ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

Seismic
design
of
steel

building
accordance
to

Eurocode
3
and
8

Valentinos
Neophytou
BEng,
MSc

JULY
2013

-‐Worked
examples
–
Hand
calculations

ETABS
manual

ABOUT THIS DOCUMENT
This publication provides a concise compilation of selected rules in the Eurocode 8, together
with relevant Cyprus National Annex, that relate to the design of common forms of concrete
building structure in the South Europe. It id offers a detail view of the design of steel framed
buildings to the structural Eurocodes and includes a set of worked examples showing the
design of structural elements with using software (CSI ETABS). It is intended to be of
particular to the people who want to become acquainted with design to the Eurocodes. Rules
from EN 1998-1-1 for global analysis, type of analysis and verification checks are presented.
Detail design rules for steel composite beam, steel column, steel bracing and composite slab
with steel sheeting from EN 1998-1-1, EN1993-1-1 and EN1994-1-1 are presented. This
guide covers the design of orthodox members in steel frames. It does not cover design rules
for regularities. Certain practical limitations are given to the scope.
Due to time constraints and knowledge, I may not be able to address the whole issues.
Please send me your suggestions for improvement. Anyone interested to share his/her
knowledge or willing to contribute either totally a new section about Eurocode 8 or within
this section is encouraged.
For further details:
My LinkedIn Profile:
http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top
Email: valentinos_n@hotmail.com
Slideshare Account: http://www.slideshare.net/ValentinosNeophytou

List of contents
1.1 DESIGN AND ANALYSIS EXAMPLE OF STEEL FRAME WITH CONCENTRIC
BRACING .................................................................................................................................7
1.1 LAYOUT OF STRUCTURE...............................................................................................7
1.2 PRELIMINARY DESIGN...................................................................................................9
1.2.1 PRELIMINARY DESIGN OF COLUMNS AND BEAMS ............................................9
1.3 MATERIAL PROPERTIES ..............................................................................................11
1.3.1 MATERIAL PROPERTIES OF CONCRETE...............................................................11
1.3.2 MATERIAL PROPERTIES OF STEEL ........................................................................12
1.3.3 MATERIAL PROPERTIES OF STEEL AND CONCRETE AS DEFINE IN ETABS 13
1.3.4.1 MODELING REQUIREMENTS OF EC8 FOR CONCRETE MEMBERS...............15
1.3.4.2 MODELING REQUIREMENTS OF EC8 FOR FLOOR DIAPHRAGMS................15
1.3.4.3 MESHING OF SLABS................................................................................................16
1.4 JOINT MODELING (EN1993-1-1,CL.5.1.2) ...................................................................17
2.0 MODAL RESPONSE SPECTRUM ANALYSIS.............................................................20
2.1 STRUCTURAL TYPES AND BEHAVIOR FACTOR ACCORDING TO EN1998-1-
1,CL.6.3 ...................................................................................................................................20
2.2 DEFINE DESIGN HORIZONTAL RESPONSE SPECTRUM........................................24
2.2.1 VERTICAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.3)................................24
2.2.2 HORIZONTAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5)..........................24
2.2.3 PARAMETERS OF ELASTIC RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5)..25
2.2.3.1 GROUND INVESTIGATION CONDITIONS...........................................................29
2.2.3.2 IMPORTANCE FACTOR...........................................................................................29
2.2.3.3 DUCTILITY CLASS...................................................................................................30
2.3 ANALYSIS TYPES ..........................................................................................................31
2.3.1 MODAL RESPONSE SPECTRUM ANALYSIS..........................................................31
2.3.1.1 ACCIDENTAL ECCENTRICITY..............................................................................32
2.3.2 LATERAL FORCE ANALYSIS REQUIREMENTS....................................................34
2.3.4 ESTIMATION OF FUNDAMENTAL PERIOD T1 ......................................................35
2.3.5 AUTOMATIC LATERAL FORCE ANALYSIS USING ETABS................................36
2.3.6 USER LOADS - LATERAL FORCE ANALYSIS USING ETABS.............................38

2.3.7 TORSIONAL EFFECTS ................................................................................................45
2.3.8 SUMMARY OF ANALYSIS PROCESS IN SEISMIC DESIGN SITUATION...........46
3.0 DEFINE STATIC LOADS................................................................................................47
4.0 SEISMIC MASS REQUIREMENTS ACCORDING TO EC8.........................................48
4.1 MASS SOURCE OPTION ................................................................................................49
5.0 WIND LOADING ON STRUCTURE (EN1991-1-4:2004)..............................................51
5.1 CALCULATION OF WIND LOAD ACCORDING TO EN1991-1-4:2004....................51
5.2 APPLICATION OF WIND LOADING USING ETABS .................................................54
6.0 LOAD COMBINATION...................................................................................................59
7.0 DESIGN PREFERENCES ................................................................................................61
8.0 ANALYSIS AND DESIGN REQUIREMENTS FOR CONCENTRICALLY BRACED
FRAMES ACCORDING TO EN1998-1-1,CL.6.7.2 ..............................................................64
8.1 STEPS OF THE DESIGN DETAIL OF CONCENTRIC STEEL FRAMES ...................65
8.2 CLASSIFICATION OF STEEL SECTIONS....................................................................66
8.3 DESIGN OF COMPOSITE SLAB UNDER GRAVITY LOADS....................................68
8.4 DESIGN OF COMPOSITE BEAM (WITH STEEL SHEETING) UNDER GRAVITY
LOADS ....................................................................................................................................72
8.5 DETAIL DESIGN OF STEEL COLUMNS UNDER GRAVITY LOADS......................79
8.6 DETAIL DESIGN RULES OF STEEL CONCENTRIC BRACED FRAMES (CBF)
ACCORDING TO EUROCODE 8..........................................................................................87
8.6.1 DETAIL DESIGN RULES OF STEEL BRACING ACCORDING TO EUROCODE 8
..................................................................................................................................................87
8.7 DETAIL DESIGN RULES OF STEEL COLUMNS AND BEAMS ACCORDING TO
EUROCODE 8.........................................................................................................................88
8.8 DETAIL DESIGN RULES OF STEEL COMPOSITE MEMBERS ACCORDING TO
EUROCODE 8.........................................................................................................................89
8.9 DETAIL DESIGN RULES OF STEEL MOMENT RESISTANCE FRAMES (MRF)
ACCORDING TO EUROCODE 8..........................................................................................90
8.9.1 DETAIL DESIGN RULES FOR MRF - DESIGN CRITERIA....................................90
8.9.2 DETAIL DESIGN RULES OF STEEL BEAM FOR MRF...........................................90
8.9.3 DETAIL DESIGN RULES OF STEEL COLUMN FOR MRF.....................................91
9.0 DESIGN OF STEEL FRAMES.........................................................................................92
9.1 DESIGN OF STEEL MEMBER OVERWRITES DATA.................................................92

9.2 DESIGN OF COLUMNS / BEAMS USING ETABS – GRAVITY LOAD ANALYSIS
ONLY ......................................................................................................................................97
9.3 DESIGN OF STEEL COLUMN (GRAVITY DESIGN SITUATION) – HAND
CALCULATIONS.................................................................................................................105
9.4 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATIONN).........................118
9.4.1 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATION – HAND
CALCULATION)..................................................................................................................124
9.5 DESIGN OF COMPOSITE BEAMS - HAND CALCULATIONS................................128
9.5 DESIGN OF STEEL BRACING.....................................................................................145
9.5.1 MAIN CONFIGURATION OF DESIGN OF STEEL BRACING..............................145
9.5.2 SIMPLIFIED DESIGN OF FRAMES WITH X BRACING (EXTRACT FROM
DESIGN GUIDANCE TO EC8) ...........................................................................................147
9.5.3 MODEL IN ETABS .....................................................................................................148
9.5.4 DESIGN OF STEEL BRACING (GRAVITY/SEISMIC DESIGN SITUATION) –
HAND CALCULATION.......................................................................................................156
10.0 MODAL RESPONSE SPECTRUM ANALYSIS.........................................................170
10.1 SET THE ANALYSIS OPTIONS.................................................................................170
10.2 EVALUATE THE ANALYSIS RESULTS OF THE STRUCTURE ACCORDING TO
THE MODAL ANALYSIS REQUIREMENTS ...................................................................171
10.2.1 ASSESS THE MODAL ANALYSIS RESULTS BASED ON THE EN1998...........172
11.0 SECOND ORDER EFFECTS (P – Δ EFFECTS) ACCORDING TO EN1998-1-
1,CL.4.4.2.2 ...........................................................................................................................173
11.1 DISPLACEMENT CALCULATION ACCORDING TO EN1998-1-1,CL.4.4.2.2 .....174
11.2 INTERSTOREY DRIFT................................................................................................174
11.3 CALCULATION OF SECOND ORDER EFFECT USING ETABS...........................175
11.3.1 INTERSTOREY DRIFT DISPLACEMENT .............................................................176
11.3.2 TOTAL GRAVITY LOAD PTOT................................................................................178
11.3.2 TOTAL SEISMIC STOREY SHEAR VTOT...............................................................180
12.0 DAMAGE LIMITATION ACCORDING TO EN1998-1-1,CL.4.4.3 ..........................184
12.1 CALCULATION OF DAMAGE LIMITATION..........................................................185
ANNEX - A ..........................................................................................................................186
ANNEX A.1 - ASSUMPTIONS MADE IN THE DESIGN ALGORITHM (MANUAL OF
ETABS – EC3 & EC8) ..........................................................................................................186

A1.1:LIMITATION MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS –
EC3&EC8).............................................................................................................................187
ANNEX –B: STEEL DESIGN FLOWCHARTS..................................................................188

1.1 Design and analysis example of steel frame with concentric bracing
1.1 Layout of structure
Figure 1.1: Plan view
Figure 1.2: Side Elevation (4) & (1)

Figure 1.3: Side Elevation (A) & (D)
Table 1.1: Dimensions of the building
Dimensions Symbol Value Units
Storey height h 3.0 m
Total height of the building H 9.0 m
Beam length in X-direction lx 5.0 m
Beam length in Y-direction ly 5.0 m
Building width in X-direction Lx 15.0 m
Building width in Y-direction Ly 15.0 m

1.2 Preliminary design
Table 1.2: Seismic design data
Data Symbol Value Units
Seismic zone - 3 -
Reference peak ground acceleration on type A
ground, agR.
agR 0.25 m/s2
Importance class γI 1.0 -
Design ground acceleration on type A ground ag 0.25 m/s2
Design spectrum - Type 1 -
Ground type - B -
Structural system Steel frame with concentric bracing
Behavior factor q 4.0 -
1.2.1 Preliminary design of columns and beams
Preliminary design of steel beam
Design data:
Span of beam
Bay width
Overall depth of slab
Loading data:
Density of concrete
Loads of floor per meter
Live load
Live load per meter
Partial factor for actions:
Safety factor are obtain from Table A.1(2)B EN1990
Permanent actions, γ G
Variable actions, γ Q
Total load
Lx 5000mm:=
wbay 5000mm:=
h 130mm:=
γ c 25kN m
3−
⋅:=
gfloor γ c h⋅ Lx⋅ 16.25 kN m
1−
⋅⋅=:=
qoffice 2kN m
2−
⋅:=
qservice qoffice Lx⋅ 10 kN m
1−
⋅⋅=:=
γ G 1.35:=
γ Q 1.5:=
Ed γ G gfloor⋅ γ Q qservice⋅+ 36.94 kN m
1−
⋅⋅=:=

Material properties:
Young Modulus of Elasticity
Structural steel (clause 6.1(1) EN 1993 1-1)
Structural steel properties:
Yield strength, fy
Ultimate strength, fu
Yield strength of reinforcement, fyk
Deflection limitation:
Deflection limit - General purpose
Second moment area required
Second moment area provided (IPE240)
Moment resistance check:
Design moment (Fixed end)
Plastic modulus required
Plastic modulus provided (IPE240)
Weak Beam - Strong column -Capacity design:
Plastic modulus of column required
Plastic modulus of column provided (HE220A)
Es 210kN mm
2−
⋅:=
γ M0 1.0:=
fy 355N mm
2−
⋅:=
fu 450N mm
2−
⋅:=
fyk 500N mm
2−
⋅:=
F
Lx
300
:=
Ireq
300 Ed⋅ Lx
3
⋅
384 Es⋅
1.718 10
3
× cm
4
⋅=:=
Iprov 3892cm
4
:=
Check_1 if Iprov Ireq> "OK", "NOT OK",( ):=
Check_1 "OK"=
MEd
Ed Lx
2
⋅
12
76.953kN m⋅⋅=:=
Wpl.y.req
MEd
fy
216.769cm
3
⋅=:=
Wpl.y 324.4cm
3
:=
Check_2 if Wpl.y Wpl.y.req> "OK", "NOT OK",( ):=
Check_2 "OK"=
Wpl.y.c.req 1.3 Wpl.y⋅ 421.72cm
3
=:=
Wpl.y.c 515cm
3
:=
Check_3 if Wpl.y.c Wpl.y.c.req> "OK", "NOT OK",( ):=
Check_3 "OK"=

