Analytic and experimental evaluation of masonry walls ... · LOPEZ, Sebastián / FE 2015 3 Figure...

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Analytic and experimental evaluation of masonry walls externally

reinforced with mortar and wire welded mesh applied to

historical building walls

LOPEZ, Sebastián

Escuela Colombiana de Ingeniería, Julio Garavito. ECI

Abstract

Colombian seismic provisions (NSR-10) had recently accepted a new system of externally reinforced

masonry walls with welded wire mesh and mortar (W.W.M). Escuela Colombiana de Ingeniería Julio

Garavito, with the objective of evaluate the response of full scale walls reinforced with this new

reinforcement system for masonry structures like existing houses and historical buildings.

Unreinforced masonry walls and reinforced masonry walls were tested; small specimens were used to

evaluate the material properties; while in plane monotonic and dynamic lateral load were run in full

scale walls. The article shows experimental results and their comparison with the values obtained by

using the equations and recommendations of NSR-10 for walls typical of some historical buildings.

Results demonstrate that calculations are conservative and safe; furthermore, the reinforcement

technique increased the strength to in plane lateral loads between 4 to 8 times when was used by one

or by two sides of the wall respectively.

Introduction

Colombian seismic construction regulations NSR-10 (Ministerio de Ambiente, Vivienda y Desarrollo

Territorial, 2010) allowed the use of externally reinforced masonry walls with mortar and wire welded

mesh (W.W.M) as the main seismic resistant system for structures with limited height (between 12 m

and 18 m) and certain occupancy category (not permitted for government facilities and public

buildings; e.g. hospitals, schools, universities, etc.). In spite of the limitations, approving the use of

this structural system represents an important opportunity to develop different solutions to improve the

behaviour of existing buildings or even to develop new ones.

Since 2011 a research program was developed in the laboratory of the Escuela Colombiana de

Ingeniería, Julio Garavito (ECI, Bogotá. Col) with the general objective of evaluate the behavior of

full scale walls, representative of Colombian housing buildings and historical buildings. This article is

one of a series of articles and a M. Sc. thesis that have been published to show the research program

methodology and experimental results (López S.,2013; López, Quiroga, & Torres Castellanos, 2013

and 2012; López & Torres Castellanos, 2012); nevertheless, this document makes a briefer

presentation of the methodology and the results and focuses mainly in the presentation of new

unreleased analysis comparing between the calculations according to the Colombian seismic code

provisions and the experimental results obtained by the Structural Behavior Research Group from the

ECI, for historical building walls, externally reinforced with mortar and W.W.M. by one or two sides

of the wall.

LOPEZ, Sebastián / FE 2015 2

Methodology

Tests of compression and diagonal tension were made to masonry assemblages to evaluate the

compression strength of the walls, elastic modulus, shear strength and shear modulus. Full scale walls

were tested under in plane lateral loads, monotonic and pseudo dynamic to determine their stiffness

and strength. Diagonal tension tests and in plane lateral load tests were done also for specimens

unreinforced and reinforced with W.W.M. Table 1 shows a summary with the characteristics of the

tested walls.

Table 1. Tested walls summary

Wall type

Characteristics

Reinforced Reinforced sides

MT2 NO N.A*

MT2R3 YES 1

MT2R4 YES 2

* N.A. Not applicable

Walls representative of the construction techniques used in Colombia during the end of XVIII century

and beginnings of the first half of XIX century, were replicated to evaluate the behaviour of the walls

under compression, diagonal tension and in-plane lateral load. Figure 1 shows a drawing form a

surveyed wall during the study for structural reinforcing of the building of The Instituto Técnico

Central La Salle (built between 1919 and 1930, Bogotá. Col); it can be seen the complex configuration

that can be found in masonry walls in historical masonry buildings.

Figure 1. Basic drawing from a surveyed masonry wall in a historical masonry building.

According to the variety and the difficulty of replicating walls with all the kind of possible

arrangements, it was decided to build walls with solid fired clay units, disposed in a regular

arrangement. Masonry walls in stretcher and header bond were selected. Mortar joints had between 10

and 15 mm thickness. Figure 2 shows a three dimensional view of the construction technique.


Figure 2. Stretcher and header bond masonry wall.

The compression strength of the units (f’cu) was determined based on the data stored on the database of

the ECI’s Structures and Materials Laboratory. The laboratory data base has information about

compression tests results of masonry units. The data was filtered according to the reported age of the

specimen and there were selected 79 results to determine statistically the average compression

strength. It was found a value of 25 MPa a representative of the compression strength.

