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Design of a steel frame according to Eurocode –
SAP2000 Training Program
CSI Portugal & Spain
3. Portal frames
1. Architectural and environmental conditions
2. Architecture
7. Actions
4. Roof and walls sheeting
5. Purlins
8. Actions combinations
6. Bracing systems
2CSI Portugal - Design of a Steel Frame
Contents of Frame Design Example
Contents
9. Steel sheeting design
10. Modeling the structure
3CSI Portugal - Design of a Steel Frame
Contents of Frame Design Example
15. Members automatic ULS check
14. Members buckling lengths
11. Load assignments
16. Members automatic design
12. Frame buckling analyses
Contents (cont.)
13. Equivalent imperfection forces
17. SLS check
Objective: Design steel structure for indoor sports facility in the suburbs
of the city of Évora (Portugal) with a covered area of 60 x 30 m2
Arquitectural requirements:
• Soil suitable for slallow foundations
• Materials: steel S275 for framework and S235 for roof and wall sheeting
concrete C25/30
rebar reinforcement: S400
4CSI Portugal - Design of a Steel Frame
1. Architectural and Environmental Conditions
5CSI Portugal - Design of a Steel Frame
2. Architecture
1) Flat frame
imin = 0.5-1%
2) Duopitch or gable frame
Slope decreases
moments in the middle
region of the rafters
Roof shapes
for drainage
6CSI Portugal - Design of a Steel Frame
2. Architecture
3) Single slope, monopitch or shed frame 4) Parabolic or circular frame
5) Multispan frame
Chosen solution: 15 steep duo-pitch roof shape
7CSI Portugal - Design of a Steel Frame
2. Architecture
Portal frame components:
8CSI Portugal - Design of a Steel Frame
3. Portal Frames
Portal frames structural behaviour
Simply supported because of (i) support
conditions or (ii) variable inertia
1) Simply supported beam
2) Articulated (pinned) frame
Isostatic
9CSI Portugal - Design of a Steel Frame
3. Portal Frames
3) Rigid connections frame
4) Cable stayed frame
Very slender rafters prone
to up-lifting by wind
Hiperstatic
Plastic stress-resultant
redistributions possible
1) Hot-rolled I- or H-section profiles 2) Welded beams (composed
of unperforated plates)
10
3. Portal Frames
Support moments higher than
span in rigid connections frame
Solution: use knee joint
knee joint
CSI Portugal - Design of a Steel Frame
Rafter solutions
L < 30 ~ 35 m
3) Tapered beams: simply supported rafter
Simply supported beam
For simply supported
rafters or articulated
frames
4) Perforated beams: honeycomb
11CSI Portugal - Design of a Steel Frame
3. Portal Frames
Increased bending resistance and
stiffness maintaining shear resistance
Tubes can pass throught the beams
Higher costs (cuting and welding)
Usually pinned beams (may not resist bending +
shear at supports)
5) Cellular beams: uniform or tapered
Tapered sectionUniform sectionFabrication
L0/h = 15-30Similar to honeycomb + esthetics
6) Planar trusses
Constant depth Variable depth
7) Spatial trusses
Cubes or tetrahedron shape
Complex connections
Hollow section profiles
Light solutions for long spans
Reduces bracing required
Boeing factory Olympic pool
12CSI Portugal - Design of a Steel Frame
3. Portal Frames
L0/h = 5-6L0/h = 10-12
20 < L < 100 m
Extreme rafter slenderness
8) Cable-stayed solutions
Additional column compression
Solution for large spans
Roof weight vs up-lifting forces
Possible up-lift due to wind forces
13CSI Portugal - Design of a Steel Frame
3. Portal Frames
Chosen solution:
Rafter: planar truss; RHS profiles;
welded connections
Column:
HEA or
HEB
14CSI Portugal - Design of a Steel Frame
3. Portal Frames
Rigid
connection
(bolted)
Rigid connection
(bolted)
• IPE, Z, U or channel purlins
15CSI Portugal - Design of a Steel Frame
3. Portal Frames
1) Regular (5-7 m)
• Moderate actions
• Economical solution
2) Reduced (< 5 m) • Very high loads (wind, snow, insulation materials, soil)
3) Increased (> 7 m, < 12 m)
• Trussed purlins
• Interior constraints to column locations
• Roof sheeting suitable for long spans
Portal frames spacing
6 m
Chosen spacing:
Elements:
2) Trapezoidal steel sheeting: longer spans, lighter, thermal insulation
possible, better esthetics, enough longitudinal strength for purlins
bracing
3) Corrugated aluminium sheeting: very light, corrosion resitant,
expensive, too deformable (shorter spans), high noise in heavy rain
4) Translucid plastics (polycarbonate): low strength (shorter spans),
sensitive to sunlight exposure (become brittle), combustible, very light
16CSI Portugal - Design of a Steel Frame
4. Roof and Walls Sheeting
1) Corrugated fibre-cement: economical, brittle, unesthetical,
heavy, low insulation, asbestos fibres are unhealthy
Sheeting:
(i) Sheeting (iii) Drainage elements
(ii) Purlins (iv) Joint elements and purlins bracing
Steel sheeting with thermal insulation; 1.5 m spans
Adopted solution:
Main:
• Transmit roof loads to the rafters
• Brace the rafters upper chords or flanges
Purlin solutions:
- Hot rolled (IPE, UNP)1) Spans up to 9 m
- Cold-formed (Z-, channel or lipped channel section)
17CSI Portugal - Design of a Steel Frame
5. Purlins
2) Spans up to 15 m - planar or spatial truss beams - Planar beam with rods
- Planar beam with profiles
Functions:
Optional:
• Brace the rafters lower chords (indirectely through the
lower chords bracing rods)
• Brace the portal frames for out-of-plane displacements
• Transmit longitudinal horizontal endwall loads to the
bracing system
UNP (channel) profiles
Chosen solution:
18CSI Portugal - Design of a Steel Frame
5. Purlins
Connection to the rafter:
Ovalisation: elongated bolt hole to function as a
movement joint for thermal action
Types of connections to the rafters: (i) lower flange
bolted, (ii) plate bolted to the web, (iii) use a channel
InclinedChosen configuration:
Purlin configurations:
Vertical Inclined
• For predominatly vertical loads (snow or life) • For predominatly normal loads (wind)
• Easier to execute
19CSI Portugal - Design of a Steel Frame
5. Purlins
1) Simply supported
Supports and joints:
2) Gerber
3) Continuous beam
4) Two-span beam
Purlin connection:
Two-span beam in alternated
configuration (see next slide)
Chosen solution:
20CSI Portugal - Design of a Steel Frame
5. Purlins
Two-span alternated configuration reactions:
Purlin
Rafter
Two-span non-
alternated:
One-span:
1.875/2 6.25/2 3.75/2 6.25/2 3.75/2
2.5/2 5/2 5/2 5/2 5/2
Two-span
alternated:
• Distributes more uniformly the loads on the rafters
21CSI Portugal - Design of a Steel Frame
5. Purlins
• Determined by the sheeting span (1.2-2 m
normally)
• Possibility of reduced spacing in localised
zones (e.g., where wind loads are higher)
Spacing
1.5 m
Chosen spacing:
3) Purlins bracing
2) Rafter lower chords bracing
1) Frame longitudinal and transversal bracing
22CSI Portugal - Design of a Steel Frame
6. Bracing systems
Transversal bracing
23CSI Portugal - Design of a Steel Frame
6. Bracing systems
• resists longitudinal horizontal loads (e.g., wind loads in the enwalls)
• prevents global buckling
Longitudinal bracing
• resists transversal horizontal loads
• prevents global buckling
• only used in highly deformable frames• braces the rafters (absorbs their imperfection equiv. loads)
Central
• thermal action generates
negligible axial forces
• purlins under compression for
wind loads (additional beams
may be necessary)
Double-sided
• thermal action may result in
high axial forces
• purlins are not subjected to
compression due to wind • No longitudinal bracing
Chosen bracing:
• Transversal double-sided
Rafter lower chord bracing
24CSI Portugal - Design of a Steel Frame
6. Bracing systems
• May be uniformly spaced or more concentrated on the most compressed zones
• Diagonal at 45
Chosen bracing:
Perpendicular
• works only in tension
• must be fixed at both ends
endwall
column
chord bracing rod
Diagonal
• normally at q=45
• low q: less flexible but may not work in compression
• transfers the instability loads to the purlins
• high q: more flexible due to purlin bending
rafter
purlin
chord bracing rod
• Absobs the roof in-plane load component
• Limits purlin minor axis bending
• Reduces purlins lateral buckling length
25CSI Portugal - Design of a Steel Frame
6. Bracing systems
Bracing rod, tie rod or sag bar:
Bracing rod anchor:
a) Ridge (eave) purlins absorb the rod tension b) Diagonal rods transmit the tension to the rafters
Purlins bracing
• Connected using nuts and washers
2) Live
EN 1991: Part 1-1
3) Wind actions
4) Thermal actions
EN 1991: Part 1-4
EN 1991: Part 1-5
26CSI Portugal - Design of a Steel Frame
7. Actions
1) Dead
EN 1991: Part 1-1
Dead
3
77 mkNs Structural elements:
Note: members dead weight is automatically determined in SAP2000
Sheeting self-weight: 2
05.0 mkNqEd 
Live
2
4.0 mkNqEd Roof:
kNQEd 1
(distributed)
(concentrated)
EN 1991-1-1 Table 6.10
H category – roof not accessible except for normal maintenance and repair
EN 1991-1-1 Table A.4
27CSI Portugal - Design of a Steel Frame
7.1 Dead and Live Actions
28CSI Portugal - Design of a Steel Frame
7.2 Wind Action
222
/456.02725.1
2
1
2
1
mkNvq bb  
Basic velocity pressure:
Wind force:
refppEkw AcqF .
peak velocity
pressure
differential pressure
coeficient
reference area
Notes:
• Fw.Ed is normal to the surface
• friction force can be neglected
when: A// 4A∟
2
2
//
2
3
aA
aA



