HINGED-WALL SOLUTIONS FOR THE STRUCTURAL STRENGTHENING OF EXISTING RC BUILDINGS

Andrea Belleri, Chiara Passoni, Alessandra Marini and Paolo Riva

Department of Engineering and Applied Sciences, University of Bergamo, Italy

ABSTRACT

The reinforced concrete (RC) constructions built after World War II represent almost half of the European building stock. Such buildings are characterized by low energy efficiency, living discomfort, and may be inherently vulnerable to seismic actions, having been designed before the enforcement of modern building codes. A multi-purpose retrofit strategy addressing in particular both energy and structural issues is therefore necessary.

The present paper considers the sole seismic retrofit interventions by investigating the suitability of external RC walls hinged connected at their base, suitable to improve the seismic performance of poorly detailed existing RC buildings. In particular, such a solution avoids the concentration of deformation at one storey of the building, i.e. the development of soft story mechanisms, and reduces the demand on the foundations of the new system, being the bending moment at the base of such walls nearly zero.

The paper shows, through non-linear pushover analyses on 2D frames, how the hinged wall solution is suitable for enhancing the seismic performance of existing buildings both in the case of strong-column weak-beam or strong-beam weak-column characteristics.

Keywords: seismic retrofit, hinged wall, R.C. frames, sustainability.

1. Introduction The reinforced concrete (RC) constructions built between 1950 and 1970 in Europe represent a high percentage of the existing building stock and were mainly built to quickly meet the pressing housing demand. These buildings are typically multi-storey frame structures (Fig. 1), with poor architectural features, characterized by low energy efficiency and living discomfort. The structural layout of such buildings has been determined by gravity loads and wind loads. Typically, the seismic excitation has not been accounted for due to the lack of knowledge of modern anti-seismic provisions and to the absence of seismic hazard maps.

Fig. 1. Typical layout of the considered buildings needing renovation.

To foster the transition toward a low carbon society, large national and European funds have been granted for the energy efficiency upgrade of existing buildings by acting on the renovation of the envelope and on the use of renewable energy sources and sustainable materials. A series of energy efficiency upgrade projects have been started throughout Europe involving, among others, the aforementioned post World

War II buildings. Being such buildings characterized by poor structural performances, the sole energy efficiency requalification or architectural redevelopment leaves such buildings dangerously unsafe. Recent studies have emphasized the substantial environmental impact associated to the seismic risk especially in regions with high seismicity (Belleri and Marini 2015, 2016), corroborating the idea that, when applied to the construction renovation, the energy efficiency and building sustainability should be integrated with the fundamental requirement of structural safety.

An integrated energy-structure approach has been recently investigated (Feroldi et al. 2013, Marini et al. 2015, Marini et al. 2016). Such approach entails the use of “double-skin” solutions and couples the energy upgrade of the envelope, the architectural restyling and the enhancement of the seismic performance, while being respectful of sustainability issues (adaptable, easily repairable, and fully demountable structures are proposed, which can be recycled or reused at the end of life). The main characteristic of this solution is to act from the outside without the need to relocate the inhabitants during the construction works. The present paper focuses on the performances of a seismic retrofit solution composed of hinged-walls, i.e. reinforced concrete shear walls pin-connected at their bases. As main advantages, a hinged-wall solution enforces linearization of the displacement demand along the building height, thus inhibiting the onset of soft-storey mechanisms, and does not require extensive foundation works due to the pin connection at the wall base. To the authors’ knowledge, the first application as a retrofit measure in an existing RC structure is presented in Wada et al. (2011). In addition, it is observed that the investigated hinged-wall solution is appropriate also in order to solve the vulnerability connected to wide RC walls typically surrounding staircases, usually not designed to withstand horizontal loads; in fact, such walls could be downgraded to hinged-walls by saw cutting their base section, reducing the influence of the stiff walls and enhancing the building seismic response at the same time.

2. Hinged-wall retrofit solutions

2.1 Concept and formulation The hinged-wall concept is expressed in Fig. 2. The lateral stiffness of the wall forces the connected frame to displace following a linear deflected shape. In such a way, the development of a soft storey mechanism, typically at the first level, is avoided and the rotation demand is spread along the building height. The concept of hinged-wall is an extension of the continuous column concept developed by MacRae et al. (2004) and then extended to different types of structures and situations (Alavi and Krawinkler 2004, Qu et al. 2012, Qu et al. 2014, Pan et al. 2015, Wada et al. 2011).

