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DiSGG, Università della Basilicata, PotenzaDiSGG, Università della Basilicata, Potenza

27° Convegno Nazionale GNGTS27° Convegno Nazionale GNGTS

Trieste 6-8 ottobre 2008Trieste 6-8 ottobre 2008

Angelo MASIAngelo MASI, Marco VONA, Marco VONA

VALUTAZIONE NUMERICA E SPERIMENTALE VALUTAZIONE NUMERICA E SPERIMENTALE DEL PERIODO DI VIBRAZIONE DI EDIFICI DEL PERIODO DI VIBRAZIONE DI EDIFICI

ESISTENTI IN C.A.ESISTENTI IN C.A.

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STATEMENT OF THE PROBLEM

• The effects of seismic actions on buildings can be determined using various methods of analysis.

• Assuming a linear-elastic behaviour of the structure, two methods can be used:- the lateral force method of analysis (LFMA), for “simple” buildings;- the modal response spectrum analysis (MRSA), applicable to all types of buildings.

• Both methods make use of an elastic ground acceleration response spectrum (elastic response spectrum) in the evaluation of the seismic response, where the calculation of the fundamental period T1 (LFMA) or periods (MRSA) of the structure has a main role.

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STATEMENT OF THE PROBLEM

• For the determination of T1, expressions based on methods of structural dynamics (e.g. Rayleigh method) may be used:

• Alternatively, many design codes provide simple expressions to calculate T1 that depend on: - building material (concrete, steel, masonry, etc.), - building type (frame, shear wall, etc.), - and overall dimensions (height, plan length, etc.).

2/1

11

21 /2

N

i ii

N

i ii uFguWT

where Wi is the weight at i-th floor, and ui are the floor displacement due to static applications of a set of lateral forces Fi at floor level i = 1, 2, …, N in an N-story building. Fi may be any reasonable distribution over the building height.

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Simplified Period – Height Relationship

The typical form of the simplified relationship is as follows:

T1 = Ct Hα

where Ct and α are coefficients theoretically or experimentally derived.

Code / Author Ct α Comments

ATC 3-06, EC8 0,075 0,75 Ct has been obtained from the measured periods of buildings during the 1971 San Fernando earthquale

NZEES 0,09 0,75

NEHRP, Goel and Chopra (1997)

0,0466 0,9 Periods measured in some US earthquakes (from San Fernando 1971 to Northridge 1994), coefficients obtained by subtracting one standard deviation from the best-fit curve

Hong-2000 0,0294 0,804 Periods measured on 21 Taiwanese buildings as subjected to moderate intensity earthquakes

Chopra and Goel (2000)

0,067 0,9 Same data of Goel-1997 but coefficients obtained by adding one standard deviation from the best-fit curve, expression proposed for displacement base design and assessment (DBD)

Crowley and Pinho (2004)

0,1 1 Expression obtained from numerical simulations and bibliographic data proposed for displacement base design and assessment (DBD) in Europe, effect of cracking on member stiffness is considered

Table 1 – Different values of coefficients of period-height relationship for concrete moment resistant frames

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Simplified Period – Height Relationship

Simplified Period-Height relationship for Concrete Moment Resistant Frames

0,00

0,50

1,00

1,50

2,00

2,50

0 5 10 15 20 25 30H (m)

T1

(s)

T1 (ATC, EC8)

T1 (NZSEE)

T1 (NEHRP, Goel-1997)

T1 (Hong-2000)

T1 (Chopra-2000), DBD

T1 (Crowley-2004), DBD

Force Based Design

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NUMERICAL SIMULATIONS

Parametric Analysis

Parameters of numerical simulations• Number of Story: 3 cases

• Dimensions in Plan: 2 cases

• Irregularity in Elevation: 3 cases

• Presence and position of Masonry Infills: 4 cases

• Member Stiffness: 3 + 3 cases

Variation in member stiffness is due to beam dimensions (Rigid Beams or Flexible Beams) and to effect of cracking