e.g.:
Terrain category: III (regular cover of vegetation or buildings)
2
/903.0456.098.1)15()15( mkNqmcmq bep 
Peak velocity pressure:
smvccv bseasondirb /27270.10.10. Basic wind velocity:
season
factor
directional factor
Évora county (Zone A): vb.0=27 m/s
(National Annex, Table NA.I)
Peak velocity pressure (qp)
fundamental
velocity
External pressure coeficient (cpe)
3.0,2.0 pic
(both should be considered)
Otherwise:
29CSI Portugal - Design of a Steel Frame
7.2 Wind Action
Internal pressure coeficient (cpi)
If area of opennings in each face is known:

 

openingsallofArea
0cwithopeningsofArea pe

Two wind directions are considered:
º0q º90q
2 wind directions × 2 internal pressures = 4 wind loading cases
Differential pressure coeficient (cp):
30CSI Portugal - Design of a Steel Frame
7.2 Wind Action
Number of loading cases:
pipep ccc 
Temperature in a element according to EN 1991-1-5:
neglected (elements are thin-walled)
31CSI Portugal - Design of a Steel Frame
7.3 Thermal Action
1) Uniform
2) Linearly varying
3) Nonlinear
neglected (elements are flexible for bending)
Uniform temperature variation of an element:
0TTTu 
average temp. of an element
in summer or winter
considering a temp. profile
average temp.
during construction
Example:
2
outin TT
T


(bright light surface)
Location: Évora
CT
CT
º5
º45
min
max


03 T CT º200 
32CSI Portugal - Design of a Steel Frame
7.3 Thermal Action
Évora county (Zone A)
(National Annex,
Tables NA.I and NA.II)
National Annex,
Table NA.5.1
CT
CT
º18
º25
2
1


Inside temp.
Summer
Winter
Members temp.
  CTTTT º355.0 13max 
Temp. variation
CTTT
CTTT
º5.13
º15
0
0