To determine the compression strength of joint mortar (f’cp) in existing historical building walls are

required specialized techniques (for example flat jack tests and chemical composition analysis)

considerable out of the scope for general objective of this study. Even though there is not enough local

research about this, a few researchers had found that compression strengths in joint mortars from walls

in historical buildings can be as low as 0.5 MPa (Jaramillo Morilla, Rodríguez Liñán, de Justo

Alpañés, Romero Hernández, & Pérez Gálvez, 2000; Useche, 1993). For the purpose of the research, it

was selected 9.0 MPa for the joint mortar compression strength, mainly to ensure the integrity of the

specimen and diminish the risk of a sudden collapse during tests setup.

Figure 3 shows unreinforced masonry walls during its construction.

Figure 3. Building a full scale masonry wall.

Reinforced walls characteristics.

Reinforced walls were built with the same arrangement of the unreinforced ones but they were

reinforced by one or two sides (front and back planes of the wall). For the reinforcement, a wire

welded mesh was installed on the surface of the wall and then a thin layer of mortar was placed by

hand. Reinforcement details for the walls reinforced by just one side are shown in Figure 4.


Figure 4. Reinforcement of walls type R3.

To fix the wire welded mesh to the wall, two techniques were used depending on how many sides of

the wall were going to be reinforced. For walls reinforced by one side (walls type MT2.R3), 4 anchors

of 6.35 mm (1/4 in) per m²were fixed over the vertical area of the wall. The anchors were installed in

a 9.53 mm (3/8") drilled hole filled with epoxy resin. For the walls reinforced on the two sides of the

wall (walls type MT2R4), the same amount and diameter of anchors were installed but the anchor rod

passed through the hole; once the anchor was inside the hole, the rod was bent 90° on both sides. The

final anchor had hooks on both sides which were tied to the W.W.M. The longitudinal and transverse

reinforcement was made of welded deformed wire fabric of 6.00 mm spaced each 150 mm in both

directions centre to centre, with a yield strength (fy) of 480 MPa. Once the W.W.M was placed and

tied to the anchors, a 25 mm layer of mortar with a compression strength (f'cre) of 20 MPa was applied

over the reinforcing mesh. Detailed drawings of the anchors for walls reinforced by one side or for

both are shown in Figure 5.

Figure 5. Anchor type B and type C. Details of reinforced walls.


Figure 5 (Continued). Anchor type B and type C. Details of reinforced walls.

Full scale walls had a foundation beam and a top beam. The reinforced walls had bars of 12.7 mm

(1/2") each 300 mm, anchored to the foundation beam through epoxy adhesive, those bars were used

to tie the mesh to the foundation. The top beam was used to apply lateral loads and it had embedded

bars of 6.35 mm (1/4”) to fix the W.W.M. Construction details of the reinforced walls are shown in

Figure 6.

Figure 6. Construction details of full scale walls.

Tests

Table 2 shows a compilation of the most important tests, including the dimensions of the specimens,

quantity of tests done and if the test included results for reinforced and unreinforced specimens. The

width of the wall shown includes the masonry unit and the thickness of the for reinforcing mortar

Tests set up

A brief description of the test set up and the standards or reference documents used to develop the tests

are shown below for the most important tests.

Diagonal tension in masonry assemblages

Diagonal tension tests were done with reference to ASTM E-519 (ASTM, 2010) and NTC 4925

(ICONTEC, 2001). Figure 7 shows the most important details of the instrumentation and test set up for

the test; test set up and specimen dimensions were slightily different compared to the specifications

from standars.


Table 2. Summary of specimens and tests quantities

Test

Wall type Dimensions Quantity of

tests Unreinforced Reinforced Height

(mm)

Length

(mm) Width (mm)

Diagonal

tension

X

1100 1100

260 3

X 285 3

X 310 3

Monotonic in

plane lateral

load

X

2000 1320

260 1

X 285 1

X 310 1

Pseudo

dynamic in

plane lateral

load

X 260 1

X 285 1

X 310 1

Figure 7. Diagonal tension test set up.

To apply the force, threaded steel rods mm (1 1/2") were placed parallel to the diagonal direction

of the masonry assemblage between upper and lower loading shoes. For unreinforced and reinforced

masonry walls load was applied using an hydraulic jack with a capacity of 150 kN and a load cell of

1000 kN to register the loads. To measure deformations, dial indicators with a precision of 10-2

mm

were installed in the four diagonals of the specimen (both sides of the wall in parallel and

perpendicular direction to the load applied). The wall specimen was built over a layer of sand to

provide temporary support during the construction. Before the test, the sand was removed and the wall

was finally supported on rolling supports placed previously during construction and imbibed into the

sand layer. Figure 8 shows in detail the load mechanism for diagonal tension tests.