1.3 Material properties
ETABS: Define > Material properties
1.3.1 Material properties of concrete
Design requirement
Poisson ratio is equal to v = 0 (cracked concrete) and v = 0.2 (un-cracked concrete) as
(EN1992-1-1,cl.3.1.3).
Table 1.3: Concrete properties (EN 1992, Table 3.1)
Property Data for concrete
C16/20
(N/mm2
)
C20/25
(N/mm2
)
C25/30
(N/mm2
)
C30/37
(N/mm2
)
Mass per unit Volume 2,5E-09 2,5E-09 2,5E-09 2,5E-09
Weight per unit volume 2,5E-05 2,5E-05 2,5E-05 2,5E-05
Modulus of Elasticity 29000 30000 31000 33000
Poisson’s Ratio (cracked concrete) 0 0 0 0
Coeff. of thermal expansion 10E-06 10E-06 10E-06 10E-06
Charact. ConcCyl. Strength, fck 16 20 25 30
Bending Reinf. Yield stress, fyk 500 500 500 500
Shear Reinf. Yield stress, fyk 500 500 500 500

1.3.2 Material properties of steel
Table 1.4: Material properties of steel
Material Properties Symbol Value Units References
Mass per unit Volume γs 7.85E-09 kg/mm3
EN1991-1-1,table A.4
Weight per unit
Volume
γs 7.70E-05 N/mm3
EN1991-1-1,table A.4
Modulus of Elasticity Es 210,000 N/mm2
EN1993-1-1,cl.3.2.6(1)
Poisson’s ratio ν 0.3 - EN1993-1-1,cl.3.2.6(1)
Coeff of Thermal
Expansion
(Steel structures)
α 1.2x10-5
per K (for T ≤ 100o
C) K EN1993-1-1,cl.3.2.6(1)
Coeff of Thermal
Expansion
(Composite Concrete-
Steel structures)
α 1.2x10-5
per K (for T ≤ 100o
C) K EN1993-1-1,cl.3.2.6(1)
Shear Modulus G ≈81,000 N/mm2
EN1993-1-1,cl.3.2.6(1)
Characteristic yield
strength of steel profile
fy 275 N/mm2 EN1993-1-1,table 3.1
Ultimate strength fu 430 N/mm2
EN1993-1-1,table 3.1
Table 1.5: Strength vales of steel sections (EN1993-1-1,table 3.1)
Steel grade
Nominal thickness of the element t (mm)
t ≤ 40mm 40mm < t ≤ 80mm Grade
referencefy (N/mm2
) fu (N/mm2
) fy (N/mm2
) fu (N/mm2
)
S235 235 360 215 360 EN 10025-2
S275 275 430 255 410 EN 10025-2
S355 355 510 335 470 EN 10025-2
S450 440 550 410 550 EN 10025-2
Note: You may use the product standard instead of those given in EN1993-1-1

1.3.3 Material properties of steel and concrete as define in ETABS
Figure 1.4: Material properties of concrete (C25/30)
Figure 1.5: Material properties of steel (S275)
1.3.4 Slab modeling

Table 1.6: Slab properties
Slab depth hs 170 mm
Diameter of stud d 19 mm
Height of stud haw 152 mm
Tensile strength of stud fu 430 N/mm2
ETABS: Define > Wall/Slab/Deck Sections/Add new deck
Figure 1.6: Deck section properties
Press “Set Modifier” in order
to modify the slab properties

1.3.4.1 Modeling requirements of EC8 for concrete members
1. Unless a more accurate analysis of the cracked elements is performed, the elastic
flexural and shear stiffness properties of concrete and masonry elements may be taken
to be equal to one-half of the corresponding stiffness of the un-cracked elements
(EN1998-1-1,cl.4.3.1(7)).
Figure 1.7: Modified “Stiffness Modifiers”
1.3.4.2 Modeling requirements of EC8 for floor diaphragms
ETABS: Select > Wall/Slab/Deck section > Select Deck
ETABS: Define > Diaphragms
ETABS: Select “D1” (Rigid diaphragms)
2. When the floor diaphragms of the building may be taken as being rigid in their planes,
the masses and the moments of inertia of each floor may be lumped at the centre of
gravity (EN1998-1-1,cl.4.3.1(4)).

1.3.4.3 Meshing of slabs
ETABS: Select > Wall/Slab/Deck section > Select Deck
ETABS: Assign > Shell area > Auto Object Auto mesh option
When you have a composite beam floor system, ETABS, by default, automatically meshes
(divides) the deck at every beam and girder. This allows ETABS to automatically distribute
the loading on the deck to each beam or girder in an appropriate manner.
Figure 1.8: Meshing of composite slab
Figure 1.9: Meshing of normal slab

1.4 Joint modeling (EN1993-1-1,cl.5.1.2)
(1) The effects of the behavior of the joints on the distribution of internal forces and
moments within a structure, and on the overall deformations of the structure, may
generally be neglected, but where such effects are significant (such as in the case of
semi-continuous joints) they should be taken into account, see EN 1993-1-8.
(2) (2) To identify whether the effects of joint behavior on the analysis need be taken into
account, a distinction may be made between three joint models as follows, see EN
1993-1-8, 5.1.1:
– simple, in which the joint may be assumed not to transmit bending
moments.
– continuous, in which the behavior of the joint may be assumed to have no
effect on the analysis.
– semi-continuous, in which the behavior of the joint needs to be taken into
account in the analysis.

Table 1.7: Example of joint types
Simple joint Continuous Fixed joint Semi- continuous joint
ETABS: Pin joint in ETABS
The pin-joint in ETABS can be achieved by selecting the members that you assumed to be
pinned in the analysis process. This can be done as follow:
Select member > Assign > Frame/Line > Frame Releases Partial Fixity
Figure 1.10: Pinned joint (both ends)

ETABS: Fixed joint in ETABS
The fixed-joint in ETABS can be achieved by selecting the members that you assumed to be
fixed in the analysis process. This can be done as follow:
Select member > Assign > Frame/Line > Frame Releases Partial Fixity
Figure 1.11: Fixed joint

2.0 Modal Response Spectrum Analysis
2.1 Structural types and behavior factor according to EN1998-1-1,cl.6.3
Table 2.1: Structural types and behavior factor
Structural Type
q-factor
DCM DCH
Moment resisting frames (MRF)
αu/ α1 =1.1 αu/ α1 =1.2 (1 bay)
αu/ α1 =1.3 (multi-bay)
dissipative zones in beams and column bases
4 5αu/ α1
Concentrically braced frames (CBF)
Dissipative zones in tension diagonals
4 4
V-braced frames (CBF)
2 2.5

Dissipative zones in tension and compression diagonals
Frames with K-bracing (CBF)
Not allowed in
dissipative design
Eccentrically braced frame (EBF)
αu/ α1 =1.2
dissipative zones in bending or shear links
4 5αu/ α1
Inverted pendulum system
αu/ α1 =1.0 αu/ α1 =1.1
dissipative zones in column base, or column ends (NEd/Npl,Rd < 0.3)
2 2αu/ α1
Moment-resisting frames with concentric bracing (MRF) + (CBF)
4 4αu/ α1

αu/ α1 =1.2
dissipative zones in moment frame and tension diagonals
Moment frames with
infills Unconnected concrete or masonry infills,
in contact with the frame 2 2
Connected reinforced concrete
Infills
See EN1998-1-1,table
5.1
Infills isolated from moment frame
4 5αu/ α1
Structures with concrete cores or walls
See EN1998-1-1,table
5.1
Note: If the building is non-regular in elevation (see EN1998-1-1,cl.4.2.3.3) the upper limit
values of q listed above should be reduced by 20 %

Table 2.2: Values of behavior factor for regular and irregular structure
Structural type Regular in plan
and elevation
Irregular in
plan / Regular
in elevation
Regular in plan
/ Irregular in
elevation
Irregular in
plan &
elevation
Irregular in
plan / Regular
in elevation
Regular in plan
/ Irregular in
elevation
Irregular in
plan &
elevation
DCM DCH DCM DCM DCM DCH DCH DCH
Moment resisting frame
Single storey portal 4.0 5.5 3.2 3.2 3.2 5.25 4.4 4.2
One bay multi-storey 4.0 6.0 3.2 3.2 3.2 5.5 4.8 4.4
Multi-bay, multi-storey 4.0 6.5 3.2 3.2 3.2 5.75 5.2 4.6
Concentrically braced frame
Diagonal bracing 4.0 4.0 3.2 4.0 4.0 4.0 3.2 3.2
V-bracing 2.0 2.5 1.6 2.5 2.5 2.5 2.0 2.0
Frame with masonry infill
panels
2.0 2.0 1.6 2.0 2.0 2.0 1.6 1.6

2.2 Define design horizontal response spectrum
2.2.1 Vertical response spectrum (EN1998-1-1,cl.3.2.2.3)
The vertical component of the seismic action should be taken into account if the avg>0.25g
(2.5m/s2) in the cases listed below:
• for horizontal structural member spanning 20m or more,
• for horizontal cantilever components longer than 5m,
• for horizontal pre-stressed components,
• for beams supporting columns,
• in based-isolated structures.
2.2.2 Horizontal response spectrum (EN1998-1-1,cl.3.2.2.5)
For the horizontal components of the seismic action the design spectrum, Sd(T), shall be
defined by the following expressions:
0 ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙
!
!
+
!
!!
∙
!.!
!
−
!
!
(ΕΝ1998-1-1,Eq. 3.13)
𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙
!.!
!
(ΕΝ1998-1-1,Eq. 3.14)
𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙
2.5
𝑞
𝑇!
𝑇
≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.15)
𝑇! ≤ 𝑇 ≤ 4𝑠: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙
!.!
!
!!!!
!!
≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.5)
Design ground acceleration on type A ground: ag=γIagR
Lower bound factor for the horizontal spectrum: β=0.2
Note: the value of q are already incorporate with an appropriation value of damping viscous,
however the symbol η is not present in the above expressions.

2.2.3 Parameters of elastic response spectrum (EN1998-1-1,cl.3.2.2.5)
Table 2.3: Parameters of Type 1 elastic response spectrum (CYS NA EN1998-1-1,table
3.2)
Ground
Type
S TB (s) TC (s) TD (s)
A 1.0 0.15 0.4 2.0
B 1.2 0.15 0.5 2.0
C 1.15 0.20 0.6 2.0
D 1.35 0.20 0.8 2.0
E 1.4 0.15 0.5 2.0
Note: For important structures (γI>1.0), topographic amplification effects should be taken
into account (see Annex A EN1998-5:2004 provides information for topographic
amplification effects).
ETABS: Define > Response spectrum function
1. Peak ground acceleration agR=0,25g,
2. Type C or D for building within category of importance I and II,
3. Define two response spectrum cases if the factor q is different in each direction,
Select EUROCODE8
Spectrum
Add New Function

4. Modify the existing values of elastic response spectrum case in order to change it into
the design response spectrum.
Figure 2.1: Response Spectrum to EC8
PERIOD
ACCELERATION
g
=
9.81
m/sec2

T
Sd(T)
β
=
0.2
-‐

0.0000
0.2000
SoilType
=
B
-‐

0.1000
0.1917
q
=
4.00
-‐

0.1500
0.1875
αgR
=
0.25
-‐

0.2000
0.1875
S
=
1.20
-‐

0.4000
0.1875
TB
=
0.15
sec

0.6000
0.1563
TC
=
0.50
sec

0.8000
0.1172
TD
=
2.00
sec

1.0000
0.0938
T
=
0.50
sec

1.5000
0.0625

2.0000
0.0469

Data
for
soil
type
-‐
Type
Spectrum
1

2.5000
0.0300

index
Soil
Type
S
TB
TC
TD

3.0000
0.0500

1
A
1
0.15
0.4
2

4.0000
0.0500

2
B
1.2
0.15
0.5
2

5.0000
0.0500

3
C
1.15
0.2
0.6
2

6.0000
0.0500

4
D
1.35
0.2
0.8
2

8.0000
0.0500

5
E
1.4
0.15
0.5
2

10.0000
0.0500

Convert the existing elastic response
spectrum case to design response
spectrum case

Figure 2.2: Amendment Response spectrum (q = 4)

2.2.3.1 Ground investigation conditions
Table 2.4: Geological studies depend on the importance class (CYS NA EN1998-1-1, NA
2.3 / cl.3.1.1 (4))
Importance class of buildings
Ground
Type
I II III IV
A NRGS NRGS RGS RGS
B NRGS NRGS RGS RGS
C NRGS NRGS RGS RGS
D NRGS NRGS RGS RGS
E NRGS NRGS RGS RGS
NRGS: Not required geological studies
RGS: required geological studies if there is not adequate information
2.2.3.2 Importance factor
Table 2.5: Importance classes for buildings (ΕΝ1998-1-1,table.4.3 and CYS NA EN1998-
1-1,cl NA2.12)
Importance
class
Buildings Important
factor γI
Consequences
Class
I
Buildings of minor importance for public
safety, e.g. argricultural buildings, etc.
0.8 CC1
II
Ordinary buildings, not belonging in the other
categories.
1.0 CC2
III
Buildings whose seismic resistance is of
importance in view of the consequences
associated with a collapse, e.g. schools,
assembly halls, cultural institutions etc.
1.2 CC3
IV
Buildings whose integrity during earthquakes
is of vital importance for civil protection, e.g.
hospitals, fire stations, power plants, etc.
1.4 CC3

CC1: Low consequence for loss of human life, and economic, social or environmental
consequences small or negligible.
CC2: Medium consequence for loss of human life, economic, social or environmental
consequences considerable.
CC3: High consequence for loss of human life, or economic, social or environmental
consequences very great
2.2.3.3 Ductility class
Table 2.6: Requirement for importance class relate to ductility class (CYS NA EN1998-
1-1,cl NA2.16 & cl.5.2.1(5))
Importance
class
Zone 1 Zone 2 Zone 3
I DCL DCL DCL
II DCM/DCH DCM/DCH DCM/DCH
III DCM/DCH DCM/DCH DCM/DCH
IV DCH DCH DCH
DCL: Ductility class low.
DCM: Ductility class medium.
DCH: Ductility class high.

