Seismic evaluation and strengthening of a 5 story building with piloti, according to EC8 using...

SEISMIC EVALUATION AND STRENGTHENING OF A 5 STORY BUILDING WITH PILOTI, ACCORDING TO EC8 USING PUSHOVER NONLINEAR STATIC ANALYSIS

ΙASON GRIGORATOS

SummaryThe present thesis examines an existing building of year 1993, with piloti plus 4 typical floors, which was designed using triangular seismic distribution. The building was analysed using Pushover Nonlinear Static Analysis (D.C.M.). The structure was checked for SD and NC compliance criteria under the design earthquake and also for the DL criterion under an earthquake with a return period of 42 years. It was then strengthened with X steel braces.

1. INTRODUCTION

1.1 SUBJECTThe goal of the present thesis is the seismic evaluation of an existing multi-store building for various compliance criteria and spectral accelerations. The effectiveness of diagonal steel braces for the strengthening of the structure is also examined.

The analysis, the seismic evaluation and the redesign of the building were done according to «ΚΑΝ.ΕΠΕ.», the Greek Code for Repairs of RC Structures, in full compliance with Eurocodes.

The software in use was by «Cubus AG» (Statik5, Hoch5, Fagus5, Cedrus5).

1.2 DATA OF THE EXISTING BUILDINGThe building was designed as a 3D frame according to the «additional restrictions» of the 1959 Greek Anti-seismic Code [1]. The total horizontal seismic force was taken equal to the total weight W of the building multiplied with a coefficient ε=0.08 and was distributed triangularly with the maximum on top.

The Knowledge Level is granted as Full, because there are reliable and sufficient information about the construction [2].

The building was designed with: • Concrete: Β225 (slabs & beams), Β300 (columns & walls)• Steel rebars: St III, Stirrups: St I• 50% increase in the seismic forces on the piloti level• Live loads: overall 2 kN/m2, staircases 3.5 kN/m2, cantilevers 5 kN/m2

• Overlay loads: overall 0.8 kN/m2, rooftop 1 kN/m2

• Ground type: Β• Importance Class: II (importance factor γt= 1)• Seismic hazard zone: II (Salonica)

«20th Annual Student Conference: Reinforcements-repairs of R.C. structures»Patras, February 2014

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Iason Grigoratos

Figure 1.1: Formwork of the piloti level

Figure 1.2: Formwork of the typical floor


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Seismic evaluation and strengthening of a 5 story building with piloti, according to EC8 using Pushover Nonlinear Static Analysis

BeamCross section(cm2)

Span middle(Φmm)

Beam end(Φmm)

Stirrups(Φmm/cm)

Β 1 65x40 8Φ20 8Φ20 4 legged Φ8/12Β 2 65x40 8Φ20 8Φ20 4 legged Φ8/12Β 3 65x40 8Φ20 8Φ20 4 legged Φ8/12Β 4 50x40 8Φ20 8Φ20 4 legged Φ8/8Β 5 50x40 8Φ20 8Φ20 4 legged Φ8/8B 6 50x40 8Φ20 6Φ20 Φ8/6B 7 50x40 8Φ20 6Φ20 Φ8/6B 8 20x60 13Φ20 10Φ20 Φ8/6Β 9 35x40 6Φ20 6Φ20 Φ8/6B10 35x40 6Φ20 6Φ20 Φ8/6Β11 20x75 5Φ20 5Φ20 Φ8/6Β12 20x75 5Φ20 5Φ20 Φ8/6Β13 20x75 5Φ20 5Φ20 Φ8/6Β16 20x60 6Φ20 6Φ20 Φ8/6Β17 25x75 8Φ20 8Φ20 Φ8/6B18 25x75 8Φ20 8Φ20 Φ8/6B19 30x75 6Φ20 8Φ20 Φ8/6B20 35x40 6Φ20 5Φ20 Φ8/6Β21 35x40 6Φ20 5Φ20 Φ8/6B22 35x40 6Φ20 5Φ20 Φ8/6B23 20x75 5Φ20 5Φ20 Φ8/6B24 20x75 5Φ20 5Φ20 Φ8/6B25 20x75 5Φ20 5Φ20 Φ8/6B26 20x75 5Φ20 5Φ20 Φ8/6

