfection
29
GLOBAL ANALYSIS
Equivalent geometric imperfection
Global initial sway imperfection
Local bow imperfection
30
GLOBAL ANALYSIS
f f
e0 e0
Global sway imperfection
f0: Basic value
h: Reduction factor for the height of the columns
but
m: Reduction factor for the number of columns per row
m is the number of columns carrying at least 50% of the average vertical load of the column row considered
31
GLOBAL ANALYSIS
mh0 ff
200/10 f
h
2h 1
3
2h
m
115,0m
EN 1993-1-1 § 5.3.2
Direction of sway imperfection
Every possible direction has to be considered, but only one direction in a time
32
GLOBAL ANALYSIS
f f f f
f f f f
System of equivalent forces replacing out-of-plumb
33
GLOBAL ANALYSIS
f
NEd
NEd
NEd
NEd
fNEd
fNEd
System of equivalent forces replacing out-of-plumb
34
GLOBAL ANALYSIS
f f
fNEd fNEd
fNEd fNEd
Possibility of disregarding global frame imperfection
Relatively high horizontal loads
Frame stability check with equivalent column method
(buckling length of columns are based on overall sway buckling mode)
35
GLOBAL ANALYSIS
EdEd 15,0 VH EN 1993-1-1 § 5.3.2
EN 1993-1-1 § 5.2.2
Local bow imperfection
Local 2nd order effects are generally included in the member verification formulas of EN 1993-1-1 §6.3
Local bow imperfection has to be considered for slender members under high compression axial force
36
GLOBAL ANALYSIS
If frame is sensitive to 2nd order effects, local bow imperfection has to be applied on:
compressed members that have at least one moment resistant joint and
whose reduced slenderness
is calculated supposing a pin ended column:
And
37
GLOBAL ANALYSIS
Ed
y5,0
N
Af EN 1993-1-1 § 5.3.2
cr
N
fA y EI
LN
2
cr
Value of local bow imperfection
38
GLOBAL ANALYSIS
e0
Buckling curve Elastic analysis Plastic analysis
e0/L e0/L
a0 1/350 1/300
a 1/300 1/250
b 1/250 1/200
c 1/200 1/150
d 1/150 1/100
EN 1993-1-1 § 5.3.2
System of equivalent forces replacing local bow imperfection
39
GLOBAL ANALYSIS
NEd
NEd
4NEde0,d/L
4NEde0,d/L
8NEde0,d/L2 e0
NEd
NEd
L
System of equivalent forces replacing local bow imperfection
40
GLOBAL ANALYSIS
e0 e0
4NEd e0,d/L
4NEd e0,d/L 4NEd e0,d/L
4NEd e0,d/L
8NEde0,d/L2 8NEde0,d/L2 L
STIFFNESS OF JOINTS
Rigid joint
42
GLOBAL ANALYSIS
Examples of Joints
Nominally pinned joint
Classification of joints by stiffness
43
GLOBAL ANALYSIS
Joint A M
f
Joint B
Joint C
EN 1993-1-8 § 5.2.2
Classification boundaries
44
GLOBAL ANALYSIS
Joint A M
f
Joint B
Joint C
beam
beam5,0L
EI
beam
beamb
L
EIk
Rigid joints
Semi-rigid joints
Nominally pinned joints
EN 1993-1-8 § 5.2.2.5
Value of kb for the classification of joints
kb = 8 : frames where the bracing system reduces the horizontal displacement by at least 80%
kb = 25 : other frames, provided that in every storey
Kb/Kc ≥ 0,1
Kb: mean value of Ib/Lb for all beams at the top
of the storey
Kc: mean value of Ic/Lc for all columns of the storey
Ic/b: second moment of area of a column/beam
Lc/b: height/length of a column/beam
45
GLOBAL ANALYSIS
Practical comments
The designer will probably choose the assumption of rigid rafter-to-column joints.
The designer will probably choose the assumption of either pinned or rigid column bases.