Outside temp.
Notes:
(construction during
spring or automn)Temp. profile is deemed
linear (conservative)
  CTTT º5.65.0 2min 
Uniform temperature variation for the steel members:
DEAD
CB_LIVE ULS_STR/GEO-B1_0 1.35 1.5 0.9
ULS_STR/GEO-B1_1 1.35 1.5 0.9
ULS_STR/GEO-B1_2 1 1.5 0.9
ULS_STR/GEO-B1_3 1 1.5 0.9
ULS_STR/GEO-B1_4 1.35 1.5
ULS_STR/GEO-B1_5 1 1.5
ULS_STR/GEO-B1_6 1.35 1.5 0.9
ULS_STR/GEO-B1_7 1.35 1.5 0.9
ULS_STR/GEO-B1_8 1.35 1.5 0.9
ULS_STR/GEO-B1_9 1.35 1.5 0.9
ULS_STR/GEO-B1_10 1.35 1.5 0.9
ULS_STR/GEO-B1_11 1.35 1.5 0.9
ULS_STR/GEO-B1_12 1.35 1.5 0.9
ULS_STR/GEO-B1_13 1.35 1.5 0.9
ULS_STR/GEO-B1_14 1 1.5 0.9
ULS_STR/GEO-B1_15 1 1.5 0.9
ULS_STR/GEO-B1_16 1 1.5 0.9
ULS_STR/GEO-B1_17 1 1.5 0.9
ULS_STR/GEO-B1_18 1 1.5 0.9
ULS_STR/GEO-B1_19 1 1.5 0.9
ULS_STR/GEO-B1_20 1 1.5 0.9
ULS_STR/GEO-B1_21 1 1.5 0.9
ULS_STR/GEO-B1_22 1.35 1.5
ULS_STR/GEO-B1_23 1.35 1.5
Load pattern
LIVE WIND_2WIND_1 WIND_3 WIND_4 TEMP+ TEMP-
• 50 combinations
• 7 are deemed the most unfavourable (green)
33CSI Portugal - Design of a Steel Frame
8. Actions Combinations
Actions combinations according to EN 1990:
Note: automatic load combinations obtained using CTM 1.0 software
CB_WIND3 ULS_STR/GEO-B1_24 1.35 1.5
CB_WIND4 ULS_STR/GEO-B1_25 1.35 1.5
CB_WIND1 ULS_STR/GEO-B1_26 1 1.5
CB_WIND2 ULS_STR/GEO-B1_27 1 1.5
ULS_STR/GEO-B1_28 1 1.5
ULS_STR/GEO-B1_29 1 1.5
ULS_STR/GEO-B1_30 1.35 0.9 1.5
ULS_STR/GEO-B1_31 1.35 0.9 1.5
ULS_STR/GEO-B1_32 1.35 0.9 1.5
ULS_STR/GEO-B1_33 1.35 0.9 1.5
ULS_STR/GEO-B1_34 1.35 0.9 1.5
ULS_STR/GEO-B1_35 1.35 0.9 1.5
ULS_STR/GEO-B1_36 1.35 0.9 1.5
ULS_STR/GEO-B1_37 1.35 0.9 1.5
ULS_STR/GEO-B1_38 1 0.9 1.5
ULS_STR/GEO-B1_39 1 0.9 1.5
ULS_STR/GEO-B1_40 1 0.9 1.5
ULS_STR/GEO-B1_41 1 0.9 1.5
ULS_STR/GEO-B1_42 1 0.9 1.5
ULS_STR/GEO-B1_43 1 0.9 1.5
ULS_STR/GEO-B1_44 1 0.9 1.5
ULS_STR/GEO-B1_45 1 0.9 1.5
CB_TEMP1 ULS_STR/GEO-B1_46 1.35 1.5
CB_TEMP2 ULS_STR/GEO-B1_47 1.35 1.5
ULS_STR/GEO-B1_48 1 1.5
ULS_STR/GEO-B1_49 1 1.5
DEAD
Load pattern
LIVE WIND_2WIND_1 WIND_3 WIND_4 TEMP+ TEMP-
34CSI Portugal - Design of a Steel Frame
8. Actions Combinations
2
max.. /03.25.1903.05.1 mkNcqq ppQEdW  Maximum wind load:
Permissable loads [kN/m2]
35CSI Portugal - Design of a Steel Frame
9. Steel Sheeting Design
Trapezoidal sheet sheeting:
• 0.5 mm
Chosen thickness:
2
/41.2 mkNqRd 
Thickness: 0.5 mm
Span: 1.5 m
Permissable load:
03.241.2 .  EdWRd qq
OK
(up-lifting)
Sheeting distributed self-weight:
6 m long sheets with 0.3 m overlaping
5% of weight increase due to
joint additional elements
23
/051.07.5681.9107.405.1 mkNpEd  
sheet mass per sqr meter
36CSI Portugal - Design of a Steel Frame
9. Steel Sheeting Design
Actions on the purlins
Sheeting self-weight: mkNLpp EdEdG 077.05.1051.0. 
Uniform life load: mkNLqp EdEdQ 58.0º15cos5.14.0cos.  
Maximum wind load: mkNLqp EdWEdW 05.35.103.2.. 
Portal frame column
Sheeting
equivalent beam
Lower chord
bracing
Purlin
Transversal bracing
Endwall column
Girt or wall purlin
Rafter truss
37CSI Portugal - Design of a Steel Frame
10. Modeling the Structure
Purlins bracing rod
Girts bracing rod
Modelled members:
38CSI Portugal - Design of a Steel Frame
10. Modeling the Structure
1) Stiffness model
• Longitudinal purlins and sheeting axially fixed
2) Strength model
• All purlins axially released (simply supported)
• Purlins connect the rafters to the transversal bracing contributing
to their stability
• Purlins do not transmit thermal loads, since they are provided with
movement joints (slotted connections)
Objective: perform buckling analyses
Objective: determine stress resultants for member design
Two frame models are used:
Local axes of roof and
wall purlins:
1- axial
2- major deflection
3- minor deflection
Axis 3 (cyan) of UNP profile should
be pointing upwards to avoid dirt or
water accumulation in the profile
Axis 2 (green) should be pointing in-wards
to make the application of wind loads easy
39CSI Portugal - Design of a Steel Frame
10. Modeling the Structure
Portal frame
Rafter (planar truss)
Column
40CSI Portugal - Design of a Steel Frame
10. Modeling the Structure
Option 2: model members with
the longest length possible
Option 1: model members with
the shortest length possible
Advantages
Disadvantages
• buckling lengths are easily
identified
• buckling lengths may be more
difficult to determine
• it is necessary to determine the
imperfection forces (and eventual
P- effects) in all minor nodes
• it is only necessary to determine
the imperfection forces and P-
effects in the major nodes
Major
node
Minor
node
• only possible if the member is
uniform (continuous) • Option 2
Chosen option:
10. Modeling the Structure
• Sheeting
contributes to
stabilize the
rafters lower
chords
Rafter lower chord P- instability:
Equivalent inertia beam:
(spaced 1 m)
Frame model: Purlin
41CSI Portugal - Design of a Steel Frame
Steel sheeting modeling
42CSI Portugal - Design of a Steel Frame
11. Load Assignments
Dead Live
43CSI Portugal - Design of a Steel Frame
11. Load Assignments
Wind 1 Wind 2
44CSI Portugal - Design of a Steel Frame
11. Load Assignments
Wind 3 Wind 4
45CSI Portugal - Design of a Steel Frame
11. Load Assignments
The thermal actions on the purlins
can be ignored because they are
provided with movement joints
Thermal
CT º0
Purlins:
Rafters, columns and bracing:
CT º15
Frame buckling loads may be determined using equations (5.1) and (5.2) of EC3-1-1:
kNVEd 120
b) Transversal buckling
mH 0015.0max. 
101.61
0015.0
11
120
1


HEd
cr
h
V
H


46CSI Portugal - Design of a Steel Frame
12. Frame Buckling Analysis
• Equation (5.2) is only valid for not significantly compressed and shallow ( 26 ) rafters
)2.5()1.5(
HEd
cr
Ed
cr
cr
h
V
H
F
F

 
• Average compression force per column (LIVE load combination):
• SAP2000 stiffness model is used and 1st order analyses are performed to determine H
a) Longitudinal buckling
104.76
0012.0
11
120
1


HEd
cr
h
V
H


mH 0012.0max. 
No global 2nd order effects need to be considered
47CSI Portugal - Design of a Steel Frame
12. Frame Buckling Analysis
The lower chords buckling length may be verified using a buckling analysis:
• Only part of the structure needs to be analysed
(decreases number of buckling modes to be checked)
• Additional restraints substitute the transversal
bracing effect
• Useful to check if lower chord bracing has enough
stiffness to function propertly
• Use stiffness model (purlins and sheeting axially fixed)
• Negative buckling loads are ignored
lower chord
bracing
additional
restraint
• Buckling length is the distance between inflection points
of the buckled lower chord
Bracing system must resist the effect of member
imperfections (eventually amplified by 2nd order
effects) (EC3-1-1: 5.3.3) compressed
chord
braced point
48CSI Portugal - Design of a Steel Frame
12. Frame Buckling Analysis
a) LIVE load combination
Buckling mode 2:
37.72. b
lower chord
buckling
bracing almost
100% effective
• Buckling length may be considered as
the distance between bracing points
• Bracing must resist imperfection forces
58.114. b
• Sheeting shear stiffness likely to prevent
this mode
Buckling mode 4:
upper chord
buckling
Chord buckling modes
49CSI Portugal - Design of a Steel Frame
12. Frame Buckling Analysis
b) WIND3 load combination
51.134. b
• Sheeting shear stiffness likely to prevent
this mode
Buckling mode 4:
upper chord
buckling
Buckling mode 1:
08.71. b
lower chord
buckling
bracing almost
100% effective
• Buckling length may be considered as
the distance between bracing points
• Bracing must resist imperfection forces
Chord buckling modes
50CSI Portugal - Design of a Steel Frame
13. Equivalent Imperfection Forces
Lower chord bracing design
Member length: mL 54.1
One took advantage of bracing compressive
stiffness therefore it must be checked for its
buckling strength
Max. chord compressive
force (LIVE comb):
kNNEd 310 Axial force (lower chord):
Braced pointLateral force: kNNEd 775.025.02 
Imperfection: 005.0
Average comp. force: EdN25.0
Bracing axial force:
kNkNN Rdb 10.193.65. 
kN10.1º45cos775.0 
OKBracing buck. strength:
Comp.
(L50x5)
51CSI Portugal - Design of a Steel Frame
13. Equivalent Imperfection Forces
2) Columns initial geometric imperfection
    76.06115.0115.0  mm
(EC3-1-1: 5.3.3)
mmLe m 175001176.05000 
number of members to brace
Slotted hole ovalisation
of +/- 4 mm every 12 m
md 24
mm812244 