Upper

Loading Shoe

Dial Indicators

(both sides)

Loading Jack

Threaded

Steel Rods

=38mm

Lower

Loading

Shoe


Figure 8. Loading mechanism for diagonal tension test.

Lateral load in full scale walls

Tests of full scale walls, under lateral monotonic and pseudo dynamic in plane loading were done

according to the appendix A of the Mexican seismic provisions for masonry buildings (GDF, 2002).

This document was developed specifically for masonry structures. Other standars developed for lateral

loading in walls for example ASTM standars for in plane lateral loading have been developed for other

materials. Figure 9 shows a general view of the test set up for monotonic loading test.

Figure 9. Test set up for monotonic in plane lateral load.

To apply the load in pseudo dynamic tests it was used a MTS dynamic actuator with 250 kN of pulling

force capacity and 300 kN of pushing force; the total path length of the actuator’s piston is 500 mm.

The wall was fixed to the actuator with a couple of drilled steel plates, subjected through threaded

steel bars of 15.9 mm (5/8"). On the side of the actuator was placed a steel plate with a rod welded

parallel to the wall thickness to generate a hinged connection between the actuator and the wall.

Displacements were registered through LVDTs (Linear Variable Differential Transducers) and strain

in extreme fibre (left and right side of the wall) on wire welded mesh was measured with

unidirectional strain gauges. A general view of the test set up is shown in Figure 10.

Load

Cell

Hydraulic

Jack

Upper

loading

shoe

Reaction

steel plates

Reinforcing

steel plate in

the piston

Loading

Jack

vertical

LVDT

horizontal

LVDT

horizontal

LVDT

Supports


Figure 10. Test set up for pseudo dynamic in plane lateral load.

Loading pattern for dynamic tests was according to Mexican seismic provisions for masonry buildings

(GDF, 2002). Loading for the first cycles of the test are a function of the wall’s nominal strength and

from experimental results obtained form monotonic tests; afterwards, the load pattern increses

gradually the drift ratio by adding 0.002 increments until the failure of the specimen. The load pattern

requires to know first the results of the monotonic loading tests. Figure 11 shows the load pattern

(figure adapted from GDF, 2002)

Figure 11. Load Pattern for pseudo dynamic tests.

Dynamic

actuator

Holding

bars

Supports

Unidirectional

strain gauges

horizontal

LVDT

horizontal

LVDT

horizontal

LVDT

43

Lateral load

Controled by

load

Controled by

drift

Cycles

Drift, q

Load 1

Load 2

Load 3

0.002

0.004

0.006

0.008

0.01

Incr

easi

ng b

y 0

.00

2

Load 1: 0.25 times calculated cracking or yielding load

Load 2: 0.50 times calculated cracking or yielding load

Load 3: Cracking load or first yielding (experimental)


Test results and analysis of results

The results of the most important tests are shown below

Figure 12. Shear stress vs average angular distortion. Unreinforced walls (TD2)and walls reinforced by one side

(TD2.R3).

Figure 13. Shear stress vs average angular distortion. Unreinforced walls (TD2)and walls reinforced by one side

(TD2.R4).

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16 18

Ss (kPa)

gprom (10-4 mm/mm)

TD2.1

TD2.3

TD2.R3.1

TD2.R3.2

TD2.R3.3

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16 18

Ss (kPa)

gprom (10-4 mm/mm)

TD2.1

TD2.3

TD2.R4.1

TD2.R4.2

TD2.R4.3


Diagonal tension in masonry assemblages

The apparent shear modulus were obtained from the stress vs average angular distortion (average form

the measurements from front and back plane of the wall) shown below in Figure 12 for walls

reinforced by one side and Figure 13 for walls reinforced by two sides. The angular distortion on each

side of the wall was calculated according to the ASTM E-519 (ASTM, 2010).

Table 3 shows the average of the maximum shear stresses obtained for each test. Table 4 shows the

apparent average shear modulus, which is the average of the slopes of each plot stress vs average

angular distortion under the elastic zone.

Table 3. Tests results diagonal tension. Shear stress.

Wall

type

Statistical values

Type Quantity. S s average

(MPa)

Variation

Coefficient.

TD2 281 5.7% Unreinforced 3

TD2R3 417 16.8% Reinforced 1

side 3


sides 3

Table 4. Tests results diagonal tension. Apparent shear modulus.