A parametric analysis has been carried out on several structural types purposely selected and designed representative of typical European RC buildings designed only to vertical loads

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•STRUCTURAL CODES IN FORCE

•HANDBOOKS TYPICALLY USED

•DESIGN CURRENT PRACTICE

SIMULATED DESIGN (only gravity loads)• Internal forces computation: simplified models• Reinforcement design (amount, details)

Information Source (from the period of construction )

STRUCTURAL TYPES SELECTION and DESIGN

TYPICAL RC STRUCTURES INVENTORY

STRUCTURAL TYPE SELECTION

Simulated Design of Existing R/C Buildings

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2 Story

8 Story

PARAMETRIC ANALYSIS:NUMBER of STORY

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Totally Infilled Frames (IF, Infilled Frame)

Partially Infilled Frames (PF, Pilotis Frame)

Without Infill Frames (BF, Bare Frame)

PARAMETRIC ANALYSIS:POSITION of INFILLS and BEAM STIFFNESS

2 story4 story8 story

Beam Stiffness

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PARAMETRIC ANALYSIS:EFFECT OF CRACKING ON MEMBER STIFFNESS

Eurocode 8: Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings

In concrete buildings the stiffness of the load bearing elements should, in general, be evaluated taking into account the effect of cracking.

Unless a more accurate analysis of the cracked elements is performed, the elastic stiffness properties of concrete elements may be taken to be equal to one-half of the corresponding stiffness of the uncracked elements Ie / Igross = 0,5

Experimental results (e.g. Kunnath et al., 1995) show that different values Ie / Igross can be adopted to take into account the different effect of cracking on columns and beams (role of the axial load value).Kunnath, K.S., Hoffmann, G., Reinhorn, A.M., Mander, J.B., , “Gravity load designed reinforced concrete buildings - part I: seismic evaluation of existing construction”, ACI Structural Journal, May – June, 1995

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30

Height [m]

Per

iod

[T

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30

Height [m]

Per

iod

[T

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30

Height [m]

Per

iod

[T

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30

Height [m]

Per

iod

[T

]

RESULTS OF NUMERICAL SIMULATIONS

Effects of Cracking and role of Infills (BF and IF types)

Igross

Ie = 0.7 Igross

Igross

Ie = 0.7 Igross

Lower valuesLower scatter

Higher valuesHigher scatter

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RESULTS OF NUMERICAL SIMULATIONS

Period-Height Relationship for RC Buildings (3-D Models)

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

0 5 10 15 20 25 30

H (m)

T1

(s)

BF_Ig

BF_Ie

IF_Ig

IF_Ie

LF1-BF_Ig

LF1-BF_Ie

LF1-IF_Ig

LF1-IF_Ie

T = C HBF_Ig BF_Ie IF_Ig IF_Ie LF1-BF_Ig LF1-BF_Ie LF1-IF_Ig LF1-IF_Ie

C 0,099 0,127 0,055 0,062 0,086 0,109 0,050 0,058Δ 0,0 28,3 -44,4 -37,4 -13,1 10,1 -49,5 -41,4

MAX MIN

PF

IF

LF1

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PROPOSED PERIOD-HEIGHT RELATIONSHIP

BARE FRAMET1 = 0,11 H

R = 0,90

INFILLED FRAMET1 = 0,055 H

R = 0,93

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0 5 10 15 20 25 30

Height [m]

Per

iod

[T

]

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EXPERIMENTAL RESULTS

Italian RC Building Stock (Gallipoli et al., 2006)

Microtremor measurements on 50 RC Italian buildings have been performed in Potenza town (Southern Italy) and in Senigallia town (Central Italy)

RC buildings under examination were designed taking into account only gravity loads, and were constructed in the period ’50s - ’70s

The buildings exhibit strongly different characteristics both in plan and in elevation