1) Bolt hole ovalisation (slotted connection) effect
• The purlins only work axially for displacements higher than the ovalisation
Purlin
m11
3) The effect of the ovalisation
must be added to the imperfection
mmee equiv 258170.0  
Instability loads on the transversal bracing
52CSI Portugal - Design of a Steel Frame
13. Equivalent Imperfection Forces
4) Bracing force
kNVEd 120 (LIVE load comb.)
Compressive force per column:
Supported by right bracingSupported by left bracing
Bracing force applied in each bracing system corner:
kN
LeVF equivEdEd
64.11110251206
6
3
.0



Neglectable (less than
1% of the wind load)
5) Effect of ovalisation displacement in columns
kNmH /0072.0
 
kN
HH
11.1
0072.0108 3





(from SAP2000 strength model)
to be applied on top of each column
53CSI Portugal - Design of a Steel Frame
13. Equivalent Imperfection Forces
Columns equivalent geometric imperfections
    866.02115.0115.0  mm
mh 0
Imperfection equivalent forces
 mm 115.0 
132with2  hh h 
32h
Portal frame in-plane imperfection
mh 15
kNNEd 35.012000289.0 
00289.0866.0
3
2
200
1

20010 
54CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
In SAP2000 the buckling lengths of members are determined by:
Buckl. length = K factor × L factor × Member length
There are 3 types of L factors:
• major axis L factor
• minor axis L factor
• lateral torsional L factor
Related to the rotational
stiffenesses at the member ends
Related to the
intermediate bracing
There are 5 types of K factors:
• K1.z – minor plane in braced mode
• K1.y – major plane in braced mode
• K2.y – major plane in sway mode
• K2.z – minor plane in sway mode
• KLT – lateral torsional mode
- K2 (sway mode) values
are used by default
Note:
55CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Determination of K factors
according to Annex E of old EC3:
),(KfactorK 21 
 
 22212
12111
KKKK
KKKK
cc
cc




• In SAP2000 the K factors are determined
from the components of the beams
stiffenesses in the considered plane:






 i
iicc KKK q cos11






 i
iicc KKK q cos22
Note:
- If ‘P-Delta done’ is
checked, K2.y= K2.z= KLT=1
Unbraced
Braced
56CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
L factor automatic determination
• In SAP2000 the effect of intermediate
bracing due to other bars intersecting the
member is incorporated by the L factor:
(i) Only members with q 60 w.r.t. the buckling
plane are considered as bracing elements
(ii) Stiffness or strength requirements for bracing
members are not checked
(iii) L factor is equal in minor axis buckling and
lateral torsional buckling












º307.0
º301
(minor)factorL
º607.0
º601
(major)factorL
q
q
q
q
if
if
if
if
57CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
1st Overwrite – Lateral Bracing
Overwriting K factors and L factors
• For L factors for minor plane and lateral torsional buckling
• Point bracing and/or uniform bracing on top and/or bottom
flange are possible
• Top or bottom always braces minor plane buckling
• Top or bottom only braces lateral buckling if the respective
flange is under compression
2nd Overwrite – Direct Overwrite
• For all K factors and L factors
• Overwrites the lateral bracing
overwrite if L factors are specified
• L factor = maximum unbraced length
58CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Lower chord buckling lengths
m5.1
m5.4
Member length:
Diagonal nodes spacing:
Bracing spacing:
Manually determined factors:
305.0752.145.4LTB)(FactorL
305.0752.145.4Minor)(FactorL
102.0752.145.1Major)(FactorL



Automatically determined factors:
OK
mL 752.14
59CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Upper chord buckling lengths
m5.1
m5.1
Member length:
Diagonal nodes spacing:
Purlins spacing:
Manually determined factors:
098.0261.155.1LTB)(FactorL
098.0261.155.1Minor)(FactorL
098.0261.155.1Major)(FactorL



mL 261.15
Automatically determined factors:
OK
60CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Purlins buckling lengths
m1
Member length: Equiv. Sheeting
bars spacing:
Manually determined factors:
















5.063LTB
5.063Minor
166Major
FactorL
1LTB
1Minor
1Major
sway)-(non
FactorK
mL 6
Automatically determined factors:
Not OKOK
Overwrites:
• Equiv. sheeting rods don’t provide
lateral bracing. L Factor Minor and
LTB are 0.5 due to the bracing rods
Braced nodes spacing: m3
OK
Factors after overwrite:
OK
Automatically determined factors:
OKNot OK
61CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Portal frame columns
m932.0
m5.1Member length:
Chord nodes spacing:
Girts spacing:
Manually determined factors:
 
















136.0115.1LTB
136.0115.1Minor
915.011932.011Major
FactorL
1LTB
1Minor
7.0~5.0Major
sway)-(non
FactorK
mL 11
OK
Factors after overwrite:
OK
Overwrites:
• Column has a K Factor Major
between 0.5 (fixed-fixed) or 0.7
(fixed-pinned). The latter value is
adopted conservatively
62CSI Portugal - Design of a Steel Frame
14. Members Buckling Lengths
Endwall columns
m5.1Member length: Girts spacing:mL 14
OK
Factors after overwrite:
OK
Automatically determined factors:
OKNot OK
Overwrites:
• Column has a major K Factor of
0.7 (fixed-pinned).
Manually determined factors:
















107.0145.1LTB
107.0145.1Minor
11414Major
FactorL
1LTB
1Minor
7.0Major
sway)-(non
FactorK
63CSI Portugal - Design of a Steel Frame
15. Members Automatic ULS Check
• Use SAP2000 frame strength model
Check members for collapse ULS
Steel frame design preferences:
• Interaction factors method
(EC3-1-1: Annex A and B)
• Check ‘P-Delta done’ if 2nd order effects
at the nodes are already determined
(Sway K Factors become unitary)
• Set design code and coutry
• Ignore seismic code (EC8)
• Demand/Capacity ratio limit should be
1 for ULS but may be user specified
64CSI Portugal - Design of a Steel Frame
16. Members Automatic Design
2) Select design groups
Design -> Steel Frame Design ->
Select Design Groups
3) Start design of structure
Design -> Steel Frame Design -> Start Design/Check of Structure
• If optimised member sections are significantly smaller
than the original ones, it may be necessary to run the
buckling analyses again with the new sections
Note:
1) Assign Auto select section properties to the groups
Define -> Section Properties -> Frame Sections
Add New Property -> Auto Select List
Action combinations for SLS:
Serviceability limit state (SLS): Limitation of vertical and horizontal displacements
(National Annex EN 1993-1-1)
DEAD LIVE WIND2 TEMP
SLS_CARAC_0 1 1 0.6
SLS_CARAC_1 1 1
SLS_CARAC_2 1 1 0.6
SLS_CARAC_3 1 1
SLS_CARAC_4 1 0.6 1
SLS_CARAC_5 1 1
65CSI Portugal - Design of a Steel Frame
17. SLS Check
Note: automatic load
combinations obtained
using CTM 1.0 software
2) Horizontal displacements:
(on columns top)
(frames without lift equipment)150limit h
mm 073.015011009.0 limitmax  Column (HE400A):
1) Vertical displacements:
(of every beam)
200limit L (general roof cathegory)
mm 030.02006025.0 limitmax  Purlins (UPN 140):
mm 150.020030027.0 limitmax  Rafter:
Endwall column span (HE300A): mm 070.020014015.0 limitmax  