Wall

type

Statistical values

Type Quantity. G apparent

average

(MPa)

Variation

Coefficient.

TD2 1020 5.7% Unreinforced 3


side 3


sides 3

Results showed that using W.W.M for one side of the wall can increase the diagonal tension strength

1.5 times in comparison to the unreinforced walls and up to 1.8 times when this technique is applied to

both planes of the wall. Failures followed cracking patterns through the diagonal load direction. There

was an important difference between the behaviour observed for unreinforced and reinforced. The

failure in unreinforced walls was brittle. For reinforced walls the failure was gradual and there was

more damaged in the mortar of the walls reinforced for both sides (M2R4) than in the other walls also

reinforced (M2R3). The reinforced walls showed an increase in the shear apparent stiffness according

to the slopes observed in the shear vs. distortion plots.

Below are shown the values of calculated diagonal tension strength according to Colombian

regulations, which are based on ACI530-08 (ACI, 2008), and the comparison between the test results

and the calculated values. The maximum allowable shear force (VALW) is the value of the shear force

that produces the maximum allowable stress on one of the composing materials when the acting force

is distributed in proportion to the stiffness of the transverse section component (López, 2013).

Allowable stresses are named with the letter “F” and the letter “f” is used for the acting ones; for the

stresses in each material. The sub index “v m” is used for the stresses on the masonry, “v cre” for the

mortar and for the reinforcing steel the letter “s”. The allowable shear stress (Ss ALW) is calculated

dividing the force VALLW by the transverse section of the wall including the mortar layer thickness for

the reinforced walls.


Figure 14. Diagonal tension failures. (a) Unreinforced masonry, (b) reinforced by one side and (c) reinforced by

two sides.

Table 5 shows the value of Ss ALW for unreinforced walls according to the equation 1.5-12 of NSR-10.

Table 6 shows the value of the allowable working stresses for each material according to equations D-

1.5-14 and D-1.5-18 from the same provisions. Table 7 shows the values of VALW and SS ALW for the

reinforced walls. In the tables below the gray colour cells represents the stress governing the

behaviour.

Table 5. Allowable working stress for diagonal tension. Unreinforced walls.

Wall type Shear strength

SS ALW=Fv=√f'm/40<=560

(kPa)

TD2 83.0

Table 6. Allowable working stresses for each material. Reinforced walls.

Wall type M/Vd Shear strength

Fv m=√f'm/12<=0.25 (MPa) Fv cre=√f'cre/12<=0.25 (MPa) Fs=0.5 fy (MPa)

TD2R3 1.0 0.25 0.25 215

TD2R4 1.0 0.25 0.25 215

Table 7. Calculated working stresses for each material. Reinforced walls.

Wall type V ALW (kN) M/Vd Shear stress

SS ALW (kPa) fv m (MPa) fv cre (MPa) fs (MPa)

TD2R3 36.3 1.0 0.11 0.22 215 98

TD2R4 36.3 1.0 0.09 0.17 215 87

Safety factors (S.F) can be estimated as the ratio between the experimental maximum shear stress and

the calculated shear strength. Table 8 shows the safety factors for shear, obtained for allowable stress

design (A.S.D).

For unreinforced masonry assemblages the average safety factor is 3.5 and the minimum is 3.2. For

the specimens reinforced the average safety factor is 5 with a minimum of 3.5. Those values are

consistent with the results obtained by other researchers, developed for different type of walls

subjected to similar tests ( López S. , 2013; Luna y Rojas, 2004).

(a) (b) (c)


Table 8. Diagonal tension safety factors for unreinforced and reinforced masonry walls. A.S.D.

Wall type SS ALW (kPa) SS exp max (kPa) 𝐹𝑆𝑆𝐻𝐸𝐴𝑅 (𝐴.𝑆.𝐷) =𝑆𝑆 exp𝑚𝑎𝑥

𝑆𝑠 𝐴𝐿𝑊

TD2.1

83

292 3.2

TD2.2 288 3.5

TD2.3 262 4.0

TD2R3.1

98

339 3.5

TD2R3.2 476 4.9

TD2R3.3 434 4.4

TD2R4.1

87

500 5.7

TD2R4.2 480 5.5

TD2R4.3 533 6.1

On the other hand, analysing the shear strength through limit state design (L.S.D), the shear strength

(n) was calculated in a conservative way according to Equation 1 (D.5.1.5, NSR-10) with a strength

reduction factor () of 0.60 and considering only the resistance of the mortar layer.