Figure 1.1: Steel reinforcement of piloti beams

BeamCross

section (cm2)

Span middle(Φmm)

Beam end(Φmm)

Stirrups(Φmm/cm)

Β 1 35x60 11Φ20 7Φ20 Φ8/6Β 2 35x60 11Φ20 7Φ20 Φ8/6Β 3 35x60 11Φ20 7Φ20 Φ8/6B 6 20x75 6Φ20 6Φ20 Φ8/6Β 9 35x60 6Φ20 6Φ20 Φ8/6B10 35x60 6Φ20 6Φ20 Φ8/6B20 20x75 6Φ20 5Φ20 Φ8/6Β21 20x75 6Φ20 5Φ20 Φ8/6B22 20x75 6Φ20 5Φ20 Φ8/6

Figure 1.2: Steel reinforcement of typical floor beams

Beams omitted from Figure 1.2 are the same as in Figure 1.1.


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ColumnPILOTIS:

Cross section & rebars

FLOORS: Cross section

& rebarsStirrups

PILOTIS: single legged

stirrups

TYP. FLOOR:single legged

stirrupsC 1 T 35x35 12Φ20 35x35 12Φ20 Φ8/6 - √C 2 D=55 29Φ20 50x35 22Φ20 Φ8/6 √ √C 3 D=55 29Φ20 50x35 22Φ20 Φ8/6 √ √C 4 T 35x35 12Φ20 35x35 12Φ20 Φ8/6 - √C 5 35x50 10Φ20 20x50 8Φ20 Φ8/6 - -C 6 30x50 10Φ20 25x50 8Φ20 Φ8/6 - -C 7 30x50 10Φ20 25x50 8Φ20 Φ8/6 - -C 8 35x50 10Φ20 20x50 8Φ20 Φ8/6 - -C 9 50x35 8Φ20 50x35 8Φ20 Φ8/6 - -C10 35x35 12Φ20 35x35 12Φ20 Φ8/6 √ √C18 80x35 14Φ20 80x35 14Φ20 Φ8/6 - √

Figure 1.3: Steel reinforcement of columns

Wall Cross section

Total reinforc. in confined boundary elements

Verctical reinforc.

Horizontal reinforc.

StirrupsSingle legged

stirrups

W11 20x150 16Φ20 Φ8/20 Φ8/20 Φ8/10 √W12 20x120 16Φ20 Φ8/20 Φ8/20 Φ8/10 √W13 Π 36Φ20 Φ8/20 Φ8/20 Φ8/10 -W14 20x120 16Φ20 Φ8/20 Φ8/20 Φ8/10 √W15 20x120 16Φ20 Φ8/20 Φ8/20 Φ8/10 √W16 20x100 24Φ20 Φ8/20 Φ8/20 Φ8/10 -W17 20x180 20Φ20 Φ8/20 Φ8/20 Φ8/10 -

Figure 1.4: Steel reinforcement of walls 2. STRUCTURAL MODELLING

2.1 SIMULATION OF THE INFILL WALLSInfill walls with an opening bigger than 50% of their frame bay dimensions are passed over. (ΚΑΝ.ΕΠΕ. §7.4.1). Therefore, frame bays with French doors were not taken into account. All inner walls (t=10cm) were also ignored, because of the buckling factor (λ>30). «λ» is the definition of the relative ratio of length to thickness. As long as λ<15 there is no decrease in the strength capacity, while when 15<λ<30 a decreasing coefficient «φ» is taken into account. (ΚΑΝ.ΕΠΕ. Table p. 7-33). All infill walls, that were passed over, are not marked in Figure 1.2. The self weight of the inner walls was granted 6 kN/m and of the outer walls 10 kN/m.

The infill walls are simulated as simply supported compressed diagonal friction members. These members have thickness «t» equal to the thickness of the infill walls and width b=0.15*L, L=(l2+h2)0.5 the length of the diagonal. The strength of the infill walls is calculated according to the mechanical properties [3] of the materials (mostly bricks) that the wall is consisted of (ΚΑΝ.ΕΠΕ. formula Σ.18).