Fig. 2. Deflected shape and plastic hinge development due to a hinged-wall solution.

The parameter suitable to describe the performance of the retrofit solution is the drift concentration factor (DCF), defined as the ratio between the maximum inter-storey drift and the roof drift. The purpose of the hinged-wall is to provide a DCF close to 1. The relationship between DCF and the hinged-wall flexural stiffness is described by the parameter α = EwIw/(k H3) (MacRae et al. 2004), where Ew and Iw are the elastic modulus and the moment of inertia of the wall respectively, H is the building height and k is the

floor lateral stiffness. Considering the target situation in which all the floors are characterized by the same inter-storey drift, it is possible to write DCF as a function of α:

3

w w

d H d N h d N V N V N HDCFh h k E I

α⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅= = = = =

⋅Δ ⋅Δ Δ ⋅Δ ⋅ ⋅Δ (1)

where V is the frame base shear associated to the development of plastic hinges at the columns’ base, h is the inter-storey height, N is the number of storeys, d is the inter-storey displacement, and Δ is the roof displacement.

In order to obtain the shear and bending moment demand on the hinged wall, it is possible to follow the formulation proposed by MacRae et al. (2004) for the continuous column concept. The seismic lateral load w acting on the system is assumed to be linear and continuous (w = w0 z /H where z is the vertical position and w0 the lateral load at the roof). In addition, the lateral load capacity of each floor of the frame is assumed to vary: β is the ratio between the lateral load capacity at the roof and base level (Vf,base). Fig. 3 shows the lateral loads acting on the frame associated to the lateral capacity of each level of the frame.

(a) Lateral loads. (b) Shear demand

Fig. 3. Lateral load and shear demand acting on the frame.

For equilibrium it is observed that Ff,roof is equal to βVf,base and that therefore a force opposite to Ff,roof is acting on the top of the hinged-wall. Therefore the lateral load on the hinged-wall is:

( )0 0 0hw f f hwz zw w w w w wH H

= − = − = (2)

Considering a base moment in the hinged-wall equal to 0: 2

, ,, , 0 00 0 3 3

3 f roof f base

hw base f roof hw hw

F VHM F H w wH H

β ⋅= → − ⋅ + = → = = (3)

Therefore from Eq. 2 it is obtained:

( ) ( ), , ,0 0 0 0 02 1 3 2 f base f base f base

hw f

V V Vw w w w w

H H Hβ

β β⋅

= − → − − = → = + (4)

The shear and bending moment demand along the hinged-wall are respectively: 2 3

, ,2( ) 1 3 ; ( )

2 f base f base

hw hw

V Vz zV z M z zH H H

β β⎛ ⎞ ⎛ ⎞⎛ ⎞= − = −⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

(4)

The maximum moment, corresponding to a height equal to / 3H , is

,max ,2 39hw f baseM Vβ= (5)

wf = 2(1-β )(z/H)V f,base/H = = wf0 (z/H)

Ff,roof

Lateral load Shear demand

V f,base

β V f,base

Fig. 4 shows the lateral loads acting on the hinged-wall and the corresponding shear and bending moment demand.

(a) Lateral loads. (b) Shear demand (c) Bending moment demand

Fig. 4. Lateral load and shear demand acting on the frame.

2.2 Considered case study The hinged-wall solution is applied as a retrofit solution to a selected case study bare frame replicating the structural typology mentioned in the introduction and represented in Fig. 1. The structural layout is shown in Fig. 5a. Only a 2D frame in the longitudinal direction is considered herein (Fig. 5b) for demonstration purposes. A representation of the hinged-wall solution is shown in Fig. 5c. The column and beam details are represented in Fig. 6. It is worth noting that, unlike what recommended in modern seismic design code, the typical reference constructions and hence the considered case study is characterized by strong-beam weak-column behaviour. The resulting rotation ductility is 2.48 and 2.59 for the column and the beam plastic hinge respectively.

(a) Typical structural layout of the considered buildings. (b) RC frame considered in the FE analyses.

whw = 3 β (z/H)V f,base/H = = whw0 (z/H)

Ff,roof

Lateral load Shear demand

β V f,base

Bending momentdemand

Mmax

0.5 β V f,base

(c) Column and beam geometry and details

Fig. 5. Typical structural layout of the considered building.