𝝓𝒗𝒏 = 𝛟(𝟎. 𝟏𝟔√𝒇′𝒄𝒓𝒆) ≤ 𝟎. 𝟐𝟗𝒇′𝒄𝒓𝒆 (1)

Where f'cre is the mortar layer compression strength in MPa. Compression strength for the mortar is

16.9 MPa for TD2R3 walls and 15.3 MPa for TD2R4 test walls. The safety factors for shear, obtained

for limit state design are shown on the Table 9.

Table 9. Diagonal tension safety factors for unreinforced and reinforced masonry walls. L.S.D.

Wall type φn (kPa) SS exp max (kPa) 𝐹𝑆𝑆𝐻𝐸𝐴𝑅 (𝐿.𝑆.𝐷) =𝑆𝑆 exp𝑚𝑎𝑥

∅𝑣𝑛

TD2.R3.1

395

339 0.86

TD2.R3.2 476 1.21

TD2.R3.3 434 1.10

TD2.R4.1

376

500 1.33

TD2.R4.2 480 1.28

TD2.R4.3 533 1.42

For more than 80% of the results the approach adopted predicted adequate strength design values.

Making apart the results of the specimen TD2.R3.1, the average safety factor for limit state design is

1.27 with a minimum of 1.10. Those values are relatively lower than those obtained for other kind of

walls under the same kind of loads (López, Quiroga, & Torres Castellanos, 2013).

Lateral load in full scale walls

Monotonic lateral loads tests were used specially to generate the load pattern for pseudo dynamic load

tests as it was exposed previously in the tests set up. M2 walls were unreinforced walls, M2R3 were

reinforced by one side and M2R4 were reinforced by both sides. Figure 15 shows simultaneously in

plane lateral load tests plots for walls M2R4.1 (monotonic) and M2R4.2 (pseudo dynamic).


Figure 15. Load vs drift plots for monotonic and pseudo dynamic lateral load test. Wall M2R4.

Table 10 shows a summary of the maximum lateral loads (VMAX) and the shear stress calculated over

the gross section of each wall.

Table 10. Results summary for in plane lateral load tests. Monotonic and dynamic.

Wall type Test type VMAX (kN) MAX (kPa)

M2.1

Monotonic

7.8 22.8

M2.R3.1 29.2 77.7

M2.R4.1 48.1 115.0

M2.2

Dynamic

6.20 30.6

M2.R3.2 32.4 160.0

M2.R4.2 67.1 331.4

Figure 16 shows the envelope plots from the hysteretic curves of unreinforced and reinforced walls.

The plots shows a considerable increment of lateral load strength for the reinforced walls comparing to

the unreinforced. Lateral load strength can be increased, compared to unreinforced walls, 4.8 times

when W.W.M is installed by one side and up to 9 times when it is used in both sides of the wall.

According to the results obtained, the reinforced walls had a lower rate of per cycle stiffness reduction

compared to the reinforced walls. Furthermore, reinforcing both sides of the walls would reduce up to

80% the stiffness reduction for drifts under the allowable values for masonry structures according to

NSR-10 (maximum drift of 0.5%). Failure patterns of unreinforced walls were due to uplift and for

reinforced walls due to foundation anchor failure and mortar failure parallel to the longitudinal

reinforcement. Figure 18 shows failures for unreinforced and reinforced walls.

Table 11 shows a summary of all the parameters required to calculate the energy dissipation

coefficient (R) according to NSR-10 or response modification coefficient according to ASCE 7

(ASCE, 2005). This value was obtained using two different approaches. R1 was calculated according

to the methodology of Newmark and Hall (Newark y Hall, 1973) and R2 was obtained according to

San Bartolomé (San Bartolomé et al, 2007). To calculate R1, was used as drift limit ( m) the drift

obtained for the maximum experimental lateral load from the pseudo dynamic tests. To calculate R2 it

Test: M2.R4.2

Pmax=50838 N/m

-196

-156

-117

-78

-39

0

39

78

117

156

196

-2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

-80000

-64000

-48000

-32000

-16000

0

16000

32000

48000

64000

80000

-40 -30 -20 -10 0 10 20 30 40

Shear stress

(kPa)Load (N)

D (mm)

Dynamic

Monotonic


was used as drift limit of 0.5%, which is 50% of the design drift allowable for walls with a flexural

failure mode or the allowable drift for any masonry structure according to NSR-10.

Figure 16. Load vs drift envelopes for unreinforced and reinforced walls.

Figure 17 shows the stiffness reduction per cycle curves for unreinforced and reinforced walls.