2.3 Analysis types
2.3.1 Modal Response spectrum analysis
Table 2.7: Requirements of modal response spectrum analysis according to Eurocode 8
Requirements Values References
Regular in plan YES / NO ΕΝ1998-1-1,table 4.1
Regular in elevation NO ΕΝ1998-1-1,table 4.1
Sum of the effective
modal masses
≥ 90%
EN1998-1-1,cl.4.3.3.1(3)
≥ 5% of total mass
Minimum number of
modes
k ≥3.√n
k: is the number of modes
n: is the number of storey
EN1998-1-1,cl.4.3.3.1(5)
Behaviour factor q
Tk ≤ 0.20sec
Tk: is the period of vibration of
mode k.
EN1998-1-1,cl.4.3.3.1(5)
Fundamental period
Tj ≤ 0.9 Ti SRSS
EN1998-1-1,cl.4.3.3.2.1(2)
Tj ≥ 0.9 Ti CQC
Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2
1. Independently in X and Y direction,
2. Define design spectrum,
3. Use CQC rule for the combination of different modes (EN1998-1-1,cl.4.3.3.3.2(3))
4. Use SRS rule for combined the results of modal analysis for both horizontal directions
(EN1998-1-1,cl.4.3.3.5.1(21)).
5. Modal Combination: “Complete Quadratic Combination” (CQC) can be used if the Tj
≤ 0,9 Ti (EN1998-1-1,cl.4.3.3.3.2(3)P).

2.3.1.1 Accidental eccentricity
Accidental eccentricity of each storey cause of uncertainties location of masses have been
taken into account 5% (EN1998-1-1,cl.4.3.2). Moreover, if there are masonry infills with a
moderately irregular and asymmetric distribution in plan, is doubled further in Eurocode 8
(i.e., to 10% of the storey orthogonal dimension in the baseline case, or 20% if accidental
torsional effects are evaluated in a simplified way when using two separate 2D models).
Table 2.8: Summary of accidental eccentricity
Percentage of
accidental
eccentricity
Geometry
of model
(3D/2D)
Asymmetric
distribution of mass
(Regular/Irregular)
Masonry infills
(Regular/Irregular)
5% 3D Regular Regular
10% 3D Irregular Irregular
20% 2D - -
Note: Accidental eccentricity is automatically included during response-spectrum analysis in
ETABS, though equivalent static-load procedures are also available for manual evaluation.
Note that floor diaphragms must be rigid, otherwise torsional effects are not substantial.
ETABS implements an efficient and practical approach while formulating dynamic response
from accidental eccentricity. After the response-spectrum load case is run, the X and Y
acceleration at each joint location is determined, then multiplied by the tributary mass and the
diaphragm eccentricity along either Y or X. The larger absolute value of these resultant
moments (m*Xacc*dY or m*Yacc*dX) is then applied as torsion about the joint location.
Static response is then added to response-spectrum output to account for the additional design
forces caused by accidental eccentricity.

Define > Response spectrum cases
Note: Add two response spectrum cases: EQX and EQY as showing below (figure 9).
Figure 2.3: Response Spectrum case Data for EQY& EQX

2.3.2 Lateral force analysis requirements
Table 2.9: Requirements of lateral force analysis according to Eurocode 8
Requirements Values References
Regular in plan YES / NO ΕΝ1998-1-1,table 4.1
Regular in elevation YES ΕΝ1998-1-1,table 4.1
Ground acceleration 0.10-0.25g
CYS NA EN1998-1-
1:Seismic zonation map
Spectrum type 1 EN1998-1-1,cl.3.2.2.2(2)P
Ground type
A,B,C,D,E
Normally type B or C can be used
normal condition
EN1998-1-1,cl.3.1.2(1)
Lower bound factor for
the horizontal design
spectrum
λ = 0.85 if T1 ≤ 2TC and more than
2 storey
λ=1.0 in all other case
EN1998-1-1,cl.4.3.3.2.2(1Ρ)
Behaviour factor q
Concrete DCM q= 1.5 – 3.90 EN1998-1-1,cl.5.2.2.2(2)
Concrete DCH q= 1.6 – 5.85 EN1998-1-1,cl.5.2.2.2(2)
Steel DCM q= 2.0 – 4.00 EN1998-1-1,cl.6.3.2(1)
Steel DCH q= 2.0 – 5.85 EN1998-1-1,cl.6.3.2(1)
Fundamental period
T1≤4Tc
T1≤2,0s
EN1998-1-1,cl.4.3.3.2.1(2)
Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2
Table 2.10: Equivalent Static Force Case
Load case name Direction and Eccentricity % Eccentricity
EQXA X Dir + Eccen. Y 0.05
EQYA X Dir – Eccen. Y 0.05
EQXB Y Dir + Eccen. X 0.05
EQYB Y Dir – Eccen. X 0.05

2.3.4 Estimation of fundamental period T1
Table 2.11: Estimation of fundamental period T1
Reference structure Period T1
Exact formula for Single Degree of Freedom
Oscillator. Mass M lumped at top of a vertical
cantilever of height H. Cantilever mass MB = 0.
𝑇! = 2𝜋
𝑀𝐻!
3𝐸𝐼
Oscillator. Vertical cantilever of height H and of
total mass MB.
𝑇! = 2𝜋
0.24𝑀! 𝐻!
3𝐸𝐼
Oscillator. Mass M lumped at top of a vertical
cantilever of height H and of total mass MB.
𝑇! = 2𝜋
𝑀 + 0.24𝑀! 𝐻!
3𝐸𝐼
Approximate Relationship (Eurocode 8).
Ct = 0,085 for moment resisting steel space frames
Ct = 0,075 for eccentrically braced steel frames
Ct = 0,050 for all other structures
𝑇! = 𝐶! 𝐻!/!
H building height in m measured from
foundation or top of rigid basement.
Approximate Relationship (Eurocode 8).
d : elastic horizontal displacement of top of
building in m under gravity loads applied
horizontally.
𝑇! = 2 𝑑

2.3.5 Automatic Lateral force analysis using ETABS
ETABS: Define > Static load cases
Figure 2.4: Apply the Equivalent Static Force Case
Figure 2.5: Modify the Equivalent Static Force Case
Note: The seismic forces
should be applied only
above the top of the
basement

Fundamental period (EN1998-1-1,Eq.4.6)
T1=CtH3/4
(For heights up to 40m)
Value of Ct(EN1998-1-1,cl.4.3.3.2.2(3))
Ct = 0.085 (for moment resisting steel frames)
Ct= 0.075 (for moment resisting concrete frames)
Ct= 0.05 (for all other structures)
(EN 1998-1-1:2004, cl. 4.3.3.2.2(3))
Ct= 0.075/√ΣAc(for concrete/masonry shear wall
structures)
(EN 1998-1-1:2004, Eq. 4.7)
Ac= Σ[Ai·(0,2+(lwi/H2
))]
(EN 1998-1-1:2004, Eq. 4.8)
Fundamental period requirements
(EN1998-1-1,Eq.4.6)
T1≤4TCT1≤2sec
IF this
YES
LATERAL FORCE
ANALYSIS
RESPONSE SPECTRUM
ANALYSIS
Correction factor λ(EN1998-1-
1,cl.4.3.3.2.2(1Ρ))
λ=0.85 if T1≤2TC and more than 2 storey
λ=1.0 in all other case
Design spectrum
Sd(T)(EN1998-1-
1,cl.3.2.2.5)
0≤T≤TB
TB≤T≤TcTC≤T≤TD
TD≤T
Seismic mass(EN1998-1-
1,cl.3.2.4)
ΣGk,j/g”+”ΣψE,i.Qk,i/g
(EN 1998-1-1:2004, Eq.3.17)
Base shear(EN1998-1-
1,cl.4.3.3.2.2)
Fb=Sd(T1).m.λ
(EN 1998-1-1:2004, Eq. 4.5)
Horizontal seismic forces
(according to displacement of
the masses)
F! = F! ∙
s! ∙ m!
s! ∙ m!
(EN 1998-1-1:2004, Eq. 4.10)
Horizontal seismic forces
(according to height of the
masses)
F! = F! ∙
z! ∙ m!
z! ∙ m!
(EN 1998-1-1:2004, Eq. 4.11)
NO

2.3.6 User loads - Lateral force analysis using ETABS
Geometrical data
Span of the longitutinal direction
Span of the transverse direction
Span of each beam
Span of each bracing
Height of each column
Total heigh of building
Area of floor for each storey
Number of floors
Number of beams IPE240 at each floor
Number of beams IPE180 at each floor
Number of columns HE280A at each floor
Number of TUBE sections D127-4 at each floor
Lx 15m:=
Ly 15m:=
Lb 5m:=
Lt 5.831m:=
hc 3m:=
H 9m:=
Af Ly Lx⋅ 225m
2
=:=
Nf 3:=
Nb 24:=
Ns 9:=
Nc 16:=
Nt 8:=

Dead load
Weight of steel column HE280A
Weight of primary beams IPE240
Weight of secondary beams IPE180
Weight of steel beams TUBE-D127-4
Slab thickness
Weigth of concrete
Weight of slab
Weigth of finishes
Total dead load
Total dead load
Live load
Combination coefficient for variable action
Live load
Total live load
Total gravity load per storey
(EN1998-1-1,cl.3.2.4(2)P)
Total gravity load per storey
(EN1998-1-1,cl.3.2.4(2)P)
Seismic mass
gc 76.4kg m
1−
⋅:=
gp 30.7kg m
1−
⋅:=
gs 18.8kg m
1−
⋅:=
gt 12.38kg m
1−
⋅:=
hs 170mm:=
γ c 25kN m
3−
⋅:=
gslab γ c hs⋅ 4.25 kN m
2−
⋅⋅=:=
gfin 1kN m
2−
⋅:=
Gk.storey gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ 1.267 10
3
× kN⋅=:=
Gk gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ Nf⋅ 3.802 10
3
× kN⋅=:=
ψEi 0.3:=
qk 2kN m
2−
⋅:=
Qk qk Af⋅ 450 kN⋅=:=
FEd.storey Gk.storey ψEi Qk⋅( )+ 1.402 10
3
× kN⋅=:=
FEd Gk ψEi Qk⋅( ) Nf⋅+ 4.207 10
3
× kN⋅=:=
S_mass
FEd
g
4.29 10
5
× kg=:=

Horizontal design response Spectrum (EN1998-1-1,cl.3.2.2.5)
Behaviour factor q
(EN1998-1-1,cl.6.3)
Lower bound factor
(EN1998-1-1,cl.3.2.2.5(4)P)
Seismic zone
(CYS NA EN1998-1-1,
zonation map)
Importance factor
(CYS NA EN1998-1-1,cl. NA2.12)
Design ground acceleration on type A
(EN1998-1-1,cl.3.2.1(3))
Value of Ct
(EN1998-1-1,cl.4.3.3.2.2(3))
Fundamental period of vibration
(EN1998-1-1,cl.4.3.3.2.2(3))
Type of soil
(EN1998-1-1,cl.3.1.2(1))
Value of parameters describing the Type 1 elastic response spectrum (EN1998-1-1,table 3.2)
Soil factor, S
q 1.5:=
β 0.2:=
Seismic_zone "3":=
agR 0.15g Seismic_zone "1"if
0.2g Seismic_zone "2"if
0.25g Seismic_zone "3"if
2.452
m
s
2
=:=
Importance_factor "II":=
γ I 0.8 Importance_factor "I"if
1.0 Importance_factor "II"if
1.2 Importance_factor "III"if
1.4 Importance_factor "IV"if
1=:=
ag γ I agR⋅ 2.452
m
s
2
=:=
Value_Ct "OTHER":=
Ct 0.085 Value_Ct "MRSF"if
0.075 Value_Ct "MRCF"if
0.05 Value_Ct "OTHER"if
0.05=:=
T1 Ct
H
m
⎛
⎜
⎝
⎞
⎟
⎠
3
4
⋅
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
s 0.26s=:=
Soil_type "B":=
S 1.0 Soil_type "A"if
1.2 Soil_type "B"if
1.15 Soil_type "C"if
1.35 Soil_type "D"if
1.2=:=