Simple and reliable methodologies have been used to estimate the fundamental period of buildings

Using a three component data acquisition system, the horizontal and vertical components of microtremors at the base and the top of the buildings are recorded

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EXPERIMENTAL RESULTS Some examples of Italian RC Buildings

Pilotis Building

Irregular in Elevation Building

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REGRESSION of EXPERIMENTAL RESULTS

T1 = 0,015 HR = 0,87

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0 5 10 15 20 25 30 35 40 45

H (m)

T1

(s)

+ SD

- SD

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EXPERIMENTAL RESULTS

Spanish RC Buildings (Navarro et al., 2004)

The dynamic behaviour characteristics of 89 RC building structures were investigated using microtremor measurements.The measurements were performed at the top of the buildings and at the centre of plan on the roof floor or at the last story of buildings.The dominant type of construction in Granada City consists in RC frames without earthquake-resistant design, with unidirectional RC tile lintel floors and exterior hollow brick walls. The RC buildings under examination were regular both in plan and elevation.

Proposed period-height relationship: T1 = 0,016 H

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NUMERICAL VS. EXPERIMENTAL RESULTS

0,00

0,50

1,00

1,50

2,00

2,50

3,00

5 10 15 20 25 30Height [m]

Per

iod

[se

c]

IF - SDIF + SDBF - SDBF + SDGranada (89 Buildings)T(Crowley & Pinho 2006)T(EC8)IFBFPotenza + Senigallia (50 Buildings)

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EXPERIMENTAL RESULTSCInEnel Building

370 370 37 0 370 3 70

370 370 250 490 370

15 16 17 19 20

7 8 9 11 12

1 2 3 4 5 62 2

18

25

25

540 550

27

1090

27

25 25

13 14

60X30 30X50

10

370 370 37 0 370 3 70

370 490 250 370 370

19' 18' 17' 16' 15'

11' 10' 9' 8' 7'

5' 4' 3' 2' 1'

ass enza d i fora ti

25

25

25

25

25 25

25

PRIMO SOLAIO

40x20

25 25

14' 13'

25

27

27

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EXPERIMENTAL RESULTSCInEnel Building

Signal

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 1 2 3 4

T (s)a

(g/1

000)

A1B2A3B4

PSD

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Freq(Hz)

a (

g/1

00

0)

A1B2A3B4

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EXPERIMENTAL RESULTSCInEnel Building

15 16 17 19 20

7 8 9 11 12

1 2 3 4 5 6

18

27

27

13 14

60X30 30X50

10

19' 18' 17' 16' 15'

11' 10' 9' 8' 7'

5' 4' 3' 2' 1'

25

25

40x20

14' 13'

27

27

15 16 17 19 20

7 8 9 11 12

1 2 3 4 5 6

18

27

27

13 14

60X30 30X50

10

19' 18' 17' 16' 15'

11' 10' 9' 8' 7'

5' 4' 3' 2' 1'

25

25

40x20

14' 13'

27

27

Building 1 (Structural Damage) Building 2 (No Damage)

Building 1 Building 2

Mode 1 Mode 2 Mode 1 Mode 2

Experimental 0.256 0.242 0.228 0.217

ATC, EC8 0.572 0.572

NZSEE 0.686 0.686

NEHRP, Goel-1997 0.533 0.533

Hong-2000 0.259 0.259

Chopra-2000, DBD 0.767 0.767

Crowley-2004, DBD 1.500 1.500

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FINAL REMARKS

• Fundamental period has a main role in the determination of the effects of seismic actions on buildings

• The strong influence of masonry infills and of cracking on the fundamental period values of RC buildings has been highlighted

• Simplified period-height expressions are provided purposely set up for some structural types widely present in the European built environment

• Further studies and in-situ tests are needed to better understand the large differences between numerical and experimental values

• Experimental results on damaged RC buildings show low period increase (frequency decrease) as a consequence of heavy damage levels