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Design of a steel frame according to Eurocode standards

  • 1. 1 Design of a steel frame according to Eurocode – SAP2000 Training Program CSI Portugal & Spain
  • 2. 3. Portal frames 1. Architectural and environmental conditions 2. Architecture 7. Actions 4. Roof and walls sheeting 5. Purlins 8. Actions combinations 6. Bracing systems 2CSI Portugal - Design of a Steel Frame Contents of Frame Design Example Contents 9. Steel sheeting design
  • 3. 10. Modeling the structure 3CSI Portugal - Design of a Steel Frame Contents of Frame Design Example 15. Members automatic ULS check 14. Members buckling lengths 11. Load assignments 16. Members automatic design 12. Frame buckling analyses Contents (cont.) 13. Equivalent imperfection forces 17. SLS check
  • 4. Objective: Design steel structure for indoor sports facility in the suburbs of the city of Évora (Portugal) with a covered area of 60 x 30 m2 Arquitectural requirements: • Soil suitable for slallow foundations • Materials: steel S275 for framework and S235 for roof and wall sheeting concrete C25/30 rebar reinforcement: S400 4CSI Portugal - Design of a Steel Frame 1. Architectural and Environmental Conditions
  • 5. 5CSI Portugal - Design of a Steel Frame 2. Architecture 1) Flat frame imin = 0.5-1% 2) Duopitch or gable frame Slope decreases moments in the middle region of the rafters Roof shapes for drainage
  • 6. 6CSI Portugal - Design of a Steel Frame 2. Architecture 3) Single slope, monopitch or shed frame 4) Parabolic or circular frame 5) Multispan frame
  • 7. Chosen solution: 15 steep duo-pitch roof shape 7CSI Portugal - Design of a Steel Frame 2. Architecture Portal frame components:
  • 8. 8CSI Portugal - Design of a Steel Frame 3. Portal Frames Portal frames structural behaviour Simply supported because of (i) support conditions or (ii) variable inertia 1) Simply supported beam 2) Articulated (pinned) frame Isostatic
  • 9. 9CSI Portugal - Design of a Steel Frame 3. Portal Frames 3) Rigid connections frame 4) Cable stayed frame Very slender rafters prone to up-lifting by wind Hiperstatic Plastic stress-resultant redistributions possible
  • 10. 1) Hot-rolled I- or H-section profiles 2) Welded beams (composed of unperforated plates) 10 3. Portal Frames Support moments higher than span in rigid connections frame Solution: use knee joint knee joint CSI Portugal - Design of a Steel Frame Rafter solutions L < 30 ~ 35 m 3) Tapered beams: simply supported rafter Simply supported beam For simply supported rafters or articulated frames
  • 11. 4) Perforated beams: honeycomb 11CSI Portugal - Design of a Steel Frame 3. Portal Frames Increased bending resistance and stiffness maintaining shear resistance Tubes can pass throught the beams Higher costs (cuting and welding) Usually pinned beams (may not resist bending + shear at supports) 5) Cellular beams: uniform or tapered Tapered sectionUniform sectionFabrication L0/h = 15-30Similar to honeycomb + esthetics
  • 12. 6) Planar trusses Constant depth Variable depth 7) Spatial trusses Cubes or tetrahedron shape Complex connections Hollow section profiles Light solutions for long spans Reduces bracing required Boeing factory Olympic pool 12CSI Portugal - Design of a Steel Frame 3. Portal Frames L0/h = 5-6L0/h = 10-12 20 < L < 100 m
  • 13. Extreme rafter slenderness 8) Cable-stayed solutions Additional column compression Solution for large spans Roof weight vs up-lifting forces Possible up-lift due to wind forces 13CSI Portugal - Design of a Steel Frame 3. Portal Frames
  • 14. Chosen solution: Rafter: planar truss; RHS profiles; welded connections Column: HEA or HEB 14CSI Portugal - Design of a Steel Frame 3. Portal Frames Rigid connection (bolted) Rigid connection (bolted)
  • 15. • IPE, Z, U or channel purlins 15CSI Portugal - Design of a Steel Frame 3. Portal Frames 1) Regular (5-7 m) • Moderate actions • Economical solution 2) Reduced (< 5 m) • Very high loads (wind, snow, insulation materials, soil) 3) Increased (> 7 m, < 12 m) • Trussed purlins • Interior constraints to column locations • Roof sheeting suitable for long spans Portal frames spacing 6 m Chosen spacing:
  • 16. Elements: 2) Trapezoidal steel sheeting: longer spans, lighter, thermal insulation possible, better esthetics, enough longitudinal strength for purlins bracing 3) Corrugated aluminium sheeting: very light, corrosion resitant, expensive, too deformable (shorter spans), high noise in heavy rain 4) Translucid plastics (polycarbonate): low strength (shorter spans), sensitive to sunlight exposure (become brittle), combustible, very light 16CSI Portugal - Design of a Steel Frame 4. Roof and Walls Sheeting 1) Corrugated fibre-cement: economical, brittle, unesthetical, heavy, low insulation, asbestos fibres are unhealthy Sheeting: (i) Sheeting (iii) Drainage elements (ii) Purlins (iv) Joint elements and purlins bracing Steel sheeting with thermal insulation; 1.5 m spans Adopted solution:
  • 17. Main: • Transmit roof loads to the rafters • Brace the rafters upper chords or flanges Purlin solutions: - Hot rolled (IPE, UNP)1) Spans up to 9 m - Cold-formed (Z-, channel or lipped channel section) 17CSI Portugal - Design of a Steel Frame 5. Purlins 2) Spans up to 15 m - planar or spatial truss beams - Planar beam with rods - Planar beam with profiles Functions: Optional: • Brace the rafters lower chords (indirectely through the lower chords bracing rods) • Brace the portal frames for out-of-plane displacements • Transmit longitudinal horizontal endwall loads to the bracing system UNP (channel) profiles Chosen solution:
  • 18. 18CSI Portugal - Design of a Steel Frame 5. Purlins Connection to the rafter: Ovalisation: elongated bolt hole to function as a movement joint for thermal action Types of connections to the rafters: (i) lower flange bolted, (ii) plate bolted to the web, (iii) use a channel InclinedChosen configuration: Purlin configurations: Vertical Inclined • For predominatly vertical loads (snow or life) • For predominatly normal loads (wind) • Easier to execute
  • 19. 19CSI Portugal - Design of a Steel Frame 5. Purlins 1) Simply supported Supports and joints: 2) Gerber 3) Continuous beam 4) Two-span beam Purlin connection: Two-span beam in alternated configuration (see next slide) Chosen solution:
  • 20. 20CSI Portugal - Design of a Steel Frame 5. Purlins Two-span alternated configuration reactions: Purlin Rafter Two-span non- alternated: One-span: 1.875/2 6.25/2 3.75/2 6.25/2 3.75/2 2.5/2 5/2 5/2 5/2 5/2 Two-span alternated: • Distributes more uniformly the loads on the rafters