The hinged-wall solution applied to the selected frame is depicted in Fig. 6. Fig. 7 shows the effects of the wall depth on the inter-storey drift and the effect of α on the DCF. In the present case study a value of α greater than 0.1 is suitable to limit the drift concentration factor: a wall depth of 2.5m is selected herein.

Fig. 6. RC frame with the hinged-wall retrofit solution

Fig. 7. Inter-storey drift as a function of hinged-wall depth.

A pushover analysis is applied to the selected frame before and after the application of the retrofit solution. A lateral load distribution according to the first fundamental mode of vibration is considered. Fig. 8 shows the base shear – roof displacement graph while Fig. 9 shows the plastic hinge distribution associated to the failure of the structural system. It is evident how the retrofit solution allows to increase the lateral displacement capacity and to avoid the development of a soft storey at the first level. The use of the hinged-wall allows spreading the inelastic demand in the plastic hinges along the whole building height.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.001 0.01 0.1 1

DCF

α

0.50%1%2%

Fig. 8. Pushover curve for the reference building with and without retrofit.

(a) Reference building (b) Reference building plus hinged wall

Fig. 9. Plastic hinges at collapse for the reference building: with and without retrofit.

The considered case study is characterized by strong-beam weak-column behaviour. In the following, the investigation of a strong-column weak-beam condition is considered. Such condition is obtained by replacing the longitudinal rebars in the beam (Fig. 5c) with 8 12mm diam. bars, 4 in the lower layer and 4 in the upper layer. The resulting rotation ductility is 2.48 and 1.93 for the column and the beam plastic hinge respectively. Fig. 10 shows the base shear – roof displacement graph while Fig. 11 shows the plastic hinge distribution associated to the failure of the structural system. It is observed how the retrofit solution allows to increase the lateral displacement capacity of the system; although, compared to the previous case study, there is a gradual decrease of the lateral load capacity associated to the gradual failure of the plastic hinges at the beam ends.

Fig. 10. Pushover curve for a building with strong-columns and weak-beams.

0

50

100

150

200

250

300

350

400

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Bas

e Sh

ear (

kN)

Roof displacement (m)

Hinged-wall solution

Reference buidling

0

50

100

150

200

250

300

350

400

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Bas

e Sh

ear (

kN)

Roof displacement (m)

Hinged-wall solution

Strong column - weak beam

(a) Building before retrofit (b) Building after retrofit

Fig. 11. Plastic hinges at collapse for a building with strong-columns and weak-beams.

Finally, the hinged wall solution also applies to those existing buildings having RC walls not designed for lateral loads. In those cases, the retrofit of such walls should be envisioned anyway, given that their large stiffness would result in large loads transferred to them and in their possible brittle shear failure prior to the activation of any possible adopted global strengthening system. Interestingly, such walls could be easily transformed into hinged walls by simply redesigning their base section, thus transforming an element that represents a major source of vulnerability into an asset of the anti-seismic resisting system. An example on how to create a hinged-wall from an existing RC wall, in particular in the case of the staircases, is presented in Fig. 12. The technological solutions to provide such behaviour are a topic of on-going research.

Fig. 12. Redesign of the base section: transforming the staircase RC-wall into a hinged-wall.

3. Conclusions The paper presented the seismic retrofit of existing reinforced concrete (RC) frame structures by means of additional RC hinged-walls. The considered buildings have a structural typology typical of the buildings, rapidly built right after World War II to meet the pressing housing demand of that time. These buildings are characterized by poor energy performances and structural deficiencies, in particular with regard to seismic loading. As part of a wider framework of renovation of existing buildings taking into account different aspects of a building such as energy efficiency, sustainability, structural safety and architectural renovation among others, the present paper focused on a particular structural retrofit solution suitable to

Ground level

1st floor

Basement/foundation Shear key

Saw cut

be included in a major “double-skin” intervention. Such solutions minimize the impairment of the inhabitants during construction works and avoid inhabitants’ relocation.

The general formulation regarding hinged-walls was presented. Pushover analyses were carried out on a selected case study and showed the suitability of the retrofit solution especially in the case of strong-beam weak-column condition, representing the common vulnerable static scheme of these constructions. The introduction of a hinged-wall connected to the existing frame by means of truss elements avoids the development of a soft-storey mechanism and allows spreading the displacement demand along the building height. Finally, an example on how to obtain a hinged-wall from an existing RC wall, particularly the staircase walls, was shown.

4. Acknowledgements The contribution of Eng. Andrea Sala in drafting some of the figures is greatly appreciated.

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