The assumptions will have to be checked afterwards.
46
GLOBAL ANALYSIS
DESIGN PROCEDURE OF PORTAL FRAMES
Structural stability of frames
cr ≥ 10 :
1st Method:
1st order analysis without imperfections
Column in-plane stability check using buckling length according to sway buckling mode
2nd Method:
1st order analysis with global imperfection
Column in-plane stability check using member length
48
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Structural stability of frames
cr < 3 :
Check if introduction of local imperfection is necessary
if necessary:
2nd order analysis with global imperfection if necessary
Column in-plane stability check = check of resistance of section
49
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Structural stability of frames
cr < 3 :
Check if introduction of local imperfection is necessary
if not necessary:
2nd order analysis with global imperfection if necessary
Column in-plane stability check using member length
50
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Structural stability of frames
3 ≤ cr < 10 :
Check if introduction of local imperfection is necessary
if necessary:
2nd order analysis with global imperfection if necessary
Column in-plane stability check = check of section resistance
51
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Structural stability of frames
3 ≤ cr < 10 :
Check if introduction of local imperfection is necessary
if not necessary:
1st Method:
1st order analysis without imperfections
Column in-plane stability check using buckling length according to sway buckling mode
Verification of joints and rafters including second order effects (amplification of sway effects)
52
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Structural stability of frames
3 ≤ cr < 10 :
Check if introduction of local imperfection is necessary
if not necessary:
2nd Method:
1st order analysis with global imperfection if necessary
Amplification of sway effects
Column in-plane stability check using member length
53
DESIGN PROCEDURE OF PORTAL FRAMES
EN 1993-1-1 § 5.2.2
Buckling length = Member length :
Buckling length according to sway buckling mode :
54
DESIGN PROCEDURE OF PORTAL FRAMES
Lcr
Lcr
DESIGN PROCEDURE OF PORTAL FRAMES
55
Geometry + Boundary conditions + Loads
Calculation of cr
cr < 3 3 ≤ cr < 10 cr ≥ 10
Slide 57
Slide 59
Slide 58
DESIGN PROCEDURE OF PORTAL FRAMES
56
Geometry + Boundary conditions + Loads
Calculation of cr
cr ≥ 10
In plane stability check of columns using buckling length according to global buckling mode
1st order analysis
In plane stability check of columns using member length
Global imperfection
DESIGN PROCEDURE OF PORTAL FRAMES
57
Geometry + Boundary conditions + Loads
Calculation of cr
cr < 3
Global imperfection if necessary: EN 1993-1-1 § 5.3.2 (4)
2nd order analysis
In plane stability check of columns using member length
Local imperfection if necessary: EN 1993-1-1 § 5.3.2 (6)
In plane stability check of columns = resistance check of section
Necessary Not necessary
Geometry + Boundary conditions + Loads
Calculation of cr
3 ≤ cr < 10
Local imperfection if necessary: EN 1993-1-1 § 5.3.2 (6)
2nd order analysis
In plane stability check of columns using buckling length according to sway buckling
mode
Amplification of sway effects
1st order analysis
In plane stability check of columns using member
length
DESIGN PROCEDURE OF PORTAL FRAMES
58
Global imperfection if necessary: EN 1993-1-1 § 5.3.2 (4)
In plane stability check of columns = resistance
check of section
Not necessary Necessary
Necessary Not necessary
STABILITY OF COLUMNS AND RAFTERS