  • 21. 21CSI Portugal - Design of a Steel Frame 5. Purlins • Determined by the sheeting span (1.2-2 m normally) • Possibility of reduced spacing in localised zones (e.g., where wind loads are higher) Spacing 1.5 m Chosen spacing:
  • 22. 3) Purlins bracing 2) Rafter lower chords bracing 1) Frame longitudinal and transversal bracing 22CSI Portugal - Design of a Steel Frame 6. Bracing systems
  • 23. Transversal bracing 23CSI Portugal - Design of a Steel Frame 6. Bracing systems • resists longitudinal horizontal loads (e.g., wind loads in the enwalls) • prevents global buckling Longitudinal bracing • resists transversal horizontal loads • prevents global buckling • only used in highly deformable frames• braces the rafters (absorbs their imperfection equiv. loads) Central • thermal action generates negligible axial forces • purlins under compression for wind loads (additional beams may be necessary) Double-sided • thermal action may result in high axial forces • purlins are not subjected to compression due to wind • No longitudinal bracing Chosen bracing: • Transversal double-sided
  • 24. Rafter lower chord bracing 24CSI Portugal - Design of a Steel Frame 6. Bracing systems • May be uniformly spaced or more concentrated on the most compressed zones • Diagonal at 45 Chosen bracing: Perpendicular • works only in tension • must be fixed at both ends endwall column chord bracing rod Diagonal • normally at q=45 • low q: less flexible but may not work in compression • transfers the instability loads to the purlins • high q: more flexible due to purlin bending rafter purlin chord bracing rod
  • 25. • Absobs the roof in-plane load component • Limits purlin minor axis bending • Reduces purlins lateral buckling length 25CSI Portugal - Design of a Steel Frame 6. Bracing systems Bracing rod, tie rod or sag bar: Bracing rod anchor: a) Ridge (eave) purlins absorb the rod tension b) Diagonal rods transmit the tension to the rafters Purlins bracing • Connected using nuts and washers
  • 26. 2) Live EN 1991: Part 1-1 3) Wind actions 4) Thermal actions EN 1991: Part 1-4 EN 1991: Part 1-5 26CSI Portugal - Design of a Steel Frame 7. Actions 1) Dead EN 1991: Part 1-1
  • 27. Dead 3 77 mkNs Structural elements: Note: members dead weight is automatically determined in SAP2000 Sheeting self-weight: 2 05.0 mkNqEd  Live 2 4.0 mkNqEd Roof: kNQEd 1 (distributed) (concentrated) EN 1991-1-1 Table 6.10 H category – roof not accessible except for normal maintenance and repair EN 1991-1-1 Table A.4 27CSI Portugal - Design of a Steel Frame 7.1 Dead and Live Actions
  • 28. 28CSI Portugal - Design of a Steel Frame 7.2 Wind Action 222 /456.02725.1 2 1 2 1 mkNvq bb   Basic velocity pressure: Wind force: refppEkw AcqF . peak velocity pressure differential pressure coeficient reference area Notes: • Fw.Ed is normal to the surface • friction force can be neglected when: A// 4A∟ 2 2 // 2 3 aA aA    e.g.: Terrain category: III (regular cover of vegetation or buildings) 2 /903.0456.098.1)15()15( mkNqmcmq bep  Peak velocity pressure: smvccv bseasondirb /27270.10.10. Basic wind velocity: season factor directional factor Évora county (Zone A): vb.0=27 m/s (National Annex, Table NA.I) Peak velocity pressure (qp) fundamental velocity
  • 29. External pressure coeficient (cpe) 3.0,2.0 pic (both should be considered) Otherwise: 29CSI Portugal - Design of a Steel Frame 7.2 Wind Action Internal pressure coeficient (cpi) If area of opennings in each face is known:     openingsallofArea 0cwithopeningsofArea pe  Two wind directions are considered: º0q º90q
  • 30. 2 wind directions × 2 internal pressures = 4 wind loading cases Differential pressure coeficient (cp): 30CSI Portugal - Design of a Steel Frame 7.2 Wind Action Number of loading cases: pipep ccc 
  • 31. Temperature in a element according to EN 1991-1-5: neglected (elements are thin-walled) 31CSI Portugal - Design of a Steel Frame 7.3 Thermal Action 1) Uniform 2) Linearly varying 3) Nonlinear neglected (elements are flexible for bending) Uniform temperature variation of an element: 0TTTu  average temp. of an element in summer or winter considering a temp. profile average temp. during construction Example: 2 outin TT T  
  • 32. (bright light surface) Location: Évora CT CT º5 º45 min max   03 T CT º200  32CSI Portugal - Design of a Steel Frame 7.3 Thermal Action Évora county (Zone A) (National Annex, Tables NA.I and NA.II) National Annex, Table NA.5.1 CT CT º18 º25 2 1   Inside temp. Summer Winter Members temp.   CTTTT º355.0 13max  Temp. variation CTTT CTTT º5.13 º15 0 0     Outside temp. Notes: (construction during spring or automn)Temp. profile is deemed linear (conservative)   CTTT º5.65.0 2min  Uniform temperature variation for the steel members:
  • 33. DEAD CB_LIVE ULS_STR/GEO-B1_0 1.35 1.5 0.9 ULS_STR/GEO-B1_1 1.35 1.5 0.9 ULS_STR/GEO-B1_2 1 1.5 0.9 ULS_STR/GEO-B1_3 1 1.5 0.9 ULS_STR/GEO-B1_4 1.35 1.5 ULS_STR/GEO-B1_5 1 1.5 ULS_STR/GEO-B1_6 1.35 1.5 0.9 ULS_STR/GEO-B1_7 1.35 1.5 0.9 ULS_STR/GEO-B1_8 1.35 1.5 0.9 ULS_STR/GEO-B1_9 1.35 1.5 0.9 ULS_STR/GEO-B1_10 1.35 1.5 0.9 ULS_STR/GEO-B1_11 1.35 1.5 0.9 ULS_STR/GEO-B1_12 1.35 1.5 0.9 ULS_STR/GEO-B1_13 1.35 1.5 0.9 ULS_STR/GEO-B1_14 1 1.5 0.9 ULS_STR/GEO-B1_15 1 1.5 0.9 ULS_STR/GEO-B1_16 1 1.5 0.9 ULS_STR/GEO-B1_17 1 1.5 0.9 ULS_STR/GEO-B1_18 1 1.5 0.9 ULS_STR/GEO-B1_19 1 1.5 0.9 ULS_STR/GEO-B1_20 1 1.5 0.9 ULS_STR/GEO-B1_21 1 1.5 0.9 ULS_STR/GEO-B1_22 1.35 1.5 ULS_STR/GEO-B1_23 1.35 1.5 Load pattern LIVE WIND_2WIND_1 WIND_3 WIND_4 TEMP+ TEMP- • 50 combinations • 7 are deemed the most unfavourable (green) 33CSI Portugal - Design of a Steel Frame 8. Actions Combinations Actions combinations according to EN 1990:
  • 34. Note: automatic load combinations obtained using CTM 1.0 software CB_WIND3 ULS_STR/GEO-B1_24 1.35 1.5 CB_WIND4 ULS_STR/GEO-B1_25 1.35 1.5 CB_WIND1 ULS_STR/GEO-B1_26 1 1.5 CB_WIND2 ULS_STR/GEO-B1_27 1 1.5 ULS_STR/GEO-B1_28 1 1.5 ULS_STR/GEO-B1_29 1 1.5 ULS_STR/GEO-B1_30 1.35 0.9 1.5 ULS_STR/GEO-B1_31 1.35 0.9 1.5 ULS_STR/GEO-B1_32 1.35 0.9 1.5 ULS_STR/GEO-B1_33 1.35 0.9 1.5 ULS_STR/GEO-B1_34 1.35 0.9 1.5 ULS_STR/GEO-B1_35 1.35 0.9 1.5 ULS_STR/GEO-B1_36 1.35 0.9 1.5 ULS_STR/GEO-B1_37 1.35 0.9 1.5 ULS_STR/GEO-B1_38 1 0.9 1.5 ULS_STR/GEO-B1_39 1 0.9 1.5 ULS_STR/GEO-B1_40 1 0.9 1.5 ULS_STR/GEO-B1_41 1 0.9 1.5 ULS_STR/GEO-B1_42 1 0.9 1.5 ULS_STR/GEO-B1_43 1 0.9 1.5 ULS_STR/GEO-B1_44 1 0.9 1.5 ULS_STR/GEO-B1_45 1 0.9 1.5 CB_TEMP1 ULS_STR/GEO-B1_46 1.35 1.5 CB_TEMP2 ULS_STR/GEO-B1_47 1.35 1.5 ULS_STR/GEO-B1_48 1 1.5 ULS_STR/GEO-B1_49 1 1.5 DEAD Load pattern LIVE WIND_2WIND_1 WIND_3 WIND_4 TEMP+ TEMP- 34CSI Portugal - Design of a Steel Frame 8. Actions Combinations