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https://www.google.com/search?q=French+door&rlz=1C1CHMB_elGR344GR344&es_sm=122&tbm=isch&tbo=u&source=univ&sa=X&ei=Px1MU4r6O6SL0AWd4IDYDQ&ved=0CCcQsAQ


Therefore: fwc,s=1.25*k* fbc0.7* fmc

0.3 (1)k=0.35, fbc=11, fmc,κυβου=1.57, fmc,κυλ.=3.43.

In the structural program STATIK the friction members are simulated as diagonals with Pushover hinges at both ends. The simulating material was C2.7/3.4 unreinforced concrete (ΚΑΝ.ΕΠΕ. formula Σ.18) with zero tensile capacity. Furthermore, the stiffness and modulus of rigidity of the members were significantly reduced in order to avoid any bending or torque stresses. The input of the walls is done in a way that ensures that they are subjected only to seismic and not to vertical loads. (ΚΑΝ.ΕΠΕ. §2.1.4.2(α))

Frame bay t (m) b (m) φΧ 4 0.20 0.45 -Χ 7 0.20 0.50 0.80Υ 1 0.20 0.50 0.90Υ 2 0.20 0.50 0.90Υ 3 0.20 0.45 -Υ 5 0.20 0.40 -Υ 6 0.20 0.40 -Υ10 0.20 0.50 0.90Υ11 0.20 0.50 0.90Υ12 0.20 0.40 -Υ13 0.20 0.50 0.80

Figure 2.1: Infill walls properties

2.2 SIMULATION OF SLABS AND FOUNDATIONThe building has a basement with RC walls in the perimeter. Therefore, the foundation is simulated as rotation and translation fixed joints at the bottom end of all columns and walls of the piloti level.

The slabs are not checked, because they are not subjected to seismic loads and they have not been damaged in any way. Their diaphragmatic function is imported into the model.

2.3 SIMULATION OF THE DIAGONAL STEEL BRACESSquare hollow diagonal steel braces were used in order to strengthen the building. According to the Greek National Annex of EC8 titled «ΚΑΝ.ΕΠΕ.», the diagonal braces are passed over under compression, because of buckling (ΚΑΝ.ΕΠΕ. Σ§8.5.5.4β). However this instruction was considered over conservative, because, after calculations [4] according to the axial forces originated from the analysis, the chosen cross sections of paragraph 5.2 are more than sufficient to avoid buckling.

The calculations were done ignoring the favourable instruction, according to which the effective length of the X bracing section bars can be reduced by 50% (ΚΑΝ.ΕΠΕ. Σ §8.5.5.4γ).

2.4 SIMULATION OF REBARS IN BEAMSThe RC beams contain cold bended rebars in order to sustain not only tension but also the seismic shear forces in a region close to the columns. Because of the lack of detailed information about the exact part of the beam that this angular rebars exist, their contribution to the shear capacity of the RC beams is passed over.


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https://www.google.com/search?rlz=1C1CHMB_elGR344GR344&es_sm=122&biw=1280&bih=937&q=significantly&spell=1&sa=X&ei=SydMU63QKYqi0QW-jIGwDA&ved=0CCMQvwUoAA

http://en.wikipedia.org/wiki/Modulus_of_rigidity

http://en.wikipedia.org/wiki/Modulus_of_rigidity

Iason Grigoratos

3. DESCRIPTION OF THE SEISMIC EVALUATION THEORY

3.1 DESCRIPTION OF THE PUSHOVER METHODThe elastic-plastic pushover analysis is based on inelastic response spectrum. It is a non-linear static analysis where the seismic deformations develop under constant gravity loads and monotonically increasing horizontal loads. Plastic hinges are gradually formed at the ends of the structural elements resulting in a decrease of their stiffness and the distribution of forces to neighbouring elements. At the point that the inelastic deformations are such, that the construction either cannot bear any more loads, or early shear failure in primary elements occurs, the building collapses.

