spacing of reinforcing bars in partially ... spacing of reinforcing bars in partially grouted...

Funded by: NCMA Education and Research Foundation

National Concrete Masonry Association Publication Number FR01

Conducted by:

W. Mark McGinley

Department of Civil, Architectural,

Agricultural and Environmental Engineering

North Carolina A & T State University Date—February 2007

SPACING OF REINFORCING BARS IN PARTIALLY GROUTED MASONRY

Final Report

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TABLE OF CONTENTS EXECUTIVE SUMMARY ..............................................................................................................3 1.0 INTRODUCTION...............................................................................................................5 2.0 LITERATURE REVIEW ....................................................................................................6 3.0 TEST PROGRAM ...........................................................................................................21

3.1 INTRODUCTION.........................................................................................................21 3.2 SPECIMEN CONSTRUCTION....................................................................................21 3.3 MATERIAL TESTING .................................................................................................24

3.3.1 Masonry Prism Testing .....................................................................................25 3.3.2 Grout Testing .....................................................................................................25 3.3.3 Mortar Testing ...................................................................................................25 3.3.4 Rebar Testing ....................................................................................................25

3.4 SET-UP AND TESTING PROCEDURES FOR WALL SPECIMENS .........................26 3.4.1 Wall Specimen Measurements and Labeling..................................................26 3.4.2 Test Setup and Procedures ..............................................................................26

4.0 TEST RESULTS .............................................................................................................37 4.1 INTRODUCTION.........................................................................................................37 4.2 GROUT COMPRESSION TESTS...............................................................................37 4.3 MORTAR COMPRESSION TESTS ............................................................................38 4.4 PRISM COMPRESSION TESTS ................................................................................38 4.5 REBAR TENSION TESTS ..........................................................................................39 4.6 WALL SPECIMEN TEST RESULTS ..........................................................................40

4.6.1 Wall 1 Test Results............................................................................................40 4.6.2 Wall 2 Test Results............................................................................................44 4.6.3 Wall 3 Test Results............................................................................................46 4.6.4 Wall 4 Test Results............................................................................................48 4.6.5 Wall 5 Test Results............................................................................................50 4.6.6 Wall 6 Test Results............................................................................................52

5.0 DISCUSSION..................................................................................................................56 5.1 INTRODUCTION.........................................................................................................56 5.2 WALL ARCHING ACTION .........................................................................................56

5.2.1 Arching Action in Continuous Walls ...............................................................56 5.2.2 Arching Action in Discontinuous Walls ..........................................................60 5.2.3 Flexural Bending in Partially Reinforced Walls ..............................................65 5.2.4 Analysis of Wall Specimens.............................................................................68 5.2.4.2 Arching Action Analysis for Wall Specimens.................................................72 5.2.4.3 A Comparative Analysis Between Arching and Flexural Models .................76

5.3 ELASTIC FINITE ELEMENT ANALYSIS ...................................................................82 5.3.1 Finite Element Model Development .................................................................82 5.3.2 Pre-cracked Behavior .......................................................................................84

5.4 A COMPARISON OF PREDICTED AND MEASURED PERFORMANCE.................93 5.4.1 Wall Specimens with #5 Vertical Reinforcement............................................93 5.4.2 Wall Specimens With #7 Vertical Reinforcement ...........................................95 5.4.3 Summary Comments ........................................................................................96

6.0 CONCLUSIONS..............................................................................................................98 7.0 ACKNOWLEDGMENTS .................................................................................................99 8.0 REFERENCES..............................................................................................................100

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EXECUTIVE SUMMARY Vertical reinforcement in 8-inch (203 mm) concrete masonry walls is commonly spaced

at distances up to 10 ft (3.0 m) in wind zones up to 110 MPH (177 KPH), provided that

unreinforced masonry can be shown to be adequate to span horizontally between the

vertical reinforcement by plain (unreinforced) masonry analysis. This method of

analysis has been challenged since the vertically reinforced sections of the masonry

wall are assumed to be cracked at peak loading and these crack isolated sections of

wall may not be able to transfer loading horizontally. This challenge, if successful,

would result in the spacing of the reinforcing being limited to six times the wall

thickness.

To evaluate how partially grouted masonry walls with widely spaced reinforcing actually

behave, five 8-inch (203 mm) thick concrete masonry panels 10’-8” (3.3 m) long and 10

ft (3.0 m) wide with vertical reinforcement at 10 ft (3.0 m) centers were constructed at

North Carolina A&T University and tested to failure under loads perpendicular to the

wall plane. Direct tension simulating the forces generated by roof uplift was applied

simultaneously with the perpendicular wall loads during the testing.

