Seismic Design of Steel Buildings

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Seismic  design  of  steel  

building  accordance  to      

Eurocode  3  and  8  

 

 

 

Valentinos  Neophytou  BEng,  MSc  

 

 

 

 

JULY  2013  

-­‐Worked  examples  –  Hand  calculations  

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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

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Page 3 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

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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

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Page 5 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

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

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Page 7 1.1 Design and analysis example of steel frame with concentric bracing

1.1 Layout of structure

Figure 1.1: Plan view

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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

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Page 9 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

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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 × ⋅cm4 = := Iprov :=3892cm4 Check_1:=if Iprov Ireq

(

> , "OK", "NOT OK"

)

Check_1="OK" MEd Ed Lx 2 ⋅ 12 =76.953 kN 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:= ⋅ =421.72cm3 Wpl.y.c 515cm:= 3

Check_3:=if Wpl.y.c Wpl.y.c.req

(

> , "OK", "NOT OK"

)

Check_3="OK"

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Page 11 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

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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/mm

3 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 ≤ 100oC) 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 ≤ 100oC) 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/mm

2 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 reference fy (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

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Page 13 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)

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Table 1.6: Slab properties

Data Symbol Value Units

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

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Page 15 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)).

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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

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Page 17 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.

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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

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Page 19

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

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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)

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Page 21 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)

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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 %

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Page 23

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

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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.

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Page 25 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

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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

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Page 29 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.

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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.

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Page 31 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).

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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.

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Page 33

Define > Response spectrum cases

Note: Add two response spectrum cases: EQX and EQY as showing below (figure 9).

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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

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Page 35

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

Exact formula for Single Degree of Freedom Oscillator. Vertical cantilever of height H and of total mass MB.

𝑇! = 2𝜋

0.24𝑀!𝐻!

3𝐸𝐼

Exact formula for Single Degree of Freedom 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.

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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

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Page 37 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

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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⋅ =225m2 Nf :=3 Nb :=24 Ns :=9 Nc :=16 Nt :=8

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Page 39

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 = :=

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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 if Seismic_zone "1" 0.2g if Seismic_zone "2" 0.25g if Seismic_zone "3" 2.452m s2 = := Importance_factor :="II" γ I 0.8 if Importance_factor "I" 1.0 if Importance_factor "II" 1.2 if Importance_factor "III" 1.4 if Importance_factor "IV" 1 = := ag γ I agR⋅ 2.452m s2 = := Value_Ct "OTHER":= Ct 0.085 if Value_Ct "MRSF" 0.075 if Value_Ct "MRCF" 0.05 if Value_Ct "OTHER" 0.05 = := T1 Ct⎛⎜Hm ⎝ ⎞ ⎟ ⎠ 3 4 ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦s =0.26s := Soil_type:="B" S 1.0 if Soil_type "A" 1.2 if Soil_type "B" 1.15 if Soil_type "C" 1.35 if Soil_type "D" 1.2 = :=

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Page 41 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 if Soil_type "A" 0.15s if Soil_type "B" 0.20s if Soil_type "C" 0.20s if Soil_type "D" 0.15s = := TC 0.40s if Soil_type "A" 0.50s if Soil_type "B" 0.60s if Soil_type "C" 0.80s if Soil_type "D" 0.5s = := TD 2.0s if Soil_type "A" 2.0s if Soil_type "B" 2.0s if Soil_type "C" 2.0s if Soil_type "D" 2 s = := λ 0.85 if T1 2TC≤ ∧Nf 2> 1 otherwise 0.85 = :=

Check_1:=if T1 4TC

(

≤ ∧ T1 2s≤ , "Lateral force analysis", "Response spectrum analysis"

)

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 ⋅ T12 ⋅ ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ ag S⋅ 2.5 q ⋅ TC TD ⋅ T12 ⋅ ≥β ag⋅ if β ag⋅

(

)

ag S⋅ 2.5 q ⋅ TC TD ⋅ T1

( )

2 ⋅ ≤β ag⋅ if :=

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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

( )

72.642m

s2 =

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( ) if 0≤T1TB S2e TB

( )

if TB T1≤ ≤TC S3e TC

( )

if TC T1≤ ≤TD S4e T1

( )

if TD T1≤ ≤4s 4.903m s2 = := Fb S_mass Se⋅ T1 s ⋅ ⋅λ =464.519kN⋅ := Fb.bracing := Fb2 =232.259kN⋅

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Page 43

Table 2.12: Summary table of the lateral force results

Story Heigth                                 zi                                         (m) Mass                                   mi                                     (kN)

zi*mi (kN)Fb                                  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:= = × 3kN

z3 9m:= z2 6m:= z1 3m:=

Σmi_zi:=FEd.storey z3⋅ +FEd.storey z2⋅ + FEd.storey z1⋅ =2.524 10× 4kN m⋅

F3:= Σmi_zimi z3⋅ ⋅Fb =232.259kN⋅ F2:= Σmi_zimi z2⋅ ⋅Fb =154.84kN⋅ F1:= Σmi_zimi z1⋅ ⋅Fb =77.42kN⋅

F:=F3 F2+ + F1=464.519kN

Check_2:=if F

(

Fb, "OK", "NOT OK"

)

Check_2 "OK"=

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ETABS: Define > Static load case >

Figure 2.6: Define manually the lateral forces

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Page 45 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

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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

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Page 47 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.

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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

𝐆𝐤,𝐣+ 𝛙𝐄𝐢𝐐𝐤,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 𝛙𝐄𝐢 (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

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Page 49 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.

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Page 51 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 vb,0

c z

v z

c z

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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* surface is covered with building and Area in which at least 15% of the

their average height exceeds 15m.

1.0 10

* For buildings in terrain category IV, displacement height h

dis 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 vm2 (z)=ce(z)·0.5·ρ·vb2

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Page 53 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)

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5.2 Application of wind loading using ETABS

Table 5.4: Wind load assumptions

Data Symbol Value Units

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

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Page 55

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”

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Wind pressure coefficient for load case WINDY

Windward load “Area D” Leeward load “Area E”

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Page 57

                  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

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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                                    

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Page 59 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

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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)

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Page 61 7.0 Design preferences

ETABS: Options > Preferences > Steel frame design

Figure 7.1: Steel frame design preferences

2 3 4 1 5 6

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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 = 𝑵𝒑𝒍,𝑹𝒅/𝑵𝑬𝒅)

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Page 63 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

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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).

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Page 65 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

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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 if t <16mm fy 10N mm− ⋅ −2 if 16mm t< <40mm fy 20N mm− ⋅ −2 if 40mm t< <80mm := fu. fu if t ≤16mm fu 10N mm− ⋅ −2 if 16mm t< ≤40mm fu 20N mm− ⋅ −2 if 40mm t< ≤80mm := 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 :=

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Page 67 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 −tw2−2.r

)

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 :=

Figure

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References