Lower limit of the period, TB
Upper limit of the period, TC
Constant displacement value, TD
Corection factor λ
(EN1998-1-1,cl.4.3.3.2.2(1)P)
Check the fundamental period of vibration requirements
(EN1998-1-1,cl.4.3.3.2.1(2))
Design spectrum for elastic analysis (EN1998-1-1,cl.3.2.2.5(4)P)
TB 0.15s Soil_type "A"if
0.15s Soil_type "B"if
0.20s Soil_type "C"if
0.20s Soil_type "D"if
0.15s=:=
TC 0.40s Soil_type "A"if
0.5s=:=
TD 2.0s Soil_type "A"if
2s=:=
λ 0.85 T1 2TC≤ Nf 2>∧if
1 otherwise
0.85=:=
Check_1 if T1 4TC≤ T1 2s≤∧ "Lateral force analysis", "Response spectrumanalysis",( ):=
Check_1 "Lateral force analysis"=
S1e T1( ) ag S⋅
2
3
T1
TB
2.5
q
2
3
−⎛
⎜
⎝
⎞
⎟
⎠
⋅+
⎡
⎢
⎣
⎤
⎥
⎦
⋅:=
S1e 0( ) 1.961 m s
2−
⋅⋅=
S2e T1( ) ag S⋅
2.5
q
⋅:= S2e TB( ) 4.903 m s
2−
⋅⋅=
S3e T1( ) ag S⋅
2.5
q
⋅
TC
T1
⋅ ag S⋅
2.5
q
⋅
TC
T1
⋅ β ag⋅≥if
β ag⋅( ) β ag⋅ ag S⋅
2.5
q
⋅
TC
T1
⋅≥if
:=
S3e TC( ) 4.903 m s
2−
⋅⋅=
S4e T1( ) ag S⋅
2.5
q
⋅
TC TD⋅
T1
2
⋅
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
ag S⋅
2.5
q
⋅
TC TD⋅
T1
2
⋅ β ag⋅≥if
β ag⋅( ) ag S⋅
2.5
q
⋅
TC TD⋅
T1( )2
⋅ β ag⋅≤if
:=

Design spectrum acceleration
Seismic base shear
(EN1998-1-1,cl.4.3.3.2.2(1))
Seismic base shear on each bracing
Note: 2 bracing on each direction
S4e T1( ) 72.642
m
s
2
=
Se T( ) if T TB< S1e T( ), if T TC< S2e T( ), if T TD< S3e T( ), S4e T( ),( ),( ),( ):=
T 0.01sec 0.02sec, 4sec..:=
0 1 2 3 4
0
2
4
6
8
Se T( )
T
Se S1e 0( ) 0 T1≤ TB≤if
S2e TB( ) TB T1≤ TC≤if
S3e TC( ) TC T1≤ TD≤if
S4e T1( ) TD T1≤ 4s≤if
4.903
m
s
2
=:=
Fb S_mass Se⋅
T1
s
⋅ λ⋅ 464.519kN⋅=:=
Fb.bracing
Fb
2
232.259kN⋅=:=

Table 2.12: Summary table of the lateral force results
Story
Heigth

zi

(m)
Mass

mi

(kN)
zi*mi
Fb

(kN)
F=Fb(zi*mi)/
Σzi*mi
Moment

M=F*zi

(kNm)
Length
of

floor
Lx=Ly
Accidental

eccentricity

ei=0.05L
Torsional

moment

M=F*ei

(kNm)
Moment
due
to

SRSS

MSRS=√Mx^2+My^2

(kNm)
STORY1 9 1402 12618 464.52 232.26 2090.34 15 0.75 174.195 246.3489315
STORY2 6 1402 8412 464.52 154.84 929.04 15 0.75 116.13 164.232621
STORY3 3 1402 4206 464.52 77.42 232.26 15 0.75 58.065 82.1163105
TOTAL 4206 25236 464.52 3251.64
Mass per storey
Heigth at roof level
Heigth at level 2
Heigth at level 1
Total mass:
Lateral force at roof level
(EN1998-1-1,Eq.4.11)
Lateral force at level 2
(EN1998-1-1,Eq.4.11)
Lateral force at level 1
(EN1998-1-1,Eq.4.11)
Check lateral force per storey
mi FEd.storey 1.402 10
3
× kN=:=
z3 9m:=
z2 6m:=
z1 3m:=
Σmi_zi FEd.storey z3⋅ FEd.storey z2⋅+ FEd.storey z1⋅+ 2.524 10
4
× kN m⋅=:=
F3
mi z3⋅
Σmi_zi
Fb⋅ 232.259kN⋅=:=
F2
mi z2⋅
Σmi_zi
Fb⋅ 154.84kN⋅=:=
F1
mi z1⋅
Σmi_zi
Fb⋅ 77.42kN⋅=:=
F F3 F2+ F1+ 464.519kN=:=
Check_2 if F Fb≠ "OK", "NOT OK",( ):=
Check_2 "OK"=

ETABS: Define > Static load case >
Figure 2.6: Define manually the lateral forces
Figure 2.7: Define manually the lateral forces/moments per storey

2.3.7 Torsional effects
FLOW CHART OF TORSIONAL EFFECTS
Carry out Lateral force analysis/
Response spectrum analysis
𝑀! = 𝑒! 𝐹! 𝑀! = 𝑒! 𝐹!
𝑒! = −0.05 ∗ 𝐿!𝑒! = +0.05 ∗ 𝐿! 𝑒! = +0.05 ∗ 𝐿!𝑒! = −0.05 ∗ 𝐿!
SRSS rule
𝑀!"!! = 𝑀!
!
+ 𝑀!
!

2.3.8 Summary of analysis process in seismic design situation
Importance class/Ductility class
I II III IV
DCL DCM
DCH
DCM
DCH
DCH
Ignore “topographic
amplification effects”
Consider “topographic
amplification effects”
IF
Slopes <15o
Cliffs height
<30m
Slopes <15o
Cliffs height
<30m
Ignore Consider
Regular in plan: YES
Regular in elevation YES
Regular in plan: NO
Regular in elevation YES
Regular in plan: YES
Regular in elevation NO
Regular in plan: NO
Regular in elevation NO
Type of soil:
A , B ,C ,D, E, S1, S2
Type 1 elastic response
spectrum
0≤T≤TB
TB≤T≤TC
TC≤T≤TD
TD≤T≤4s
LATERAL
FORCE
MODAL
ANALYSIS
Displacement
ds=qd·de
P-Δ effects
θ≤0.1 – Ignore
0.1≤θ≤0.2 Consider
0.2≤θ≤0.3 Consider
θ≥0.3 Not Permitted
Interstorey drift
drv≤0.005h - Brittle
drv≤0.0075h - Ductile
drv≤0.010h - Other
Frame joint
ΣMRC≥1.3ΣMRB
Storey ≥ 2

3.0 Define static loads
Here define as many load cases for your model as you need e.g. dead loads, live loads, wind
loads, seismic loads, thermal loads etc. To be simple define only one dead load with self
weight multiplier 1(including finishes, dead, walls etc) and one live load.
Figure 3.1: Static load cases

4.0 Seismic mass requirements according to EC8
Combination of the seismic action with other actions (EN 1998-1-1,cl.3.2.4):
1. Define the category of building (EN 1991,Table 6.1),
2. Define the reduce factor (EN 1991, Table A.1.1).
Combination of seismic mass
𝐆 𝐤,𝐣 + 𝛙 𝐄𝐢 𝐐 𝐤,𝐢 (ΕΝ1998-1-1,Eq. 3.17)
Combination coefficient for variable action is: ψ!" = ϕ ∙ ψ!" (ΕΝ1998-1-1,Eq. 4.2)
Table 4.1: Values of φ for calculating 𝛙 𝐄𝐢 (CYS NA EN1998-1-1:2004)
Type of Variable
action
Storey φ
Categories A-C1
Roof
Storeys with correlated occupancies
Independently occupied storeys
1,0
0,8
0,5
Categories A-F1
1.0
Table 4.2: Values of ψ coefficients
Category Specific Use ψο ψ1 ψ2
A Domestic and residential 0.7 0.5 0.3
B Office 0.7 0.5 0.3
C Areas for Congregation 0.7 0.7 0.6
D Shopping 0.7 0.7 0.6
E Storage 1.0 0.9 0.8
F Traffic < 30 kN vehicle 0.7 0.7 0.6
G Traffic < 160 kN vehicle 0.7 0.5 0.3
H Roofs 0.7 0 0
Snow, altitude < 1000 m 0.5 0.2 0
Wind 0.5 0.2 0

4.1 Mass Source Option
In ETABS, the user has the option of choosing one of three options for defining the source of
the mass of a structure. Click the Define menu > Mass Source command to bring up the
Define Mass Source form. The following options appear on the form:
1. From Self and Specified Mass:
Each structural element has a material property associated with it; one of the items specified
in the material properties is a mass per unit volume. When the ‘From Self and Specified
Mass’ box is checked, ETABS determines the building mass associated with the element
mass by multiplying the volume of each structural element times it’s specified mass per unit
volume. This is the default. It is also possible to assign additional mass to account for
partitions and cladding, etc. ETABS adds any additional mass assignments to the element
mass to derive a total mass. You cannot have a negative mass in ETABS.
2. From Loads:
This specifies a load combination that defines the mass of the structure. The mass is equal to
the weight defined by the load combination divided by the gravitational multiplier, g. This
mass is applied to each joint in the structure on a tributary area basis in all three translational
directions.
3. From Self and Specified Mass and Loads:
This option combines the first two options, allowing you to consider self- weight, specified
mass, and loads in the same analysis.
It is important to remember when using the ‘From Self and Specified Mass and Loads’
option, NOT to include the Dead Load Case in the ‘Define Mass Multiplier for Loads’
box. This will account for the dead load of the structure TWICE.

Figure 4.1: Seismic source

5.0 Wind loading on structure (EN1991-1-4:2004)
5.1 Calculation of Wind load according to EN1991-1-4:2004
Step by step procedure
Figure 5.1: Fundamental Basic wind velocity, vb,0
(CYS NA EN1991-1-4,Fig.1)
Season factor
(CYS EN1991-1-4,NA 2.4)
cseason=1.0
Directional factor
(CYSEN1991-1-4,NA 2.4)
cdir=1.0
(Conservative value for all direction)
Basic wind velocity
(EN1991-1-4, Eq. 4.1)
vb=cdir.cseasonvb,0
Figure 1 Isotach contours of the fundamental value of the basic wind velocity v
c z
v z
c z
c

Table 5.1: Terrain category and terrain parameters (EN1991-1-4, Tab.:4.1)
Terrain
category
Description z0 (m) zmin(m)
0
Sea, costal area exposed to the open
sea.
SEA 0.003 1
I
Lakes or area with negligible
vegetation and without obstacles.
COUNTRY
0.01 1
II
Area with low vegetation such as
grass and isolated obstacles trees,
buildings) with separations of at least
20 obstacle height.
0.05 2
III
Area with regular cover of vegetation
or buildings or woth isolatd obstacles
with seperations of maximum 20
obstacle height (such as villages,
suburban terrain, permanent forest). TOWN
0.3 5
IV*
Area in which at least 15% of the
surface is covered with building and
their average height exceeds 15m.
1.0 10
*
For buildings in terrain category IV, displacement height hdis should be consider and information can be found
in Aneex A.5 of EN1991-1-4:2005.
Roughness factor, cr(z)
(EN1991-1-4,Eq.4.3-4.5)
cr(z)=kr . ln(z/z0) for zmin≤z≤zmax
cr(z)=cr . (zmin) for z≤zmin
z0: is the roughness length
Maximum height, zmax
(EN1991-1-4, cl. 4.3.2)
zmax=200m
Orography factor co(z)
co(z)=1
Terrain factor,
(EN1991-1-4,cl.4.4)
kr=0.19(z0/z0,II)0.07
Mean wind velocity, vm(z)
(EN1991-1-4 cl.4.3.1 )
vm(z)=cr(z).co(z).vb
Wind turbulence, Iv(z)
(EN1991-1-4,Eq.4.7)
Iv(z)=σv/vm(z)=kl/co(z)ln(z/z0) for
zmin≤z≤zmax
Iv(z)=Iv(zmin) for
z≤zmin
Turbulence factor: kl=1.0
(NA CYS EN1991-1-4, cl. NA 2.10)
Note: for co(z)=1 Iv(z) is not
important
Peak velocity pressure, qpeak(z)
(EN1991-1-4 Eq.4.8 )
qpeak(z)=[1+7 Iv(z)]0.5ρ vm
2
(z)=ce(z)·0.5·ρ·vb
2
Air density:ρ=1.25kg/m3

Table 5.3: Values of external pressure coefficient for vertical walls of rectangular plan building
(EN1991-1-4, Tab.:4.1)
ZONE A B C D E
h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1
5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.7
1 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.5
≤0.25 -1.2 -1.4 -0.8 -1.1 -0.5 +0.7 +1.0 -0.3
Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2
or
less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the
overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for
loadaded area of 1m2
and 10m2
respectively.
Key for vertical walls – Flat Roof
(EN1991-1-4, Fig.7.5)
Key for vertical walls –Mono&dual pitch
Roof
(EN1991-1-4, Fig.7.5)
Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5)
we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref
Table 5.2: Reference height ze, depending on h and b, and corresponding velocity pressure
profile (EN1991-1-4, Fig. 7.4)

5.2 Application of wind loading using ETABS
Table 5.4: Wind load assumptions
Basic wind velocity vb,0 24 m/s
Terrain category - II -
Structural factor cscd 1 -
Turbulence factor kl 1 -
Orography factor co(z) 1 -
ETABS: Clink on
ETABS: Select from first drop-down menu
ETABS: Click on select “NONE” and draw rectangular cover all side of plan view
Draw walls in plan