  • 35. 2 max.. /03.25.1903.05.1 mkNcqq ppQEdW  Maximum wind load: Permissable loads [kN/m2] 35CSI Portugal - Design of a Steel Frame 9. Steel Sheeting Design Trapezoidal sheet sheeting: • 0.5 mm Chosen thickness: 2 /41.2 mkNqRd  Thickness: 0.5 mm Span: 1.5 m Permissable load: 03.241.2 .  EdWRd qq OK (up-lifting)
  • 36. Sheeting distributed self-weight: 6 m long sheets with 0.3 m overlaping 5% of weight increase due to joint additional elements 23 /051.07.5681.9107.405.1 mkNpEd   sheet mass per sqr meter 36CSI Portugal - Design of a Steel Frame 9. Steel Sheeting Design Actions on the purlins Sheeting self-weight: mkNLpp EdEdG 077.05.1051.0.  Uniform life load: mkNLqp EdEdQ 58.0º15cos5.14.0cos.   Maximum wind load: mkNLqp EdWEdW 05.35.103.2.. 
  • 37. Portal frame column Sheeting equivalent beam Lower chord bracing Purlin Transversal bracing Endwall column Girt or wall purlin Rafter truss 37CSI Portugal - Design of a Steel Frame 10. Modeling the Structure Purlins bracing rod Girts bracing rod Modelled members:
  • 38. 38CSI Portugal - Design of a Steel Frame 10. Modeling the Structure 1) Stiffness model • Longitudinal purlins and sheeting axially fixed 2) Strength model • All purlins axially released (simply supported) • Purlins connect the rafters to the transversal bracing contributing to their stability • Purlins do not transmit thermal loads, since they are provided with movement joints (slotted connections) Objective: perform buckling analyses Objective: determine stress resultants for member design Two frame models are used:
  • 39. Local axes of roof and wall purlins: 1- axial 2- major deflection 3- minor deflection Axis 3 (cyan) of UNP profile should be pointing upwards to avoid dirt or water accumulation in the profile Axis 2 (green) should be pointing in-wards to make the application of wind loads easy 39CSI Portugal - Design of a Steel Frame 10. Modeling the Structure
  • 40. Portal frame Rafter (planar truss) Column 40CSI Portugal - Design of a Steel Frame 10. Modeling the Structure Option 2: model members with the longest length possible Option 1: model members with the shortest length possible Advantages Disadvantages • buckling lengths are easily identified • buckling lengths may be more difficult to determine • it is necessary to determine the imperfection forces (and eventual P- effects) in all minor nodes • it is only necessary to determine the imperfection forces and P- effects in the major nodes Major node Minor node • only possible if the member is uniform (continuous) • Option 2 Chosen option:
  • 41. 10. Modeling the Structure • Sheeting contributes to stabilize the rafters lower chords Rafter lower chord P- instability: Equivalent inertia beam: (spaced 1 m) Frame model: Purlin 41CSI Portugal - Design of a Steel Frame Steel sheeting modeling
  • 42. 42CSI Portugal - Design of a Steel Frame 11. Load Assignments Dead Live
  • 43. 43CSI Portugal - Design of a Steel Frame 11. Load Assignments Wind 1 Wind 2
  • 44. 44CSI Portugal - Design of a Steel Frame 11. Load Assignments Wind 3 Wind 4
  • 45. 45CSI Portugal - Design of a Steel Frame 11. Load Assignments The thermal actions on the purlins can be ignored because they are provided with movement joints Thermal CT º0 Purlins: Rafters, columns and bracing: CT º15
  • 46. Frame buckling loads may be determined using equations (5.1) and (5.2) of EC3-1-1: kNVEd 120 b) Transversal buckling mH 0015.0max.  101.61 0015.0 11 120 1   HEd cr h V H   46CSI Portugal - Design of a Steel Frame 12. Frame Buckling Analysis • Equation (5.2) is only valid for not significantly compressed and shallow ( 26 ) rafters )2.5()1.5( HEd cr Ed cr cr h V H F F    • Average compression force per column (LIVE load combination): • SAP2000 stiffness model is used and 1st order analyses are performed to determine H a) Longitudinal buckling 104.76 0012.0 11 120 1   HEd cr h V H   mH 0012.0max.  No global 2nd order effects need to be considered
  • 47. 47CSI Portugal - Design of a Steel Frame 12. Frame Buckling Analysis The lower chords buckling length may be verified using a buckling analysis: • Only part of the structure needs to be analysed (decreases number of buckling modes to be checked) • Additional restraints substitute the transversal bracing effect • Useful to check if lower chord bracing has enough stiffness to function propertly • Use stiffness model (purlins and sheeting axially fixed) • Negative buckling loads are ignored lower chord bracing additional restraint • Buckling length is the distance between inflection points of the buckled lower chord Bracing system must resist the effect of member imperfections (eventually amplified by 2nd order effects) (EC3-1-1: 5.3.3) compressed chord braced point
  • 48. 48CSI Portugal - Design of a Steel Frame 12. Frame Buckling Analysis a) LIVE load combination Buckling mode 2: 37.72. b lower chord buckling bracing almost 100% effective • Buckling length may be considered as the distance between bracing points • Bracing must resist imperfection forces 58.114. b • Sheeting shear stiffness likely to prevent this mode Buckling mode 4: upper chord buckling Chord buckling modes
  • 49. 49CSI Portugal - Design of a Steel Frame 12. Frame Buckling Analysis b) WIND3 load combination 51.134. b • Sheeting shear stiffness likely to prevent this mode Buckling mode 4: upper chord buckling Buckling mode 1: 08.71. b lower chord buckling bracing almost 100% effective • Buckling length may be considered as the distance between bracing points • Bracing must resist imperfection forces Chord buckling modes
  • 50. 50CSI Portugal - Design of a Steel Frame 13. Equivalent Imperfection Forces Lower chord bracing design Member length: mL 54.1 One took advantage of bracing compressive stiffness therefore it must be checked for its buckling strength Max. chord compressive force (LIVE comb): kNNEd 310 Axial force (lower chord): Braced pointLateral force: kNNEd 775.025.02  Imperfection: 005.0 Average comp. force: EdN25.0 Bracing axial force: kNkNN Rdb 10.193.65.  kN10.1º45cos775.0  OKBracing buck. strength: Comp. (L50x5)
  • 51. 51CSI Portugal - Design of a Steel Frame 13. Equivalent Imperfection Forces 2) Columns initial geometric imperfection     76.06115.0115.0  mm (EC3-1-1: 5.3.3) mmLe m 175001176.05000  number of members to brace Slotted hole ovalisation of +/- 4 mm every 12 m md 24 mm812244   1) Bolt hole ovalisation (slotted connection) effect • The purlins only work axially for displacements higher than the ovalisation Purlin m11 3) The effect of the ovalisation must be added to the imperfection mmee equiv 258170.0   Instability loads on the transversal bracing
