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DESIGN METHODOLOGIES FOR THEASSESSMENT AND RETROFITTING OF EXISTING

MASONRY BUILDINGS

by

R. POPESCU1, GH. POPESCU

1, A. CRAIFALEANU

2

1IPCT Structuri SRL, Senior Research Engineer, Bucharest, Romania, ipctstructuri@yahoo.com

2Politehnica University of Bucharest, PhD, Associate Professor, Romania

ABSTRACT

A rather important proportion of the building stock in Romania consists of pre-code unreinforced masonrybuildings, which do not comply with the requirements of the present Romanian seismic code. A number of thesebuildings are historical monuments, while other cannot be demolished due to social and economic reasons.Consequently, retrofitting is the only acceptable solution in order to ensure their seismic safety.

At present, jacketing is the common and cost-effective retrofitting solution used in Romania for masonry walls.The paper presents an analytical method for the calculation of the lateral strength capacity of unreinforced

masonry elements, and its adaptation to account for the presence of jacketing. The method is applied to theretrofitting of rectangular or multiflanged masonry walls. Based on some case studies, comparisons are madebetween the pre- and post-retrofitting strength capacities of unreinforced masonry walls.

1. INTRODUCTION

The paper presents an analytical method for the calculation of the lateral strength capacity of unreinforcedmasonry walls, subjected to in-plane bending, shear and axial force. Developed in perspective of the revision ofthe Romanian design code for masonry buildings, the method is the result of studies carried out over a period ofmore than a decade [1-8].

Presently implemented into the design handbook [6], the method can be used both for the evaluation ofexisting buildings and for the design of new unreinforced masonry buildings. Moreover, with some simpleadaptations, presented in the paper, the method can also be used for the calculation of the lateral strengthcapacities of unreinforced masonry walls retrofitted by jacketing.

The numerical and engineering aspects related to the application of the method were studied in depth by usinga specially designed computer code [9].

In an independent study [1], strength capacities predicted by the method were verified against valuesdetermined by laboratory tests, showing good agreement between analytical and experimental results.

2. DESCRIPTION OF THE METHOD

2.1 AssumptionsThe assumptions of the method are presented below.

1. It is accepted that, for structural unreinforced masonry walls, the main failure criterion is diagonal failure, dueto shear stresses.

2. The law of Bernoulli applies.

3. The mortar in the bed joints at the bottom of the wall has null tension strength.

4. The normal compression stresses () have a linear variation on the elastic zones ( c ) of the section.

5. On the plastic zones of the section ( c> ), the normal compression stresses are constant and equal to the

compression strength of masonry (f).

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6. The distribution of shear stresses, , over the height of the section conforms to the average flexural shear

stress formula (i.e. it is parabolic); the shear stresses are distributed only over the compressed, elastic zone

of the section (where c ).

7. For flanged sections, the distribution of shear stresses over the flange width has a constant variation (seeFigure 1).

The stress-strain curve of masonry is assumed to be of the type shown in Figure 2, where c is the yield strain

in compression, u is the ultimate strain in compression, fis the design compression strength of masonry, and

the letters Cand Udenote the yielding and the ultimate state, respectively. The ratio between u and

c expresses the ductility of masonry, z .

Insert Figure 1 here Insert Figure 2 here

2.2 Deformation stagesUnreinforced masonry elements subjected to constant axial loads and to gradually increasing lateral forces are

analysed, as shown in Figure 3.

Insert Figure 3 here

The section at the base of a structural unreinforced masonry shear wall passes through successivedeformation stages, as the lateral force gradually increases. The described method considers three referencestages, characterised by the stress and strain distributions shown in Figures 4, 5 and 6, respectively.

Insert here

Figure 4 Figure 5 Figure 6 Figure 7

The moment-rotation relationship is represented in Figure 7.

For small and moderate axial loads (i.e. 2AfN , where Nis the axial force and A is the overall

cross-sectional area), the order of occurrence of the above stages is F-C-U.For large axial loads, yielding at the extreme compression fibre of the cross-section occurs prior to cracking at

the tension fibre; therefore, the order of occurrence of the three stages is C-F-U.

2.3 Calculation of the lateral strength capacityThe lateral strength capacity of unreinforced masonry walls (Figure 3) is calculated by considering diagonal

failure due to principal tensile stresses as the main failure criterion.

The calculation involves the following two steps.

1. For each deformation stage (F, Cand U), the following quantities are determined:

a) the values of the lateral force, Q, corresponding to the stress and strain distributions in Figures 4 to 6:QM,F, QM,Cand QM,U;

b) the values of the lateral force, Q, corresponding to diagonal failure due to principal tensile stresses: QQ,F,QQ,Cand QQ,U.

The QQvalues are those for which, by conserving the normal stress ( ) distribution in the concerned stage

(Figures 4 to 6) and by amplifying the shear stress ( ) distribution, diagonal failure occurs at a point of the

section. The shear stress distribution at diagonal failure can be deduced from the equation of principal stresses

(1), in the assumption that, at the respective point, the principal tensile stress, 2 , equals the strength to

principal tensile stresses of the mortar in the bed joints of the masonry, fp.

22

1,2 4

2

+= . (1)

2. With the six values above, the lateral strength capacity, QR, is determined from the condition:

MQR QQQ == . (3)

The Qvalues can be obtained by manual calculations or by using the specialised computer code ZINEX [6].

2.4 Determination of the failure mode

By comparing the values of lateral forces corresponding to diagonal failure due to principal tensile stresses (QQ)with the values associated to bending capacity(QM), the failure mode can be determined, analytically or

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graphically, for each of the three deformation stages, as follows:1. ductile failure MMM(Figure 8):

if UMR

UMUQ

CMCQ

FMFQ

QQ

QQ

QQ

QQ

,

,,

,,

,,

then =

>

>

>

.

2. low ductility failure MMQ(Figure 9):

if QMR

UMUQ

CMCQ

FMFQ

QQQ

QQ

QQ

QQ

andcurvestheofonintersectitheatfoundisthen

,,

,,

,,

>

.

3. brittle failure MQQ(Figure 10):

if QMR

UMUQ

CMCQ

FMFQ

QQQ

QQ

QQ

QQ

andcurvestheofonintersectitheatfoundisthen

,,

,,

,,