ETABS: Select the area of elevation A-A
ETABS: Assign > Shell/Area loads > Wind pressure coefficients
Figure 5.2: Wind load areas
Table 5.5: Wind pressure coefficient applied on walls
Wind pressure coefficient for load case WINDX
Windward load “Area D” Leeward load “Area E”
Side load “Area A & B” Side load “Area A & B”

Wind pressure coefficient for load case WINDY
Windward load “Area D” Leeward load “Area E”
Side load “Area A & B” Side load “Area A & B”

WIND LOADING ACCORDING TO
EN1991-1-4:2005
Job No.:

Sheet No.:

Date: December 2012 Check by:
CALCULATION OF WIND LOADING TO EN 1991-1-4:2005.
Loading available for rectangular, clad buildings with flat
roofs only.
Obstruction height, have = 7.5 m
Distance to nearest adjacent building, x = 50 m
Height of building, h = 9 m
Longitudinal length of the building
,
d = 15 m
Transverse length of the building, b = 15 m
Edge distance, (Wind direction - θ=90°) e = 15
Basic Wind Velocity, Vbo = 24 m/s ( Figure1)
Season Factor, Cseason = 1.0 (cl.NA2.4)
Directional Factor, Cdir = 1.0 (cl.NA2.4)
Basic Wind Velocity, Vb0=CdirCseasonVb,o Vb = 24 m/s (Eq.4.1)
Structural factor, CsCd = 1.0 (cl.6.2)
Orography factor, Co(z) = 1.0 cl.4.3.1(1))
Turbulence factor, kI = 1.0 (cl.NA2.10)
z0 zmin (Τable 4.1)
Terrain Category Define terrain category II 0.05 2
Max heigh, zmax = 200 m (cl. 4.3.2)
Height above ground, z = 100 m
Dispacement height, hdis = 4.5 m (Annex A.5)
Clear height of
building,
h-hdis = 4.5
Define height z
5

External
Pressure
Coefficients
Walls
Cpe

Wind
direction

θ=0°

Width

b

=

15
m

Height

h

=

9
m

Depth

d

=

15
m

Edge distance, (Wind direction - θ=0°)

e

= 15 m

Actual
h/b
(For
zone
D
-‐
windward
face)

h/b

=

0.60

Length
in

Zone
A

Zones
A
&
B

exist

3
m

Length
in

Zone
B

12
m

Length
in

Zone
C

0
m

Wind
direction

θ=90°

Width

b

=

15
m

Height

h

=

9
m

Depth

d

=

15
m

Edge distance, (Wind direction - θ=90°)

e

= 15 m

Actual
h/b
(For
zone
D
-‐
windward
face)

h/b

=

0.60

Length
in

Zone
A

Zones

A
&
B

exist

3
m

Length
in

Zone
B

12
m

Length
in

Zone
C

0
m

Table
7.1
values
of
Cpe
for

wind
on

Front
(θ=90°)

Front
(θ=0°)

Zones
(θ=90°)

Zones
(θ=0°)

D

0.747

0.747

A

3
m
A
-‐1.2
m

E

-‐0.567

-‐0.567

B

12
m
B
-‐0.8
m

A

-‐1.2

-‐1.2

C

0
m
C
0
m

B

-‐0.8

-‐0.8

C

0

0

6.0 Load combination
Table 6.1: Load combination factors and coefficients
Data Symbol Value Reference
Permanent action γG 1.35 EN1990,cl.6.4.3.2
Variable action γQ 1.5 EN1990,cl.6.4.3.2
Office areas (Type B), ψ0 0.7 CYS NA EN1990:2002, Table A1.1
Roofs ψ0 0.7 CYS NA EN1990:2002, Table A1.1
Wind loads ψ0 0.5 CYS NA EN1990:2002, Table A1.1
Persistent and transient design situation – STR/GEO Equation 6.10
Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2
Ultimate limit state (ULS)
Static load combination
STATIC 2. 1.35DL + 1.5LL
STATIC 3. 1.35DL + 1.5LL + 0.75WINDX
STATIC 4. 1.35DL + 1.5LL - 0.75WINDX
STATIC 5. 1.35DL + 1.5LL + 0.75WINDY
STATIC 6. 1.35DL + 1.5LL - 0.75WINDY
STATIC 7. 1.35DL + 1.5WINDX + 1.05LL
STATIC 8. 1.35DL - 1.5WINDX – 1.05LL
STATIC 9. 1.35DL + 1.5WINDY + 1.05LL
STATIC 10. 1.35DL - 1.5WINDY – 1.05LL
Seismic load combination for “Modal Analysis”
SEISMIC 2. DL + 0.3LL + EQX + 0.3EQY
SEISMIC 3. DL + 0.3LL + EQX – 0.3EQY
SEISMIC 4. DL + 0.3LL - EQX + 0.3EQY
SEISMIC 5. DL + 0.3LL - EQX – 0.3EQY
SEISMIC 6. DL + 0.3LL + EQY + 0.3EQX
SEISMIC 7. DL + 0.3LL + EQY – 0.3EQX
SEISMIC 8. DL + 0.3LL - EQY + 0.3EQX
SEISMIC 9. DL + 0.3LL - EQY – 0.3EQX

Seismic load combination for “Lateral force Analysis”
SEISMIC 10. DL + 0.3LL + EQXA + 0.3EQYA
SEISMIC 11. DL + 0.3LL + EQXA – 0.3EQYA
SEISMIC 12. DL + 0.3LL - EQXA + 0.3EQYA
SEISMIC 13. DL + 0.3LL - EQXA – 0.3EQYA
SEISMIC 14. DL + 0.3LL + EQYA + 0.3EQXA
SEISMIC 15. DL + 0.3LL + EQYA – 0.3EQXA
SEISMIC 16. DL + 0.3LL - EQYA + 0.3EQXA
SEISMIC 17. DL + 0.3LL - EQYA – 0.3EQXA
SEISMIC 18. DL + 0.3LL + EQXB + 0.3EQYB
SEISMIC 19. DL + 0.3LL + EQXB – 0.3EQYB
SEISMIC 20. DL + 0.3LL - EQXB + 0.3EQYB
SEISMIC 21. DL + 0.3LL - EQXB – 0.3EQYB
SEISMIC 22. DL + 0.3LL + EQYB + 0.3EQXB
SEISMIC 23. DL + 0.3LL + EQYB – 0.3EQXB
SEISMIC 24. DL + 0.3LL - EQYB + 0.3EQXB
SEISMIC 25. DL + 0.3LL - EQYB – 0.3EQXB
Serviceability limit state (SLS)
STATIC 1. DL + LL

7.0 Design preferences
ETABS: Options > Preferences > Steel frame design
Figure 7.1: Steel frame design preferences
2
3
4
1
5
6

Table 7.1: Steel frame design parameters
Note 1: Reliability class
Class section classification according to EN1998-1-1,cl.6.5.3(2)
1. Depending on the ductility class and the behavior factor q used in the design, the
requirements regarding the cross-sectional classes of the steel elements which
dissipate energy are indicated in table below (EN1998-1-1,cl.6.5.3(2).
Ductility class Reference q factor Cross-Section Class
Lower
limit
q factor Upper
limit
DCM
1.5< q ≤ 2 Class 1, 2 or 3
2.0< q ≤ 4 Class 1 or 2
DCH 4.0< q Class 1
Note 2: Frame type
See section 2.0 of this manual
Note 3: Gamma factors
Partial factors Values Reference
Resistance of cross-sections whatever the
class
γΜ0=1.00 EN1993-1-1,cl.6.1(1)
Resistance of members to instability assessed
by member checks
γΜ1=1.00 EN1993-1-1,cl.6.1(1)
Resistance of cross-sections in tension to
fracture
γΜ1=1.25 EN1993-1-1,cl.6.1(1)
Note 4: Behavior factor
See section 2.0 of this manual
Note 5: System Omega
Omega Factor (System Overstrength Factor) axial load member: (𝛀 = 𝑵 𝒑𝒍,𝑹𝒅/𝑵 𝑬𝒅)
Omega factor may different for each diagonal member.

1. Run the design analysis with the Ω=1
2. Find the Npl,Rd and NEd of the bracing member and then overwrite the omega factor for
each diagonal member separately and then re-run the analysis.(Ω=1).
Note: Omega factor should be limited to the following for all diagonal members
Note 6: Vertical deflection limits
STEEL MEMBERS
(CYS NA EN1993-1-1,table NA.1)
Vertical deflection Limits
wmax
Cantilevers L/180
Beams carrying plaster or other brittle finish L/360
Other beams (except purlin and sheeting
rails)
L/250
Purlins and sheeting rails To suit cladding
General use L/300
ETABS deflection limits
DL limit, L/ 360
Super DL+LL Limit, L/ 360
Live load Limit, L/ 360
Total Limit, L/ 360
Total Camper Limit, L/ 360
Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK",( ):=

8.0 Analysis and design requirements for Concentrically braced frames according to
EN1998-1-1,cl.6.7.2
Analysis requirements according to EN1998-1-1,cl.6.7.2
Beams & Columns
1. Under gravity load conditions, only beams and columns shall be considered to resist
such loads, without taking into account the bracing members (EN1998-1-
1,cl6.7.2(1)P).
Diagonal members
2. The diagonals shall be taken into account as follows in an elastic analysis of the
structure for the seismic action:
a) in frames with diagonal bracings, only the tension diagonals shall be taken into
account,
b) in frames with V bracings, both the tension and compression diagonals shall be
taken into account (EN1998-1-1,cl6.7.2(2).
3. Taking into account of both tension and compression diagonals in the analysis of any
type of concentric bracing is allowed provided that all of the following conditions are
satisfied:
a) a non-linear static (pushover) global analysis or non-linear time history analysis is
used,
b) both pre-buckling and post-buckling situations are taken into account in the
modeling of the behavior of diagonals and,
c) background information justifying the model used to represent the behavior of
diagonals is provided (EN1998-1-1,cl6.7.2(3).

8.1 Steps of the design detail of Concentric steel frames
Table 8.1: Detail steel frame design
Design step
number
Description
Step 1 Design of slab under gravity loads (without CBF bracings) considering columns
as fixed supports
Step 2 Design columns under gravity loads (without CBF bracings)
Step 3 Design beams under gravity loads (without CBF bracings)
Step 4 Check concentric bracings under gravity loads combination
Step 5 Accidental torsional effects
Step 6 Second order effects (P-Δ) (P loads are those taken in the definition of the
seismic mass “m”)
Step 7 Check of beams and of concentric bracings under gravity loads combination
Step 8 Design of concentric bracing under seismic combination of loads with the
accidental torsional effects and P-Δ effects taken into account
Step 9 Check of beams and columns under seismic combination of loads with bracings
overstrength factors Ω and with second order effects taken into account
Step 10 Re-run the analysis with the modified overstrength factors Ω

8.2 Classification of steel sections
Table 8.2: Section classification (EN1993-1-1,cl.5.5)
Classes Analysis type Description
Class 1 Plastic analysis Section can form a plastic hinge with the rotation capacity
required from plastic analysis, without reduction of the resistance
Class 2 Plastic/ Elastic analysis Section can develop its plastic moment capacity, but has limited
rotation capacity.
Class 3 Elastic analysis Section in which the stress in the extreme compression fiber of the
section, assuming an elastic distribution of stresses, can reach the
yield strength, but local buckling is likely to prevent the
development of the plastic moment capacity.
Description of detail
requirements
Equations References
Reduction of yield and
ultimate strength of sections
EN10025-2
ε - Factor
EN1993-1-1,Table 5.2
Depth of a part of section for
internal compression
(I-sections)
EN1993-1-1,Table 5.2
Section classification for web
element
EN1993-1-1,Table 5.2
fy. fy t 16mm<if
fy 10N mm
2−
⋅− 16mm t< 40mm<if
fy 20N mm
2−
⋅− 40mm t< 80mm<if
:=
fu. fu t 16mm≤if
fu 10N mm
2−
⋅− 16mm t< 40mm≤if
fu 20N mm
2−
⋅− 40mm t< 80mm≤if
:=
ε
235
fy
:=
cw h 2 tf⋅− 2 r⋅−:=
Class_type web "CLASS 1"
cw
tw
72 ε⋅≤if
"CLASS 2" 84 ε⋅
cw
tw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅
cw
tw
< 124 ε⋅≤if
:=

Depth of a part of section for
oustand flange
(I-sections)
EN1993-1-1,Table 5.2
Section classification for
flange element
EN1993-1-1,Table 5.2
cf
b tw− 2.r−( )
2
:=
Class_type flange "CLASS 1"
cf
tf
9 ε⋅≤if
"CLASS 2" 9 ε⋅
cf
tf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅
cf
tf
< 14 ε⋅≤if
:=