  • 52. 52CSI Portugal - Design of a Steel Frame 13. Equivalent Imperfection Forces 4) Bracing force kNVEd 120 (LIVE load comb.) Compressive force per column: Supported by right bracingSupported by left bracing Bracing force applied in each bracing system corner: kN LeVF equivEdEd 64.11110251206 6 3 .0    Neglectable (less than 1% of the wind load) 5) Effect of ovalisation displacement in columns kNmH /0072.0   kN HH 11.1 0072.0108 3      (from SAP2000 strength model) to be applied on top of each column
  • 53. 53CSI Portugal - Design of a Steel Frame 13. Equivalent Imperfection Forces Columns equivalent geometric imperfections     866.02115.0115.0  mm mh 0 Imperfection equivalent forces  mm 115.0  132with2  hh h  32h Portal frame in-plane imperfection mh 15 kNNEd 35.012000289.0  00289.0866.0 3 2 200 1  20010 
  • 54. 54CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths In SAP2000 the buckling lengths of members are determined by: Buckl. length = K factor × L factor × Member length There are 3 types of L factors: • major axis L factor • minor axis L factor • lateral torsional L factor Related to the rotational stiffenesses at the member ends Related to the intermediate bracing There are 5 types of K factors: • K1.z – minor plane in braced mode • K1.y – major plane in braced mode • K2.y – major plane in sway mode • K2.z – minor plane in sway mode • KLT – lateral torsional mode - K2 (sway mode) values are used by default Note:
  • 55. 55CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Determination of K factors according to Annex E of old EC3: ),(KfactorK 21     22212 12111 KKKK KKKK cc cc     • In SAP2000 the K factors are determined from the components of the beams stiffenesses in the considered plane:        i iicc KKK q cos11        i iicc KKK q cos22 Note: - If ‘P-Delta done’ is checked, K2.y= K2.z= KLT=1 Unbraced Braced
  • 56. 56CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths L factor automatic determination • In SAP2000 the effect of intermediate bracing due to other bars intersecting the member is incorporated by the L factor: (i) Only members with q 60 w.r.t. the buckling plane are considered as bracing elements (ii) Stiffness or strength requirements for bracing members are not checked (iii) L factor is equal in minor axis buckling and lateral torsional buckling             º307.0 º301 (minor)factorL º607.0 º601 (major)factorL q q q q if if if if
  • 57. 57CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths 1st Overwrite – Lateral Bracing Overwriting K factors and L factors • For L factors for minor plane and lateral torsional buckling • Point bracing and/or uniform bracing on top and/or bottom flange are possible • Top or bottom always braces minor plane buckling • Top or bottom only braces lateral buckling if the respective flange is under compression 2nd Overwrite – Direct Overwrite • For all K factors and L factors • Overwrites the lateral bracing overwrite if L factors are specified • L factor = maximum unbraced length
  • 58. 58CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Lower chord buckling lengths m5.1 m5.4 Member length: Diagonal nodes spacing: Bracing spacing: Manually determined factors: 305.0752.145.4LTB)(FactorL 305.0752.145.4Minor)(FactorL 102.0752.145.1Major)(FactorL    Automatically determined factors: OK mL 752.14
  • 59. 59CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Upper chord buckling lengths m5.1 m5.1 Member length: Diagonal nodes spacing: Purlins spacing: Manually determined factors: 098.0261.155.1LTB)(FactorL 098.0261.155.1Minor)(FactorL 098.0261.155.1Major)(FactorL    mL 261.15 Automatically determined factors: OK
  • 60. 60CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Purlins buckling lengths m1 Member length: Equiv. Sheeting bars spacing: Manually determined factors:                 5.063LTB 5.063Minor 166Major FactorL 1LTB 1Minor 1Major sway)-(non FactorK mL 6 Automatically determined factors: Not OKOK Overwrites: • Equiv. sheeting rods don’t provide lateral bracing. L Factor Minor and LTB are 0.5 due to the bracing rods Braced nodes spacing: m3 OK Factors after overwrite: OK
  • 61. Automatically determined factors: OKNot OK 61CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Portal frame columns m932.0 m5.1Member length: Chord nodes spacing: Girts spacing: Manually determined factors:                   136.0115.1LTB 136.0115.1Minor 915.011932.011Major FactorL 1LTB 1Minor 7.0~5.0Major sway)-(non FactorK mL 11 OK Factors after overwrite: OK Overwrites: • Column has a K Factor Major between 0.5 (fixed-fixed) or 0.7 (fixed-pinned). The latter value is adopted conservatively
  • 62. 62CSI Portugal - Design of a Steel Frame 14. Members Buckling Lengths Endwall columns m5.1Member length: Girts spacing:mL 14 OK Factors after overwrite: OK Automatically determined factors: OKNot OK Overwrites: • Column has a major K Factor of 0.7 (fixed-pinned). Manually determined factors:                 107.0145.1LTB 107.0145.1Minor 11414Major FactorL 1LTB 1Minor 7.0Major sway)-(non FactorK
  • 63. 63CSI Portugal - Design of a Steel Frame 15. Members Automatic ULS Check • Use SAP2000 frame strength model Check members for collapse ULS Steel frame design preferences: • Interaction factors method (EC3-1-1: Annex A and B) • Check ‘P-Delta done’ if 2nd order effects at the nodes are already determined (Sway K Factors become unitary) • Set design code and coutry • Ignore seismic code (EC8) • Demand/Capacity ratio limit should be 1 for ULS but may be user specified
  • 64. 64CSI Portugal - Design of a Steel Frame 16. Members Automatic Design 2) Select design groups Design -> Steel Frame Design -> Select Design Groups 3) Start design of structure Design -> Steel Frame Design -> Start Design/Check of Structure • If optimised member sections are significantly smaller than the original ones, it may be necessary to run the buckling analyses again with the new sections Note: 1) Assign Auto select section properties to the groups Define -> Section Properties -> Frame Sections Add New Property -> Auto Select List
  • 65. Action combinations for SLS: Serviceability limit state (SLS): Limitation of vertical and horizontal displacements (National Annex EN 1993-1-1) DEAD LIVE WIND2 TEMP SLS_CARAC_0 1 1 0.6 SLS_CARAC_1 1 1 SLS_CARAC_2 1 1 0.6 SLS_CARAC_3 1 1 SLS_CARAC_4 1 0.6 1 SLS_CARAC_5 1 1 65CSI Portugal - Design of a Steel Frame 17. SLS Check Note: automatic load combinations obtained using CTM 1.0 software 2) Horizontal displacements: (on columns top) (frames without lift equipment)150limit h mm 073.015011009.0 limitmax  Column (HE400A): 1) Vertical displacements: (of every beam) 200limit L (general roof cathegory) mm 030.02006025.0 limitmax  Purlins (UPN 140): mm 150.020030027.0 limitmax  Rafter: Endwall column span (HE300A): mm 070.020014015.0 limitmax  