Figure 17. Per cycle stiffness reduction vs per cycle maximum drift for unreinforced and reinforced walls.

-2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

-204

-153

-102

-51

0

51

102

153

204

-40 -30 -20 -10 0 10 20 30 40

Shear stress

(kPa)

D (mm)

M2.2

M2.R3.2

M2.R4.2

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

110.0%

120.0%

0.00% 0.25% 0.50% 0.75% 1.00% 1.25% 1.50% 1.75% 2.00%

Stifness

D(%)

M2.2

M2.R3.2

M2.R4.2


Figure 18. Failure patterns for lateral load test results. (a) Unreinforced wall uplift. Reinforced wall (b)

compression failure on the edge and (c) mortar failure parallel to longitudinal reinforcement.

Table 11. Calculation of energy dissipation coefficient or response modification coefficient.

Wall Type Δy (mm) μ=Δu/Δy EH (N.mm) VR (N) R1=√(2μ-1) R2=√(2K0EH)/VR

M2R3.2 3.22 1.8 552283 31590 1.6 3.0

M2R4.2 8.08 1.8 1026103 67106 1.6 1.6

The values obtained shows that there is only a really big difference between both approaches for wall

M2.R3.2. Conservatively a value of R=1.6 would be used as energy dissipation coefficient,

independently if one or two sides of the wall is reinforced. This value is close enough to the value

assigned to this structural system by NSR-10, R=1.5. Finally it was found that the walls reinforced can

develop up to 1.8 times greater drifts than the elastic limit drifts.

Below would be shown the strength calculations for allowable stress design and limit state design for

laterally loaded walls. The conventions used were the conventions already shown above for the

calculation of strength in the analysis of the diagonal tension tests. Table 12 shows the results of the

maximum allowable shear force (VALW), the allowable stresses and the stresses calculated according to

the acting force for unreinforced masonry walls.

Table 12. Allowable stresses for bending and shear in laterally loaded walls.

Wall

type

VALW

(kN)

Bending Shear

Ft*

(MPa)

Fb=0.33 f'm

(MPa)

ft

(MPa)

fb

(MPa)

Fv=√f'm/40<=0.56

(MPa)

fv

(MPa)

M2 6.9 0.17 3.83 0.17 0.17 0.09 0.03

Conservatively it was assumed an allowable stress of 0.17 MPa for tension due to bending on the

extreme fibre (minimum allowable stress for M and S mortars with hollow units according to table D-

1.5-1 NSR-10 page. D-71 or table 2.2.3.2 page C-28 ACI 530-05). The safety factor would be

calculated as the ratio between VALW form Table 12 and the minimum ultimate load for pseudo

dynamic and monotonic tests from Table 10. For unreinforced walls the safety factor is 6.9/6.2=1.11.

Table 13. Allowable stresses due to bending for laterally loaded walls.

Wall

type

VALW

(kN)

Bending

x

(mm)

Fb m=0.33 f'm

(MPa)

Fb cre=

0.33 f'cre

(MPa)

Fs=

0.5 fy

(MPa)

fb m

(MPa)

fb cre

(MPa)

fs

(MPa)

M2.R3 13.6 263

3.50 5.58 226 0.714 1.38 226

M2.R4 32.5 3.60 5.05 226 1.426 2.63 226

(a) (b) (c)


Table 14. Allowable stresses due to shear for laterally loaded walls.

Wall

type

VALW

(kN)

M/V

d

Shear

Fv m=

√f'm/12<=0.25

(MPa)

Fv cre=

√f'cre/12<=0.25

(MPa)

Fs=0.5 fy

(MPa)

fv m

(MPa)

fv cre

(MPa)

fsv

(MPa)

M1.R3 13.6 1.48 0.25 0.25 215 0.04 0.08 76.6

M1.R4 32.5 1.48 0.25 0.25 215 0.08 0.16 183.8

Below are shown the analysis of the results for reinforced walls according to the allowable stress

design method. Table 13 shows the maximum allowable shear force (VALW) and the allowable stresses

as the stresses due to bending. Table 14 shows the allowable and acting stresses due to shear.

The governing stress is tension due to bending in the longitudinal reinforcement bars. Table 15 shows

the calculation of the safety factors for bending and shear for laterally loaded walls according to the

allowable stress design method.

Table 15. Bending and shear safety factors for reinforced masonry walls. L.S.D.