8.3 Design of composite slab under gravity loads
Table 8.3: Detail design of composite slab (with steel sheeting)
Partial factor Value References
Partial factor of longitudinal shear in composite slabs γvs = 1.25 CYS EN1994-1-
1cl.2.4.1.2(6)P
Partial factor for shear connector γv = 1.25 CYS EN1994-1-
1cl.2.4.1.2(5)P
Partial factor for steel reinforcement γs = 1.15 CYS EN1992-1-1,table 2.1
Partial factor of concrete γc = 1.5 CYS EN1992-1-1,table 2.1
Partial factor of structural steel γM0 = 1.0 CYS EN1993-1-1,cl 6.1(1)
Description of detail requirements Equations References
Minimum nominal thickness of profile steel sheets t ≥ 0.70mm CYS EN1994-1-1,cl.3.5(2)
Minimum depth of slab h ≥ 90mm EN1994-1-1,cl.9.2.1(2)
Depth of concrete slab above steel sheeting hc ≥ 50mm EN1994-1-1,cl.9.2.1(2)
Minimum steel reinforcement in both direction As.prov ≥80mm2
/m EN1994-1-1,cl.9.2.1(4)
Spacing of the reinforcement bars s = min{2h,350mm} EN1994-1-1,cl.9.2.1(5)
Maximum height of steel decking hp ≤ 85mm EN1994-1-1,cl.6.6.4.2(3)
Minimum width per ribs b0 ≥ hp EN1994-1-1,cl.6.6.4.2(3)
Diameter of stud that welded in the sheeting d ≤ 20mm EN1994-1-1,cl.6.6.4.2(3)

For holes provided in the sheeting, the diameter of the stud d ≤ 22mm EN1994-1-1,cl.6.6.4.2(3)
Maximum overall height of stud hsc ≤ hp +75mm EN1994-1-1,cl.6.6.4.1(2)
Design
stage
Description of checks Equations References
Resistance verifications of metal decking at the construction stage
Construction Stage
Moment resistance of steel sheeting From manufacture data -
Concrete compressive strength fcd = fck / γc EN1994-1-1,cl.2.4.1.2(2)P
Design yield strength fyo,d = fyp / γM0 -
Bending resistance of metal decking MEd / MRd <1.0 EN1993-1-3,cl.6.1.1
Shear resistance of metal decking 𝑉!,!" =
!!
!"#$
𝑡 𝑓!"
𝛾!!
EN1993-1-3,cl.6.1.5(1)
Deflection of metal decking
𝛿!"# =
!"!
!"#!"
(W in kN/m2
) -
δmax ≤ min {L/ 180,20mm) EN1994-1-1,cl.9.6(2)
Resistance verifications of composite slab at the composite stage
Composite Stage
Area of concrete Ac = b hc (b=1m) -
Compression design force of concrete Nc = 0.85 fcd Ac EN1994-1-1,cl.6.2.1.2
Tensile resistance of profiles steel sheeting Np = fyp,d Ap EN1994-1-1,cl.6.2.1.2

Location of neutral axis Neutral axis=if{Np < Nc “Lie above steel sheeting”, “Lie
below steel sheeting”}
EN1994-1-1,9.7.2(5) & (6)
Depth of concrete in compression xpl = Ape fyp,d / 0.85 b fcd EN1994-1-1,fig.9.6
Moment resistance (full shear connection) Mpl, Rd = Ap fyd (dp – 0.5 xpl) -
Bending resistance of slab MEd / Mpl,Rd <1.0 -
The design values of m and k Should be obtain from the manufacture -
Shear span (for UDL load) Ls = L / 4 EN1994-1-1,cl.9.7.3(5)
Shear span (for UDL & point load) Ls = 3L/8 EN1994-1-1,cl.9.7.3(5)
Shear resistance (in longitudinal direction) Vl,Rd = bdp /γvs [(mAp / bLs ) + k] EN1994-1-1,Eq. 9.7
Longitudinal shear resistance of slab VEd / Vl,Rd -
Coefficient factor k k = 1+(200 / dp)1/2
EN1992-1-1,cl.6.2.2(1)
Value of vmin vmin = 0.035k3/2
fck
1/2
CYS EN1992-1-1,Eq.6.3
Design vertical shear resistance Vv,Rd = vmin bs dp
1
EN1992-1-1,Eq.6.2b
Vertical shear resistance check VEd / Vv,Rd < 1.0 -
Serviceability limit state (SLS) - Deflection
Calculation of deflection (simply supported slab)
𝛿!"# =
!"!
!"#!"
(W in kN/m2
) -
Deflection limits (imposed load) L / 350 (not greater than 20mm)
Deflection limits (total load) L / 250 (not greater than 30mm) EN1992-1-1,cl.7.4.1(4)
Serviceability limit state (SLS) - Cracking
Minimum amount of steel ratio (un-propped) As = 0.2% Ac EN1994-1-1,cl.9.8.1(2)
Minimum amount of steel ratio (propped) As = 0.4% Ac EN1994-1-1,cl.9.8.1(2)

Serviceability limit state (SLS) – Floor vibration
Floor vibration limits f = 18 / √δa
SCI-P-076 : Design guide
on the vibration of floors
Note 1: Although in reality the slab is continuous, it is normally convenient to design it as simply supported. As a consequence of this, the beneficial effect of
compression from the hogging moment at the support is neglected, such that σcp = 0.

8.4 Design of composite beam (with steel sheeting) under gravity loads
Table 8.4: Detail design of composite beam
Minimum height of stud EN1994-1-1,cl.6.6.1.2(1)
Nominal diameter of stud EN1994-1-1,cl.6.6.1.2(1)
Ultimate strength of shear connector EN1994-1-1,cl.6.6.4.2(1)
Check the minimum spacing of studs EN1994-1-1,cl.6.6.5.5(3)
Preliminary depth of beams EN1994-1-1,cl.6.4.3(1)
Ultimate limit state
Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5)
Moment resistance of steel
section Y-Y axis
Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)
Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)
Shear area 1
Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)
Shear resistance of steel Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
hmin if hsc 4d≥ "OK", "NOT OK",( ):=
dlim if 16mm d< 25mm< "OK", "NOT OK",( ):=
fus 450N mm
2−
⋅:=
slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK",( ):=
hmax 600mm fy 235N mm
2−
⋅≤if
550mm 235N mm
2−
⋅ fy< 275N mm
2−
⋅≤if
400mm 275 N⋅ mm
2−
⋅ fy< 355N mm
2−
⋅≤if
270mm 355 N⋅ mm
2−
⋅ fy< 460N mm
2−
⋅≤if
:=

Construction
Stage
section Y-Y axis
Check if the verification of
shear buckling resistance
required or not
(EN1993-1-1,cl.6.2.6(6))
Bending and shear interaction check (cl.6.2.2.4)
Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)
Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2
EN1993-1-1,cl.6.2.8(3)
Reduced design plastic
resistance moment Y-Y axis
EN1993-1-1,cl.6.2.8(5)
Lateral torsional buckling of the steel beam
It is assumed that the steel beam is laterally restrained by the steel sheeting during construction. In order to provide restraint, the sheeting is
fixed to the beam either by the action of through-deck welding or by short-fired pins
Effective width of composite beam (cl.5.4.1.2(5))
Effective width of composite
beam
(EN1994-1-1cl. 5.4.1.2(5))
Plastic resistance moment of composite section with full shear connection (cl.6.2)
hw
tw
72
ε
η
⋅<
Ma.pl.Rd.
Wpl.y
ρ Aw
2
⋅
4tw
−
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
fy⋅
γ M0
vy 0.5>if
Ma.pl.Rd vy 0.5<if
:=
beff bo 2 min
L1
2
L2
2
+
Le
8
,
⎛
⎜
⎝
⎞
⎟
⎠
⎛
⎜
⎝
⎞
⎟
⎠
+:=

Composite
Stage
Tensile resistance of steel
section
(EN1993-1-1,cl.6.2.3(2))
Compression resistance of
concrete slab
(EN1994-1-1,cl.6.2.1.2(1d)
Tensile resistance in web of
steel section
-
Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1))
Bending resistance with full
shear connection
(EN1994-1-1,cl.6.1.2)
Bending resistance
check checks
(EN1993-1-1,cl.6.2.5(1))
Vertical Shear resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6)
Design of shear
resistance check
(EN1993-1-1,cl.6.2.6(1)P)
Check if the verification of
shear buckling resistance
(EN1993-1-1,cl.6.2.6(6))
Npl.a
fy A⋅
γ M0
:=
Nc.f 0.85 fcd⋅ beff⋅ hc⋅:=
Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=
Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if
"Lies in the top flange of the beam" Nc.f Npl.a≤if
"Lies in the web of the beam" Nc.f Npl.w<if
:=
Mpl.Rd Npl.a
ha
2
h+
Npl.a
Nc.f
hc
2
⋅−
⎛
⎜
⎝
⎞
⎟
⎠
⋅ Location_neutral axis "Lies in the concrete slab"if
Npl.a
ha
2
⋅ Nc.f
hc
2
hp+
⎛
⎜
⎝
⎞
⎟
⎠
⋅+ Location_neutral axis "Lies in the top flange of the beam"if
Ma.pl.Rd Nc.f
hc ha+ 2hp+
2
⎛
⎜
⎝
⎞
⎟
⎠
⋅+
Nc.f
2
Npl.w
ha
4
⋅− Location_neutral axis "Lies in the top flange of the beam"if
:=
Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK",( ):=
Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK",( ):=
Check_9 if
hw
tw
72
ε
η
⋅< "Not required shear buckling resistance", "Required shearbuckling resistance",
⎛
⎜
⎝
⎞
⎟
⎠
:=

Composite
Stage
required or not
Design resistance of shear stud connector (cl.6.6.3.1(1))
Upper limit of reduction
factor kt
(EN1994-1-1,Table:6.2)
Reduction factor kt
Ribs transverse to the supporting beams
(EN1994-1-1,cl.6.6.4.2)
Limitation of kt (EN1994-1-1,cl.6.6.4.2(2))
Reduction factor kt
Ribs parallel to the supporting beams
(EN1994-1-1,cl.6.6.4.1)
Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1))
Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1))
Factor α (EN1994-1-1,cl.6.6.3.1(1))
kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if
1.0 nr 1 1mm ts<∧ d 20mm<∧if
0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if
0.70 nr 2 1mm ts≥∧ d 20mm<∧if
0.80 nr 2 1mm ts<∧ d 20mm<∧if
0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if
0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if
:=
kt
0.7
nr
bo
hp
⋅
hsc
hp
1−
⎛
⎜
⎝
⎞
⎟
⎠
⋅:=
Check_10 if kt kt.max< "OK", "NOT OK",( ):=
kt 0.6
bo
hp
⋅
hsc
hp
1−
⎛
⎜
⎝
⎞
⎟
⎠
⋅ 1.0≤:=
hmin if hsc 4d≥ "Ductile", "Not Ductile",( ):=
dlim if 16mm d< 25mm< "Ductile", "Not ductile",( ):=
α 0.2
hsc
d
1+
⎛
⎜
⎝
⎞
⎟
⎠
⋅ 3
hsc
d
≤ 4≤if
1
hsc
d
4>if
1=:=

Composite
Stage
Design shear resistance of a
headed stud
(EN1994-1-1,cl.6.6.3.1(1))
Degree of shear connection (cl.6.6.1.2(1))
Ratio of the degree shear
connection
(EN1994-1-1,cl.6.2.1.3(3))
Minimum degree of shear
connection for equal flange (EN1994-1-1,cl.6.6.1.2(1))
Check the degree of shear
interaction within the limits
(EN1994-1-1,cl.6.6.1.2(1))
Number of shear connector
required
-
Stud spacing -
Check the minimum
spacing of studs
(EN1994-1-1,cl.6.6.5.7(4))
Adequacy of the shear
connection
(EN1994-1-1,cl.6.6.1.3(3))
Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4)
Length under consideration -
PRd kt min
0.8 fus⋅ π⋅
d
2
4
⋅
γ v
0.29 α⋅ d
2
⋅ fck Ecm⋅⋅
γ v
,
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
⋅:=
η
Nc.f
Npl.a
:=
ηmin 1
355
fy
N mm
2−
⋅
⎛⎜
⎜
⎜
⎝
⎞⎟
⎟
⎟
⎠
0.75 0.03
Le
m
⋅−
⎛
⎜
⎝
⎞
⎟
⎠
⋅− Le 25m<if
1.0 Le 25m>if
:=
Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK",( ):=
n
2 Npl.a⋅
PRd
:=
sprov
Le
Nstud
:=
slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK",( ):=
Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing",( ):=
Δ x
Le
2
:=

Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3))
Strength reduction factor
(EN1992-1-1,Eq.6.6N)
Area of transverse
reinforcement required (EN1992-1-1,cl.6.2.4(4))
Check the crushing
compression in the flange
(EN1992-1-1cl.6.2.4(4))
Serviceability limit state
Vertical deflection
Construction
Stage
Maximum deflection at
construction stage
-
Vertical deflection limit
(CYS NA EN1993-1-1,table
NA.1)
Composite
Stage
Short term elastic modular
ration (EN1994-1-1,cl.7.2.1)
Second moment of area of the
composite section
-
Deflection with full shear
connection
-
Vibration of floor (Simplified analysis) (EN1990 A1.4.4)
vEd
Npl.a
2 hc⋅ Δ x⋅
:=
v 0.6 1
fck
250 N⋅ mm
2−
⋅
−
⎛⎜
⎜
⎝
⎞⎟
⎟
⎠
⋅:=
As.req
vEd hc⋅ sf⋅
fyd
sin θf( )
cos θf( )
⋅
:=
Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK",( ):=
δc
5 Gk.c Qk.c+( )⋅ Le
4
⋅
384 Es⋅ Iyy⋅
:=
Check_15 if δc
Le
250
< "OK", "NOT OK",
⎛
⎜
⎝
⎞
⎟
⎠
:=
no
Es
Ecm
:=
r
A
beff hc⋅
:=
Ic
A h 2 hp⋅+ hc+( )2
⋅
4 1 no r⋅+( )⋅
beff hc
3
⋅
12 no⋅
+ Iyy+:=
δcom
5 Gk Qk+( )⋅ Le( )4
⋅
384 Es⋅ Ic⋅
:=