Stability of columns and rafters
Columns and rafters are subjected to axial forces and moments
Use of interaction formula
60
DESIGN PROCEDURE OF PORTAL FRAMES
1
1
,
,,
1
,
,,
1
D
D
M
Rkz
EdzEdzyz
M
RkyLT
EdyEdyyy
M
Rky
Ed
M
MMk
M
MMk
N
N
1
1
,
,,
1
,
,,
1
D
D
M
Rkz
EdzEdzzz
M
RkyLT
EdyEdyzy
M
Rkz
Ed
M
MMk
M
MMk
N
N
EN 1993-1-1 § 6.3.3
Simplification for common frames
Columns and rafters are not subjected to out-of-plane moments
Columns and rafters are usually double symmetric sections
61
DESIGN PROCEDURE OF PORTAL FRAMES
1
1
,
,
1
M
RkyLT
Edyyy
M
Rky
Ed
M
Mk
N
N
1
1
,
,
1
M
RkyLT
Edyzy
M
Rkz
Ed
M
Mk
N
N
ROOF BRACING
63
ROOF BRACING
Photo APK
64
ROOF BRACING
Rafters
Purlins transmitting horizontal loads to roof bracing
Roof bracing
Ground view of roof bracing
65
ROOF BRACING
6 Rafters Roof bracing
Purlins transmitting horizontal loads to roof bracing
Idealisation of roof bracing
66
ROOF BRACING
m rafters whose flanges are subjected to the axial force NEd
(including rafters acting as upper and lower flange of roof bracing)
Roof bracing
Horizontal loads transmitted by purlins
Fexterior NEd
NEd
NEd
NEd
NEd
NEd
NEd
NEd
Imperfection for roof bracing
67
ROOF BRACING
m rafters whose flanges are subjected to the axial force NEd and that are subjected to imperfection e0
Roof bracing
Horizontal loads due to imperfection e0 and axial forces NEd and to Fexterior
EN 1993-1-1 § 5.3.3
Fexterior NEd
NEd
NEd
NEd
NEd
NEd
NEd
NEd
e0
e0
e0
e0
Imperfection for roof bracing
68
ROOF BRACING
EdRafter,Section
upFlange
Section
EdRafter,Ed N
A
A
h
MN
500
m0
Le
m
115,0m
Fexterior NEd
NEd
NEd
NEd
NEd
NEd
NEd
NEd
e0
e0
e0
e0
Roof bracing
Horizontal loads due to imperfection e0 and axial forces NEd and to Fexterior
Calculation of roof bracing
Use of geometric imperfection and 2nd order analysis
Use of equivalent forces and 1st order analysis
69
ROOF BRACING
Fexterior NEd
NEd
NEd
NEd
NEd
NEd
NEd
NEd
e0
e0
e0
e0
Equivalent load concept
g: deflection of the roof bracing due to exterior load Fexterior and equivalent load qd
iterative calculation of qd
1 or 2 iterations sufficient
70
ROOF BRACING
2
g0d 8
L
eNq Ed
qdL/4
qd
qdL/2 qdL/2
qdL/8 qdL/8 qdL/4 qdL/4
Fexterior
L
VERTICAL BRACING
72
VERTICAL BRACING
Photo APK
Design procedure
Calculation of cr
1st order or 2nd order theory
Determination of horizontal loads
Wind
Loads due to global imperfection if necessary
Calculation of internal forces and moments
Verification of stability in bracing plane
Verification of out of bracing plane stability as before
73
VERTICAL BRACING
Calculation of cr for vertical bracings
74
VERTICAL BRACING
meantotal
unit
h
V
Hcr
V V V V
Hunit
h
Vtotal
In-plane loads on vertical bracing
Ntot: Sum of axial forces of all columns stabilized by bracing
H: External horizontal loads
V: Vertical loads on columns
f: Sway imperfection
75
VERTICAL BRACING
Ntotf + H
Ntotf
V V
CONCLUSION
Generally 2nd order effects and imperfections have to be accounted for in the design of portal frames.
Depending on the value of cr different calculation methods can be adopted.
For portal frames it is convenient to account for global imperfection and global 2nd order effects in the global analysis.
77
CONCLUSION
Local 2nd order effects are generally included in the member verification formulas of EN 1993-1-1 §6.3.
Physical imperfections are replaced by either equivalent geometric imperfections or equivalent loads.
Bracing systems are subjected to external horizontal loads and loads due to their function as stabilizing elements.
78
CONCLUSION
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