Wall type VALW (kN) Lateral load test results

𝐹𝑆𝐵+𝑆 (𝐴.𝑆.𝐷) =𝑉exp𝑚𝑎𝑥

𝑉𝐴𝐿𝑊

Vexp max MONO (kN) Vexp max DYNA (kN)

M2.R3.1 13.6

29.2 - 2.16

M2.R3.2 - 32.4 2.39

M2.R4.1 32.5

48.6 - 1.49

M2.R4.2 - 67.1 2.06

For reinforced walls the average safety factor is 2.03 with a minimum value of 1.49.

Calculations of the strength of the walls according to the limit strength design were made using

Equation 2 and Equation 3 which correspond to modified equations originally used for concrete walls

designs with uniformly distributed reinforcement. The equations were modified considering the total

thickness of the wall the same as the thickness of the mortar layer (or the sum of the thicknesses in the

case of the walls reinforced into both sides) and the compression strength from the concrete (f’c) was

replaced by the compression strength of the mortar layer (f'cre).

𝑀𝑢 ≤ ∅𝑀𝑛 = ∅0.5𝐴𝑠𝑓𝑦𝐿 �1 +𝑃𝑢∅

𝐴𝑠𝑓𝑦 (1 −

𝑐

𝐿) (2)

𝑐

𝐿=

𝑃𝑢∅

+ 𝜌cre

𝑓𝑦𝑓 ′

𝑐𝑟𝑒

2𝜌𝑓𝑦

𝑓 ′𝑐𝑟𝑒

+ .7225

(3)

Where

=Strength reduction coefficient. For walls under bending without axial force is taken as 0.85.

As=Total area of steel in the transverse section, mm².

fy=Yielding strength of the reinforcing steel, MPa.

L=Length of the wall, mm.

Pu=Ultimate load of the wall, corresponding to the factored ultimate bending moment (Mu), N.

c/L=Ratio between the length of the compressed zone due to bending and the total length of the wall.

Table 16 and


Table 17 shows the calculation of the strength of the walls for bending and shear according to the limit

state design. Safety factors calculated according to the limit strength design are shown in Table 18.

Table 16. Bending strength for laterally loaded reinforced masonry walls. L.S.D.

Wall type

Boundary

stresses Boundary

Elements

required?

Bending

(MPa) C/L As (mm²) φMn (kN.m) φMn/H (kN)

M2.R3 7.3 SI 0.18 254 53.0 27.6

M2.R4 6.1 SI 0.17 509 107 55.9

Table 17. Shear strength for laterally loaded reinforced masonry walls. L.S.D.

Wall type Shear

Mu/(Vu d)=H/d Vm (kN) Vs (kN) φVn (kN)

M2.R3 1.48 25.7 0 15.4

M2.R4 1.48 57.5 0 34.5

Table 18. Safety factors for lateral loaded reinforced masonry walls. L.S.D.

Wall type VL.S.D (kN) Lateral load test results

𝐹𝑆𝐵+𝑆 (𝐿.𝑆.𝐷) =𝑉exp𝑚𝑎𝑥

𝑉𝐿.𝑆.𝐷

Vexp max MONO (kN) Vexp max DYNA (kN)

M2.R3.1 15.4

29.2 - 1.89

M2.R3.2 - 32.4 2.10

M2.R4.1 34.5

48.6 - 1.41

M2.R4.2 - 67.1 1.94

The minimum safety factor is 1.41 and the average is 1.84.

Compared to the results obtained for the same walls according to the allowable stress design method

where the average was 2.03 and the minimum was 1.49, it was found similarity between the results

and in both cases the calculations would be consider as appropriated because they always showed

safety factors higher than one.

Conclusions

Diagonal tension strength in masonry walls externally reinforced with W.W.M, can be increased

respect to the unreinforced masonry walls, in almost 1.5 times when this technique is applied by one

side of the wall and up to almost 1.9 times when it is applied by both faces of the wall.

Considering the results for monotonic and pseudo dynamic in plane lateral loads, it was observed that

applying W.W.M and mortar by one of the sides of the walls, increases the ultimate strength of the

wall comparing the results with the unreinforced walls, in more than 4 times when W.W.M and mortar

is applied by one side and up to 8 times when is applied on both sides of the wall.

Even if the reinforcement technique is applied just by one side of the wall, this would always improve

the stiffness reduction of the wall when is subjected to pseudo dynamic loads and the strength is being

increased as well for both monotonic and pseudo dynamic loads.