Total load on beam is EN1990,A1.4.4
Increase the inertia, Ic by 10% to allow for the
increased dynamic stiffness of the composite beam
-
Instantaneous deflection caused by re-application of
the self weigth of the floor and the beam to the
composite beam
-
Natural frequency SCI P354
Check natural frequency limitation -
Fv Gk ψ1 Qk⋅+:=
Icl Iy Iy 0.1⋅( )+:=
δα
5 Fv Le⋅( )⋅ Le
3
⋅
384 Es⋅ Icl⋅
:=
f
18 Hz⋅
δα
mm
:=
Check_17 if f 4Hz< "OK", "NOT OK",( ):=

8.5 Detail design of steel columns under gravity loads
Table 8.5: Detail design of composite beam
Partial factor Value References
Partial factor of cross-sections whatever the class
is
γM0 = 1.0
CYS EN1993-1-1,cl 6.1(1)
Partial factor of member to instability assessed by
member checks
γM1 = 1.0
CYS EN1993-1-1,cl 6.1(1)
Description of detail requirements Equations References
Design plastic resistance of the gross cross-section Npl,Rd = A fy / γM0 EN1993-1-1,cl.6.2.3(2)
Compression resistance of steel section Nc,Rd =A fy / γM0 EN1993-1-1,cl.6.2.4(1)
Bending interaction check
Moment resistance of steel section Y-Y axis Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2)
Moment resistance of steel section Z-Z axis Mc,Rd,z= Mpl,Rd,z = Wpl,z fy / γM0 EN1993-1-1,cl.6.2.5(2)
Shear interaction check
Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g)
Shear area 1
Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a)
Shear resistance of steel section Y-Y axis Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
Shear resistance of steel section Z-Z axis Vpl,Rd,z = 2b tf (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2)
Bending and shear interaction check
Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)

Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2
EN1993-1-1,cl.6.2.8(3)
Reduced design plastic resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5)
Coefficient of interaction vz=VEd / VRd,y EN1993-1-1,cl.6.2.8(5)
Reduced yield strength ρ = [(2VEd / Vpl.Rd,z) – 1] 2
EN1993-1-1,cl.6.2.8(3)
Reduced design plastic resistance moment Z-Z axis EN1993-1-1,cl.6.2.8(5)
Check combination of axial and bending EN1993-1-1,cl.6.2.1(7)
Bending and axial interaction check
Criteria 1 – Y-Y axis c1=NEd ≤ Npl,Rd EN1993-1-1,cl.6.2.9.1(4)
Criteria 2 – Y-Y axis c2=NEd ≤ (0.5 hw tw fy )/ γM0 EN1993-1-1,cl.6.2.9.1(4)
Check criteria c= max(cy1, cy2)
Factor a a = min {(A-2 b tf) / A) ,0.5} EN1993-1-1,cl.6.2.9.1(5)
Factor n n = NEd / Npl,Rd EN1993-1-1,cl.6.2.9.1(5)
Factor β EN1993-1-1,cl.6.2.9.1(6)
Reduced design value of the resistance to bending MN,y,Rd = Mpl,y,Rd (1-n)/(1-0,5a) if c>1.0
and
EN1993-1-1,cl.6.2.9.1(5)
Mc.Rd.y
Wpl.y
ρ Aw
2
⋅
4tw
−
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
fy⋅
γ M0
vy 0.5>if
Mc.Rd.y vy 0.5<if
:=
Mc.Rd.z
Wpl.z
ρ Aw
2
⋅
4tw
−
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
fy⋅
γ M0
vz 0.5>if
Mc.Rd.z vz 0.5<if
:=
Check_1 if
NEd
Npl.Rd
MEd.y
Mc.Rd.y
+
MEd.z
Mc.Rd.z
+ 1.0≤ "OK", "NOT OK",
⎛
⎜
⎝
⎞
⎟
⎠
:=
β 5n 5n 1≥if
1 otherwise
1=:=

moments making allowance for the presence of
axial forces (Y-Y axis)
MN,y,Rd = Mpl,y,Rd if 0 ≤ c ≤ 1.0
Reduced design value of the resistance to bending
moments making allowance for the presence of
axial forces (Z-Z axis)
MN,z,Rd = Mpl,z,Rd for n<a
and
MN,z,Rd = Mpl,z,Rd [1-(n-a/1-a)2
] for n>a
EN1993-1-1,cl.6.2.9.1(5)
Check combination of bi-axial bending EN1993-1-1,cl.6.2.9.1(6)
Buckling interaction check
Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)
Elastic critical force for the relevant buckling mode based on the
gross cross sectional properties
𝑁!".! =
𝐸! 𝐼! 𝜋!
𝐿!".!
! -
Non dimensional slenderness λ! =
𝐴𝑓!
𝑁!".!
EN1993-1-1,cl.6.3.1.2(1)
Buckling curve EN1993-1-1,table 6.2
Imperfection factor a EN1993-1-1,table 6.1
Check_1 if
MEd.y
MN.y.Rd
⎛
⎜
⎝
⎞
⎟
⎠
a
MEd.z
MN.z.Rd
⎛
⎜
⎝
⎞
⎟
⎠
β
+
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
1.0≤ "OK", "NOT OK",
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
:=
Buckling_class_Y
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
h
b
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
h
b
1.2≤if
:=

Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2
EN1993-1-1,cl.6.3.1.2(1)
Reduction factor χ χ =
1
Φ + Φ! − λ!
≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)
Design buckling resistance of a compression member 𝑁!,!" =
𝜒𝐴𝑓!
𝛾!!)
EN1993-1-1,cl.6.3.1.1(3)
Buckling length See: Figure 1: Effective length columns Design Guidance of EC3)
Elastic critical force for the relevant buckling mode based on the
gross cross sectional properties
𝑁!".! =
𝐸! 𝐼! 𝜋!
𝐿!".!
! -
Non dimensional slenderness λ! =
𝐴𝑓!
𝑁!".!
EN1993-1-1,cl.6.3.1.2(1)
Buckling curve EN1993-1-1,table 6.2
Imperfection factor a EN1993-1-1,table 6.1
αy 0.1 Buckling_class_Y "ao"if
0.21 Buckling_class_Y "a"if
0.34 Buckling_class_Y "b"if
0.49 Buckling_class_Y "c"if
0.76 Buckling_class_Y "d"if
:=
Buckling_class_Y
"a" tf 40mm<if
"b" 40mm tf< 100mm<if
h
b
1.2>if
"b" tf 100mm≤if
"d" tf 100mm>if
h
b
1.2≤if
:=

Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2
EN1993-1-1,cl.6.3.1.2(1)
Reduction factor χ χ =
1
Φ + Φ! − λ!
≤ 𝜒 ≤ 1,0 EN1993-1-1,cl.6.3.1.2(1)
Design buckling resistance of a compression member 𝑁!,!",! =
𝜒𝐴𝑓!
𝛾!!)
EN1993-1-1,cl.6.3.1.1(3)
Non dimensional slenderness EN1993-1-1,cl.6.3.1.2(1)
Check the bukling effects if can be ignored and only cross
section check is adequate
EN1993-1-1,cl.6.3.1.2(4)
Lateral torsional buckling interaction check
Elastic critical moment for lateral torsional buckling NCCI: SN003a-EN-EU
Effective length factor (Pinned End) k = 1.0 NCCI: SN003a
Factor for end warping kw = 1.0 NCCI: SN003a
Coefficient factor C1 (Load condition: UDL)
NCCI: SN003a
Coefficient factor C2 C2 = 1.554 NCCI: SN003a
Distance between the point of load application and the
shear centre (load applied on centre)
zg = 0m NCCI: SN003a
αz 0.1 Buckling_class_Z "ao"if
0.21 Buckling_class_Z "a"if
0.34 Buckling_class_Z "b"if
0.49 Buckling_class_Z "c"if
0.76 Buckling_class_Z "d"if
:=
λ max λy λz,( ):=
Check if λ 0.2< "Ignored buckling effects", "Consider bucklingeffects",( ):=
Mcr C1
π
2
Es⋅ Izz⋅
k Lcr⋅( )2
⋅
k
kw
⎛
⎜
⎝
⎞
⎟
⎠
2 Iw
Izz
⋅
k Lcr⋅( )2
G It⋅
π
2
Es Izz⋅
+ C2 zg⋅( )2
+⋅ C2 zg⋅−:=
C1 1.88 1.40ψ− 0.52ψ
2
+:=
Check_5 if C1 2.7≤ "OK", "NOT OK",( ):=

Lateral torsional buckling curves EN1993-1-1,table 6.4
Imperfection factors for lateral torsional buckling curves EN1993-1-1,table 6.3
Non dimensional slenderness for lateral torsional buckling EN1993-1-1,cl.6.3.2.2(1)
Value to determine the reduction factor χLT EN1993-1-1,cl.6.3.2.2(1)
Reduction factor for lateral-torsional buckling EN1993-1-1,cl.6.3.2.2(1)
Check if the lateral torsional buckling
can be ignored
EN1993-1-1,cl.6.3.2.2(4)
Moments due to the shift of the centroidal axis for
class sections 1,2 & 3
EN1993-1-
1,cl.6.3.3(4)/table 6.7
Characteristic resistance to normal force of the
critical cross-section
EN1993-1-
1,cl.6.3.3(4)/table 6.7
Characteristic moment resistance of the critical
cross-section
E1993-1-1,cl.6.3.3(4)/table
6.7)
Buckling_curve_Z "a"
h
b
2≤if
"b"
h
b
2>if
:=
αLT 0.21 Buckling_curve_Z "a"if
0.34 Buckling_curve_Z "b"if
0.49 Buckling_curve_Z "c"if
0.76 Buckling_curve_Z "d"if
:=
λLT
Wpl.y fy⋅
Mcr
:=
φ LT 0.5 1 αLT λLT 0.2−( )⋅+ λLT
2
+⎡
⎣
⎤
⎦⋅:=
χLT
1
φ LT φ LT
2
λLT
2
−+
:=
Check_6 if λLT λLTO< "Ignored torsional buckling effects", "Consider torsional buckling effects",( ):=
Check_7 if
MEd.y
Mcr
λLTO
2
< "Ignored torsional buckling effects", "Consider torsional buckling effects",
⎛
⎜
⎝
⎞
⎟
⎠
:=
ΔM Ed.z 0:=
ΔM Ed.y 0:=
NRk fy A⋅:=
My.Rk fy Wpl.y⋅:=
Mz.Rk fy Wpl.z⋅:=

Ratio of end moments EN193-1-1,Table B2)
Equivalent uniform moment factor EN1993-1-1,table B.1&B.2
Interaction factors EN1993-1-1,table B.1&B.2
Combined bending and axial compression EN1993-1-1,Eq.6.61
ψy
MEd.y1
MEd.y2
1−
MEd.y1
MEd.y2
≤ 1≤if
MEd.y2
MEd.y1
1−
MEd.y2
MEd.y1
≤ 1≤if
:=
ψz
MEd.z1
MEd.z2
1−
MEd.z1
MEd.z2
≤ 1≤if
MEd.z2
MEd.z1
1−
MEd.z2
MEd.z1
≤ 1≤if
:=
Cmy 0.6 0.4 ψy⋅+:=
Cmz 0.6 0.4 ψz⋅+:=
kyy min Cmy 1 λy 0.2−( )
NEd
χy
NRk
γ M1
⋅
⋅+
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
⋅
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
Cmy 1 0.8
NEd
χy
NRk
γ M1
⋅
⋅+
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
⋅,
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
:=
kzz min Cmz 1 2λz 0.6−( )
NEd
χz
NRk
γ M1
⋅
⋅+
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
⋅
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
Cmz 1 1.4
NEd
χz
NRk
γ M1
⋅
⋅+
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
⋅,
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
:=
kyz 0.6kzz:=
kzy 0.6kyy:=
NEd
xy NRk⋅
γ M1
kyy
MEd.y ΔM Ed.y+
χLT
My.Rk
γ M1
⋅
⋅+ kyz
Mz.Ed ΔM Ed.z+
Mz.Rk
γ M1
⋅+

Combined bending and axial compression EN1993-1-1,Eq.6.62
Note: This equations is applicable only for I and H sections with section class 1 and 2
Note 1: The shear area is for rolled I and H sections, load parallel to web
NEd
χz NRk⋅
γ M1
kzy
MEd.y ΔM Ed.y+
χLT
My.Rk
γ M1
⋅
⋅+ kzz
MEd.z ΔM Ed.z+
Mz.Rk
γ M1
⋅+