It should be pointed out that the elastic-plastic pushover analysis is ideal, because it takes into account the behaviour of the structure only due to plastic hinges, ignoring any early shear failures. In other words the final «λ-δ» capacity curve (lateral seismic ratio - control displacement) of the method is meaningful, only if the potential early shear failures are restored. Finally, because of the very nature of the method, its application is not indicated if one of the first two vibration modes of the building is torsional and not horizontal.

Diagrams relating the internal moment M with the chord rotation «θ» are used for checking the inelastic behaviour of the structural elements. The required verifications are: ductility in terms of deformations, resistance in terms of forces and deformations for functionality reasons [5].

Prerequisite for these verifications is the calculation of a target displacement «δτ». The effective eigenperiod «Te» of the building is calculated based on a bilinear approximation of the capacity curve. Afterwards, the target displacement δτ is calculated according to the spectrum. (ΚΑΝ.ΕΠΕ., formula Σ5.6):δt = C0 C1 C2 C3 (Te

2 / 4π2) Se(T) (2) The values of the coefficients were:

• C0=1.40, since the building had 5 floors and is built after the year 1985• C2=1.00, since the building is built after the year 1985 (type 2 structure)• C3=1.00, since second order effects (P-delta) were not taken into account in the Pushover

method• Cm=0.85, since the analysis concerns a frame structure of RC concrete with Τ<1s.

3.2 COMPLIANCE CRITERIAThe compliance criteria define the acceptable degree of structural damage in the event of the design earthquake. The three compliance criteria [6] are determined by the ultimate chord rotation θu and are:

• Damage Limitation (DL). The structure is only lightly damaged, with structural elements prevented from significant yielding and retaining their strength and stiffness properties. Non-structural components, such as partitions and infills, may show distributed cracking, but the damage could be economically repaired. Permanent drifts are negligible. The structure does not need any repair measures.

• Significant Damage (SD). The structure is significantly damaged, with some residual lateral strength and stiffness, and vertical elements are capable of sustaining vertical loads. Non-structural components are damaged, although partitions and infills have not failed out-of-plane. Moderate permanent drifts are present. The structure can sustain after-shocks of moderate intensity. The structure is likely to be uneconomic to repair.


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• Near Collapse (NC). The structure is heavily damaged, with low residual lateral strength and stiffness, although vertical elements are still capable of sustaining vertical loads. Most non-structural components have collapsed. Large permanent drifts are present. The structure is near collapse and would probably not survive another earthquake, even of moderate intensity.

Based on the existing steel reinforcement, program «Fagus5» calculates the actual resistance of the cross sections and forms automatically the corresponding plastic hinge. The elements do not fail, but continue to deform by forming plastic rotations and drifts.

There are two types of failure the program detects:• Brittle failure in terms of forces.• Ductile failure, e.g. due to bending or drift, in terms of deformation (chord plastic rotation)

[5].

Depending on the corresponding compliance criterion, the static program calculates different ultimate chord rotations θu as acceptable. The shear capacity of the elements, because it is the only bear capacity that is checked in terms of forces, is the same for all three compliance criteria. In NC criterion the model actually develops bigger shear forces and inadequacies, since the contribution of the infill walls is passed over.

Bellow there is a table with the performance objectives according to EC8 for the hazard levels of SEAOC (1999).

Probability of exceedance in

50 yearsReturn period

Compliance CriteriaDamage

LimitationSignificant

DamageNear Collapse

10% 457 Α1 Β1 C1115% 42 Α3 Β3 C3

Table 3.1

An earthquake, with a return period shorter than the life expectancy of the building, was included in order to check the behavior of the structure for performance objective A3. In other words it is checked whether the building can be in immediate use after a «frequent» earthquake.

As far as the present thesis is concerned and given the importance of the building, it did not seem advisable to check the structure for performance objectives A1, B3, C3.

According to «EAK2003» Code [7] the design earthquake (levels B1, C1) for the building’s region has a peak ground acceleration coefficient a=0.24. According to SEAOC (1999) the corresponding coefficient for a «frequent» earthquake (A3) is equal to 0.08.