In all the tests done, it was found a critical change between the failure mechanism of the unreinforced

and reinforced masonry walls. All the walls reinforced for one or both sides, had a ductile and gradual

failure mechanism while the unreinforced walls had a sudden and brittle failure mechanism. This

difference would be valuable specially when the structural elements are approaching to the ultimate

limit state, allowing to the users to evacuate before the failure of the element. This feature would be

impossible in structure totally made of unreinforced masonry wall.


The calculated strength for diagonal tension and lateral load for the methodologies allowed by

Colombian regulations, for reinforced and unreinforced masonry walls, showed that the calculations

developed were safe in comparison to the experimental results

Calculations of the response modification coefficient according to Newmark and Hall, and San

Bartolomé, showed in a conservative way, that reinforcing both sides W.W.M and mortar does not

improve the value of the coefficient for the walls studied. This results are compatible with the results

obtained for this technique in other kind of walls and also confirms that the value of 1.5 adopted for

the response modification coefficient by NSR-10 is adequate.

Special care should be taken during the construction of this kind of walls. It has to be done an strict

quality control during installation of the anchors to the wall, to the foundation beam and top beam.

Before pouring the mortar an inspection should be required

High plasticity mortars are required for this kind of application. All the measurements should be taken

to avoid the lost of humidity and reduce the compression strength of the mortar. Previously to the

installation of the mortar, should be applied directly to the surface of the wall, enough water to

guaranty the saturation of the base surface.

References

ACI. (2008). 530/530.1-08: Building Code Requirements and Specification for Masonry Structures

and Related Commentaries. Farmington Hills, MI: ACI.

ASCE. (2005). ASCE 7-05 Minimum Design Loads for Buildings and Other Structures. Reston, VA:

American Society of Civil Engineers.

ASTM. (2010). Standard Test Method for Diagonal Tension (Shear) in Masonry Assemblages. ASTM

E519 / E519M - 10 Standard Test Method for Diagonal Tension (Shear) in Masonry Assemblages

. West Conshohocken, PA: ASTM International.

GDF. (2002). Normas Técnicas Complementarias para el Ciseño y Construcción de Estructuras de

Mampostería. México, DF.

ICONTEC. (2001, 03 21). Método de ensayo para determinar la resistencia a la tracción diagonal -

cortante - en muretes de mampostería. NTC 4925 - Prefabricados de concreto. Método de ensayo

para determinar la resistencia a la tracción diagonal - cortante - en muretes de mampostería.

Bogotá, Cundinamarca, Colombia: ICONTEC.

Jaramillo Morilla, A., Rodríguez Liñán, C., de Justo Alpañés, J. L., Romero Hernández, R., & Pérez

Gálvez, F. (2000). Características de los muros antiguos de Sevilla. Tercer Congreso Nacional de

Historia de la Construcción, (pp. 527-535). Sevilla.

López, S. (2013). Evaluación del comportamiento de muros de mampostería no reforzada recubiertos

con mortero reforzado. Bogotá: Escuela Colombiana de Ingeniería Julio Garavito.

López, S., & Torres Castellanos, N. (2012). Evaluación del comportamiento de muros de mampostería

no reforzada recubierta con mortero reforzado. XXII CONGRESO NACIONAL, XI CONGRESO

INTERNACIONAL DE ESTUDIANTE DE INGENIERIA CIVIL, (pp. 1-10). Manizales, Col.

López, S., Quiroga, P. N., & Torres Castellanos, N. (2013). Evaluación analítica y experimental de

muros de mampostería no reforzada y reforzada. VI CONGRESO NACIONAL DE INGENIERIA

SISMICA, (pp. 1-20). Bucaramanga, Col.

López, S., Quiroga, P. N., & Torres Castellanos, N. (2012). Evaluation of unreinforced masonry walls

covered with reinforced mortars. xxxv Jornadas Sul Americanas de Engenharia Estrutural, (pp.

1-14). Rio de Janeiro, Bra.

Ministerio de Ambiente, Vivienda y Desarrollo Territorial. (2010). NSR-10. Reglamento Colombiano

de Construcciones Sismorresistentes. Bogotá.


Newark Nathan M., H. W. (1973). Seismic design criteria for nuclear reactor facilities. Building

Practices for Disaster Mitigation, National Bureau of Standards, U.S., Department of Commerce,

Reporte Nº 46 . Washington.

San Bartolomé, Á. ,. (2007). Comportamiento a fuerza cortante de muretes de concreto reforzados con

malla electrosoldada, acero dúctil y fibra metálica. 1-10.

Useche, L. A. (1993). Estudio de lo morteros y pañetes para la conservación de monumentos

históricos. Bogotá: Universidad Nacional de Colombia.

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