8.6 Detail design rules of steel Concentric Braced Frames (CBF) according to Eurocode 8
8.6.1 Detail design rules of steel bracing according to Eurocode 8
Description Value References
Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P
Non-dimensional slenderness (X bracing) EN1998-1-1,cl.6.7.3(1)
Non-dimensional slenderness (one diagonal) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(2)
Non-dimensional slenderness (V bracing) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(3)
Non-dimensional slenderness (V,X & one bracing) EN1998-1-1,cl.6.7.3(4)
Yield resistance check EN1998-1-1,cl.6.7.3(5)
Check Ω factor EN1998-1-1,cl.6.7.3(8)
Ductility class require for seismic design EN1998-1-1,cl.6.5.3(2)
Check_6 if 1.3 λy< 2< "OK", "NOT OK",( ):=
Check_5 if Ns 3≥ "Consider limitation (AsEC8)", "Ignorelimitation (As EC3)",( ):=
Check_15 if NEd Npl.Rd≤ "OK", "NOT OK",( ):=
Ω.
Npl.Rd
NEd
:=
Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK",( ):=
Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if
"CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if
"CLASS 1" q 4> Ductility_class "DCH"∧if
:=

8.7 Detail design rules of steel columns and beams according to Eurocode 8
Yield resistance check EN1998-1-1,cl.6.7.3(5)
Minimum resistance requirement, NEd EN1998-1-1,cl.6.7.4(1)
Check_15 if NEd Npl.Rd≤ "OK", "NOT OK",( ):=
Ω.
Npl.Rd
NEd
:=
NEd. NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+:=
:=

8.8 Detail design rules of steel composite members according to Eurocode 8
Minimum concrete strength C20/25 – C40/50 CYS EN1998-1-1cl.7.2.1(1)
Steel reinforcement class B or C EN1998-1-1,cl.7.2.2(2)
Minimum degree of connection η ≤ 0.8 EN1998-1-1,cl.7.6.2(3)
Reduction factor kt = 0.75 EN1998-1-1,cl.7.6.2(4)
Profiled steel sheeting with ribs transverse to the
supporting beams is used, the reduction factor
kt = kt * kr
EN1998-1-1,cl.7.6.2(6)
Yield strength of steel EN1998-1-1,cl.7.6.2(8)
fy "fy=355" 1.5 q< 4≤ Ductility_class "DCM"∧
x
d
0.27≤∧if
"fy=235" 1.5 q< 4≤ Ductility_class "DCM"∧ 0.27
x
d
< 0.36≤∧if
"fy=355" q 4> Ductility_class "DCH"∧
x
d
0.20≤∧if
"fy=235" q 4> Ductility_class "DCH"∧ 0.20
x
d
< 0.27≤∧if
:=
xx
:=

8.9 Detail design rules of steel moment resistance frames (MRF) according to Eurocode 8
8.9.1 Detail design rules for MRF - Design criteria
Below design criteria apply to (Bottom – Top) Single/Multi-story buildings EN1998-1-1cl.6.6.1(1)
Moment capacity (where fixed support is provided) ∑MRc ≥ 1.3MRb EN1998-1-1,cl.4.4.2.3(4)
8.9.2 Detail design rules of steel beam for MRF
Moment capacity verification
𝑀!"
𝑀!".!"
≤ 1.0 EN1998-1-1,cl.6.6.2.(2)
Design shear force
VEd = VEd.G + VEd.M
Where
VEd.M = (Mpl.Rd.A + Mpl.Rd.B)/L
EN1998-1-1,cl.6.6.2.(2)
Shear capacity verification
𝑉!"
𝑉!".!"
≤ 0.5 EN1998-1-1,cl.6.6.2.(2)
Axial capacity verification
𝑁!"
𝑁!".!"
≤ 0.15 EN1998-1-1,cl.6.6.2.(2)

8.9.3 Detail design rules of steel column for MRF
Check Ω factor (derivate from all beam with
moment connection)
Ω!"# =
!!".!"
!!".!
MEd.E : Lateral force
EN1998-1-1cl.6.6.3(1P)
Design axial compression force NEd = NEd.G +1.1γvoΩ NEd.E NEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design bending moment MEd = MEd.G +1.1γvoΩ MEd.E MEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design shear force VEd = VEd.G +1.1γvoΩ VEd. VEd.E : Lateral force EN1998-1-1cl.6.6.3(1P)
Design shear force verification 𝑉!"
𝑉!".!"
≤ 0.5
EN1998-1-1cl.6.6.3(4)

9.0 Design of steel frames
9.1 Design of steel member overwrites data
Figure 9.1: Steel design result of the member
Overwrites

Figure 9.2: Steel frame design overwrites for Eurocode 3
3
2
1
4
7
8
9
10
11
12
5
6

Table 9.1: Steel frame design overwrites for Eurocode 3
Explanation of Steel frame design overwrites for Eurocode 3
Note No. Parameter Values
1
Effective length
factor
2 Moment coefficient
kyy
kzz

3
Bending Coefficient
(C1)
4 Moment coefficient
5
Overstrength factor
used in design1
6
Omega gamma
factor
γov = 1.25
7
Compressive/Tensile
capacity
8
Major bending
capacity, Mc3Rd
9
Minor bending
capacity, Mc2Rd
10
Buckling resistance
moment
Ω.
Npl.Rd
NEd
:=

11
Major shear
capacity, Vc3Rd
12
Minor shear
capacity, Vc2Rd
Notes: 1
Ω is not calculated automatically by the program. Rather, its value can be overwritten by the user through design Preference and Overwrites.

9.2 Design of columns / beams using ETABS – Gravity load analysis only
STEP 1: Analyze > Run Analysis
STEP 2: Design > Steel frame design > Select design combo…
Note: Under gravity load conditions, only beams and columns shall be considered to resist
such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P).
Design combination at ULS
Figure 9.3: Gravity load combination at ULS
Design combination at SLS
DSTLD 1. DL + LL
DSTLD 2. DL

Figure 9.4: Gravity load combination at SLS
Figure 9.5: Steel design under gravity load ONLY
Write click on each
member in order to check
it individually
Column name: C2
Storey level: Storey 1

Figure 9.6: Steel design result of the member
Figure 9.7: Ultimate moment results under worst case combination
ETABS: Display > Show tables
Worst case combination

Take the ultimate moment and shear force from the above table and place them into the Excel
spreadsheet or Mathcad file in order to verify the steel design results of ETABS.
Table 9.2: Summarize of design values required to carry out the design of steel member
Design value Symbol
Results
(kN)
Design axial force for gravity load combination (G+0.3Q) NEd.GV 344.75
Design moment at y-y at end 1 (seismic load combination) MEd.GV.y1 -1.293
Design moment at y-y at end 2 (seismic load combination) MEd.GV.y2 3.195
Design moment at z-z at end 1 (seismic load combination) MEd.GV.z1 -0.173
Design moment at z-z at end 2 (seismic load combination) MEd.GV.z2 -0.142
Shear forces at y-y at end (seismic load combination) VEd.GV.y -0.01
Shear force at z-z at end 1 (seismic load combination) VEd.GV.z -1.63
Press the button summary

Design results of ETABS
ETABS/HAND
Description of
comparison
Results
ETABS
Equation 6.62 in EC3
0.160
HAND (see section 9.3) 0.135

ETABS/HAND N.c.Rd N.t.Rd N.pl.Rd
ETABS 2675.75 2675.75 2675.75
HAND (see section 9.3) 2675.75 2675.75 2675.75
ETABS/HAND
Curve Alpha LambarBar Phi Chi Nb.Rd
y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z
ETABS “b” “c” 0.340 0.490 0.268 0.454 0.548 0.66 0.976 0.868 2610 2322
HAND (see section 9.3) “b” “b” 0.340 0.340 0.248 0.42 0.539 0.625 0.983 0.918 2630 2534

ETABS/HAND
M.c.Rd M.v.Rd
M.b.rd
y-y z-z y-y z-z
ETABS 305.8 142.45 305.8 142.45 302.05
HAND (see section 9.3) 305.8 142.45 305.8 142.45 305.80
ETABS/HAND Curve AlphaLT LambdaBarLT PhiLT ChiLT C1 Mcr
ETABS a 0.21 0.255 0.538 0.988 2.532 4694
HAND (see section 9.3) b 0.34 0.24 0.535 0.986 2.532 4679
ETABS/HAND kyy kyz kzy kzz
ETABS 0.442 0.582 0.964 0.970
HAND (see section 9.3) 0.441 0.576 0.265 0.96

ETABS/HAND
V.c.Rd
V.pl.Rd η
y-y z-z
ETABS 504 1234 504 1.2
HAND (see section 9.3) 504 1156 504 1.0

9.3 Design of steel column (Gravity design situation) – Hand calculations
1. Rolled I - section
2. Limit to class 1 and 2 section
3. Column not susceptible to torsional deformations
Length of column
Total axial load on column, NEd
Shear force y-y axis
Shear force z-z axis
Design moment y-y axis
Design moment y-y axis
Maximum moment
Design moment z-z axis
Design moment z-z axis
Maximum moment
Section properties:
Depth of section,h:
Width of section,b:
Thickness of web, tw:
Thickness of flange, tf :
Thickness of element
Second moment of area z-z:
Second moment of area y-y:
Cross section area, A:
Radius of section:
Heigth of web, hw
hc 3m:=
NEd 344.798kN:=
VEd.y 0.011kN:=
VEd.z 1.626kN:=
MEd.y1 3.195kN m⋅:=
MEd.y2 1.293− kN m⋅:=
MEd.y max MEd.y1 MEd.y2,( ) 3.195kN m⋅⋅=:=
MEd.z1 0.142− kN m⋅:=
MEd.z2 0.173− kN m⋅:=
MEd.z max MEd.z1 MEd.z2,( ) 0.142− kN m⋅⋅=:=
h 270mm:=
b 280mm:=
tw 8mm:=
tf 13mm:=
t max tw tf,( ) 13 mm⋅=:=
Izz 47630000mm
4
:=
Iyy 1.367 10
8
⋅ mm
4
:=
A 9730mm
2
:=
r 24mm:=
hw h 2tf− 2r− 196 mm⋅=:=

Area of the web
Warping Constant, Iw:
Torsional Constant, IT:
Plastic Modulus, Wply
Plastic Modulus, Wplz
Elastic modulus, E:
Yield strength of steel , fy:
Ultimate strength, fu:
Shear modulus
Reduction of yield and ultimate
strength of sections EN10025-2
Partial safety factor
Resistance of cross-sections whatever the class
(CYS EN1993-1-1,cl 6.1(1))
Resistance of members to instability
(CYS EN1993-1-1,cl 6.1(1))
Resistance of cross-section in tension
(CYS EN1993-1-1,cl.6.1(1))
Section classification
For section classification the coefficient ε is:
For a flange element:
Aw hw tw⋅ 1.568 10
3
× mm
2
⋅=:=
Iw 753.7 10
9
⋅ mm
6
⋅:=
It 635000mm
4
:=
Wpl.y 1112000mm
3
:=
Wpl.z 518000mm
3
:=
Es 210kN mm
2−
⋅:=
fy 275N mm
2−
⋅:=
fu 430N mm
2−
⋅:=
G 81kN mm
2−
⋅:=
fy fy t 16mm≤if
fy 10N mm
2−
⋅− 16mm t< 40mm≤if
fy 20N mm
2−
⋅− 40mm t< 80mm≤if
:=
fy 275 N mm
2−
⋅⋅=
fu fu t 16mm≤if
fu 10N mm
2−
⋅− 16mm t< 40mm≤if
fu 20N mm
2−
⋅− 40mm t< 80mm≤if
:=
fu 430 N mm
2−
⋅⋅=
γ M0 1:=
γ M1 1:=
γ M2 1.25:=
ε
235
fy
N mm
2−
⋅
0.924=:=

For a web element:
Tension resistance (cl.6.2.3)
Design plastic resistance of the cross section
(EN1993-1-1,cl.6.2.3(2)
Design ultimate resistance
(EN1993-1-1,cl.6.2.3(2b))
Design tension resistance
(EN1993-1-1,cl.6.2.3(2))
Check tension capacity
cf
b tw− 2.r−( )
2
112 mm⋅=:=
Class_type flange "CLASS 1"
cf
tf
9 ε⋅≤if
"CLASS 2" 9 ε⋅
cf
tf
< 10 ε⋅≤if
"CLASS 3" 10 ε⋅
cf
tf
< 14 ε⋅≤if
:=
Class_type flange "CLASS 2"=
cw h 2 tf⋅− 2 r⋅− 196 mm⋅=:=
Class_type web "CLASS 1"
cw
tw
72 ε⋅≤if
"CLASS 2" 84 ε⋅
cw
tw
< 83 ε⋅≤if
"CLASS 3" 105 ε⋅
cw
tw
< 124 ε⋅≤if
:=
Class_typeweb "CLASS 1"=
Class_type if Class_typeflange Class_typeweb Class_typeflange, "ADD MANUALY",( ):=
Class_type "ADD MANUALY"=
Npl.Rd
A fy⋅
γ M0
2.676 10
3
× kN⋅=:=
Nu.Rd
0.9A fy⋅
γ M2
1.927 10
3
× kN⋅=:=
Nt.Rd min Nu.Rd Npl.Rd,( ) 1.927 10
3
× kN⋅=:=
Check1 if
NEd
Nt.Rd
1.0≤ "OK", "NOT OK",
⎛
⎜
⎝
⎞
⎟
⎠
:=
Check1 "OK"=

ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

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ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8