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4. RESULTS OF THE EXISTING BUILDING ANALYSIS

Figure 4.1: 3D representation of the building including infill walls

4.1 RESULTS OF THE ANALYSIS FOR B1 OBJECTIVE

Figure 4.2: (ADRS) capacity curve for POx+ load


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The demand for ductility in the POx+ combination load is μ=δt /δy equal to 1.80.

Figure 4.3: (ADRS) capacity curve for POy+ load

The demand for ductility in POy+ combination load is μ=δt /δy equal to 1.67.

Figure 4.4: Deformation of the structural model for combinations loads POx+ and POx-


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Figure 4.5: Deformation of the structural model for combinations loads POy- in 3D and POy+ in 2D (X-Ζ)

Despite the ominous combination of piloti with infill walls at floor levels, no soft-story mechanism is observed.

Figure 4.6: Plastic strains (POy-) and plastic hinges (POy+) of infill wall elements


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The wall strains are approximately 14mm in 3.3m of length, namely ε1=4‰. According to Mohr's circle: γ/2=4‰ → γ=8‰. As a result, the infill walls will not suffer any significant damages.

The right side of Figure 4.6 indicates the immediate formation of plastic hinges at the infill walls, due to tension, occurs after the very first step of POy+.

The inadequacies of the vertical and horizontal elements for SD compliance criterion are stated in the Table bellow.

BEAMS WALLSStirrups Ζ Stirrups Ζ Stirrups Y

Β25L1,2,3

B18L1,2,3

B19L1,2,3

W17L1,2

W 13L1

W 12L1,2,3

W 15L3

3 - 3.4 2.2 3 - 3.3 4 - 4.8 4.6 2.5 - 3 2.3Table 4.1: Inadequate ratios of beams and walls according to SD criterion

(L1 = roof of piloti)

The inadequacies are calculated as the ratio of the imposed forces to the allowable ones and have as basis the number one. Therefore, the acceptable ratio for the plastic hinges of all structural elements is ≤1. As far as shear failure is concerned, the adequate-inadequate ratios are calculated for a strut inclination angle of 45 degrees. However according to EC2 [8] we can assume of a strut inclination angle equal to 30 degrees, regarding that it does not concern short beams or that the shear forces are combined with tension. As a result we accept the value 2 as the highest limit for the shear failure of the structural elements.

Ιnter alia, beam B25 L1 has inadequacy of shear capacity equal to 362kN and wall W13 L1 equal to 1340kN.

Evidently there are shear strength inadequacies despite that the building does not develop significant chord plastic rotations. The range of the brittle failures in primary structural elements practically means that the building collapses under the design earthquake.

4.2 RESULTS OF THE ANALYSIS WITH UNIFORM DISTRIBUTIOΝIn the previous analysis (Table 4.1) the model was submitted to horizontal triangularly distributed loads. In this paragraph, loads originate from the same earthquake as before, but with a uniform distribution. That leads to slightly different results.

As indicated in Figure 4.7, the δτ was slightly smaller both in x and y axis in comparison to the triangular distribution (Figures 4.2 and 4.3). As far as the inadequacies of the beams are concerned, they remain the same. The inadequacies of the columns are slightly smaller, while those of the walls are slightly bigger. The smaller δτ, in combination with the very small diversifications in the results, led to the use of triangular distribution for the following analysis.

Figure 4.8 indicates that in the POx load the uniform distribution causes more torsional displacement and therefore there is a slightly smaller δτ.


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Figure 4.7: Capacity curves for uniformly distributed seismic loads

Figure 4.8: Deformation of the structural model for POx+, POy+ loads with uniform distribution

4.3 RESULTS OF THE ANALYSIS FOR OBJECTIVE C1In NC criterion the contribution of infill walls is passed over (ΚΑΝ.ΕΠΕ. §7.4.1(β)). Beyond that, the structural model and the response spectrum remain the same. The absence of the diagonal bars of infill walls slightly reduces the total stiffness of the building and increases δτ by 5mm in x direction and by 6mm in y direction.


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BEAMS WALLSstrirrups Ζ strirrups Ζ strirrups Y

Β25L1,2,3

B18L1,2,3

B19L1,2,3

W17L1,2

W13L1,2

W12L1,2,3

W15L3

W14L1,2,3

W11L1

3.2 - 3.6 2.5 2.7 - 3.3 4 - 4.8 2.2 - 3 2.5 - 3 2.3 2.5 - 3.1 2.3Table 4.2: Inadequacies in performance objective C1

As a result of the bigger δτ, the inadequacies appear generally bigger and in more elements. That makes criterion NC seem paradoxically more adverse than SD. Of course this is misleading, because any early shear failures lead to the collapse of the building, regardless of the selected compliance criterion. Therefore, the criteria are meaningful, only if the building is strengthened so that it will not collapse due to potential early shear failures.

4.4 RESULTS OF THE ANALYSIS FOR OBJECTIVE A3

Figure 4.9: Capacity curve regarding α=0.08

In this performance objective, the δτ is smaller than the δy for all four directions of Pushover loads. Despite that, there is an exceedance in the verification of the chord rotations.

BEAMS COLUMNSstirrups Ζ Plastic chord rotations

Β25L1

C6L2,3

C7L2

2.2 1.2 - 1.6 1.2Table 4.3: Ratios of inadequacy in objective A3

Ιnter alia, beam B25 L1 (piloti roof) has inadequacy of shear capacity equal to 60kN. It goes without saying that for a less intense earthquake, shear forces are significantly smaller. Due to


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Iason Grigoratos

the DL criterion, the tolerance in chord rotations is dramatically reduced. Infill walls have a maximum strain of 1.5mm and therefore they will not suffer any damage.

5. STRENGTHENING OF THE BUILDING FOR OBJECTIVES Β1, C1, Α3

5.1 STRENGTHENING FOR OBJECTIVES Β1, C1Building was strengthened using variable cross sections of X bracing section bars, in different combinations of frame bays, either only in piloti or across the full height of the building. No realistic combination dealt successfully with the shear inadequacies of the beams and walls, despite the fact that the δτ was slightly reduced. The Table bellow indicates the crucial results of the application of X bracing steel 80x80x10 square hollow elements in all perimeter frame bays of the piloti level in y axis direction (Figure1.2). This time, the steel section bars under compression were not taken into account in the structural modelling.

BEAMS WALLSstirrups Ζ stirrups Ζ stirrups Y

Β25L1,2,3

B18L1,2,3

B19L1,2,3

W17L1,2,3

W13L1,2

W12L1,2

W15L3

W14L1,2,3

3 - 3.4 2.1 3 - 3.1 2.4 - 3.6 2.4 - 4 2.5 - 3 2.3 2.2 - 2.9Table 5.1: Inadequacies of the strengthening with X bracing 80x80x10 section bars

for objective B1

The application of 110x110x10 square hollow elements instead of 80x80x10 lead to negligible improvements. The results were similar when the strengthening was applicated in the frame bays of the piloti level in x direction. Finally, neither the application of X braces allong the full height of the building in frame bays Y1, Y3, Y6, Y10, Y13 (see Figure 1.2) dealt with the shear capacity problems in the beams and the walls W17, W13, W14.

In conclusion, X steel braces, despite increasing the stiffness, are not suitable for dealing with great inadequacies in shear capacity. As an alternative, the use of FRP in the problematic elements is recommended (ΚΑΝ.ΕΠΕ. §8.2.2).

5.2 STEEL BRACING STRENGTHENING FOR OBJECTIVE Α3In performance objective A3, there are very small inadequacies in shear capacity (Table 4.3) and significant exceedancies in chord rotations. After parametric solving it is recommended to use 130x130x8 hollow X braces in frame bays of beams B17 and B4 of the 1st floor roof (see Figure 1.2) and 80x80x6 in frame bay Y12 in the same level,.

For the reasons mentioned in §2.3 above, the compressed diagonal steel section bars are not taken into account in the process of the Pushover analysis.

BEAMS COLUMNSstirrups Ζ Plastic chord rotations

Β25L1

C6L2,3

C7L2

1.98 0.93 0.97Table 5.2: The crucial elements for objective A3 after strengthening


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It is inferred that, with the contribution of the steel braces, the inadequacies in shear capacity and chord ration are successfully dealt with.

Figure 5.1: 3D representation of L1 and L2 after strengthening, without infill walls(The above drawing imperfections are due to the eccentricity of joints)

Figure 5.2: Capacity curves for objective Α3 after strengthening

In perfect consistency with the calculations, no steel section bar in any load direction forms plastic hinge.


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6. FINAL CONCLUSIONS• The «additional restrictions» of 1959 Greek Anti-seismic Building Code do not ensure

the adequacy of elements under shear stresses and do not exclude the collapse of the structure under the design earthquake. Even though the restrictions for the spacing of stirrups were sufficient as far as the ductility of the structure is concerned, the use of smooth S220 (St I) stirrups lead to extended brittle failures. If the stirrups were St III (likewise with the horizontal rebars) the structural model could avoid collapsing under the design earthquake.

• The 50% accretion rate in the seismic forces in the piloti level helped preventing any soft-story mechanism, but did not protect the building from brittle failures.

• Despite the ominous combination of piloti with infill walls at the floor levels, no soft-story mechanism is observed. That is mainly because of the large number of walls in the y direction (ny=80%).

• Even though the seismic base shear ratio of RC walls is ny=80% and nx=76%, the structure was unable to cope with an earthquake of moderate to great intensity.

• The short beams (<1.5m) suffer from shear stresses, even under a frequent/weak earthquake.

• A building may not have problems concerning the exceedance of chord rotations for the SD performance criterion under the design earthquake, but still faces problems for the DL criterion under a frequent/weak earthquake.

• If a building has enough ductility and does not exceed the acceptable chord rotations of the objective B1, the restriction ΚΑΝ.ΕΠΕ. §7.4.1(β) makes the objective C1 seem at first glance as more ominous. Of course, as explained, the compliance criteria are meaningful only if the building is already retrofitted so that it does not collapse due to early shear failures.

• The X steel braces are more efficient in dealing with shear forces, when placed above the crucial beam instead of underneath. This happens perhaps because the gravity loads of the building are better distributed.

• The use of X steel braces increases the total stiffness of the building, but it is not recommended for dealing with inadequacies in shear strength in the absence of a soft-story mechanism.

• The simulation of the infill walls did not make a great difference in the behaviour of the building, mainly because their position was between frame bays with walls at both ends.

• Even though the ductility factor «μ» for the objective B1 is >1.5, the building has enough ductility to cope with the demands of the SD criterion.

• Even though the ductility factor «μ» for the objective B1 is <1, two columns develop unacceptable chord rotations.

• The uniform distribution of the seismic loads does not lead to significantly different conclusions in comparison to the triangular. Having said that, it does lead to more torsional displacements due to the position of the elevator RC wall. This fact affects badly the corner columns of the perimeter, but not the beams.

• The instruction of paragraph §8.5.5.4 of «ΚΑΝ.ΕΠΕ.» Code, i.e. that the compressed diagonal steel section bars regardless of cross section are passed over due to buckling, was proven over conservative, since, for the chosen hollow cross sections, no section bar in any load direction forms plastic hinge.


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7. BIBLIOGRAPHY [1] «Additional restrictions» of year 1984 to the Greek Anti-seismic Code of year 1959[2] «ΚΑΝ.ΕΠΕ. (2013)», Greek Code for Repairs of RC Structures, in full compliance with Eurocodes and their Greek Annexes[3] Dr. Georgia Mpei, «Φέρουσα τοιχοποιία από ωμοπλίνθους – Research and innovation in Greece», Table 3 & 4, library.tee.gr/digital/m2316/m2316_bei.pdf[4] EC3 §5.5.1.1 [5] Antonis P. Kanellopoulos, «Earthquake resistant design and strengthening of reinforced concrete buildings», cubus Hellas, 2007. cubushellas.gr/30-PDF/Part-1-EN.pdf[6] ΕC8 Part 3[7] «EAK2003» Greek Anti-seismic Code (2003), Table 2.1[8] ΕC2 §6.2.3


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http://cubushellas.gr/30-PDF/Part-1-EN.pdf

http://library.tee.gr/digital/m2316/m2316_bei.pdf

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