The performance of the wall specimens clearly showed that the conventional plain

masonry analysis is adequate to predict wall behavior for the range of wind loads used

in the high wind standards. In addition, these tests also showed that there is a

significant reserve capacity in the masonry walls provided by arching action, even after

the masonry wall cracks. This arching behavior is similar to that found in masonry infill

panels.

Since it was shown that masonry walls with widely spaced reinforcing bars provide more

than adequate strength to resist significant loading, the results of this research should

allow the continued use of these systems at least up to 10 ft (3.0 m) on center. There

appears to be not need to arbitrarily limit reinforcing spacing to six times the wall

thickness, or 4 ft (1.2 m), for 8-inch masonry walls. This same conclusion was reached

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in numerous high wind damage investigation reports, particularly when compared to the

performance of competitive systems.

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SPACING OF REINFORCING BARS IN PARTIALLY GROUTED MASONRY

FINAL REPORT

By W. Mark McGinley

North Carolina A & T State University

1.0 INTRODUCTION Currently, the Masonry Standards Joint Committee [MSJC, 2005] code has no

maximum spacing requirements for vertical reinforcing bars in either the allowable

stress (ASD) or strength design (Strength) sections. The Code only limits the amount of

masonry in compression that is effective around the reinforcing bars to 6 times the

nominal wall thickness, 72 inches, or the spacing of the bars, whichever is smaller. As

discussed by Drysdale et la [Drysdale et-la, 1999], if the reinforcing bars are spaced at

distances larger than the effective width and partially reinforced masonry walls are

subject to out-of-plane loading, it is usual to assume that the unreinforced masonry

spans horizontally to the vertically reinforced wall sections.

Discussion in a task-group developing high wind masonry code provisions suggests that

the above assumption of horizontal spanning of the unreinforced masonry is not totally

consistent with the cracked section assumption used for the design of a vertically

reinforced section of masonry wall. If all the mortar bed joints parallel to the horizontal

span crack, a series of stack bond masonry sections are created. Since the code states

that no stress can be transferred across the head joint of units in the wall, little or no

force can be transferred horizontally in sections were the wall is cracked unless

transferred by bed joint torsion, or some other mechanism such as arching. However,

none of these other mechanisms have been proven to be present in masonry

assemblies with widely spaced reinforcing, and it has been argued that the spacing of

the reinforcing bars should be limited to 6t (the effective width of the masonry).

However, at lower wind velocities and pressures, limiting reinforcing to a spacing of 6t

can be overly conservative and wider spacing of reinforcement appears to have worked

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well for these situations in the past. This issue also relates to pilasters and would

impact their effectiveness since the masonry walls between the pilasters are typically

not reinforced.

It is the premise of the proposed investigation that this discrepancy in analysis

assumptions is a deficiency in how we model the behavior of the wall and not

necessarily an indication of inadequacy in the wall strength.

It is suggested that the unreinforced masonry wall sections spanning horizontally out-of-

plane may be carrying the load through some sort of tied arch mechanism, in addition to

any plain masonry flexural resistance and other redundancies that may be present. It is

also suggested that the thrusts that this arching produces will be balanced except at

discontinuities in the wall. Where these discontinuities occur, it is further postulated that

the bond beams and reinforcing bars in the footings will act to, at least partially, tie the

arch.

To evaluate whether this action is possible and the magnitude of the loads that may be

carried by this mechanism, a research investigation was proposed. The first step in this

investigation was to conduct a literature review to determine what research related to

this issue had been published. The investigation then conducted a series of full-sized

wall tests and analyzed the results. The following report summarizes the result of this

investigation.

2.0 LITERATURE REVIEW

A literature review was conducted in the North Carolina A & T State University library

Engineering Data Bases, the NCMA On line Data Base, the TMS On line Data Base,

the American Concrete Institute’s On line Data Base, general web searches and direct

email contact with Dr. Ingham at the University of Auckland, New Zealand, Dr. Willis,

The University of Adelaide in Australia, and Dr. R. Drysdale at McMaster University in

Canada. Information relative to the effective width of reinforced masonry, out of plane

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flexure in masonry walls, reinforcing spacing in masonry and concrete walls, and the

behavior of unreinforced masonry infill panels were investigated. Relatively little

information was found related to the performance of widely spaced reinforcing bars in

masonry walls loaded out-of-plane, or on the effective width of the masonry. However,

a number of the publications thought to be most closely related to this investigation are

summarized in the following discussion.

The most directly related research publication found to date was published by Dickey

and Mackintosh and titled, “Results of Variation of “b” or Effective Width in Flexure in

Concrete Block Panels [Dickey and Mackintosh, 1971]. During this investigation, the

authors state that research (non-referenced) on the effective width of reinforcing in

prestressed concrete suggests that this wall assembly characteristic is related to span,

flange thickness, and spacing. This work was used to suggest that 8’ to 10’ effective

compression width "b" and reinforcement spacing would be appropriate for use on 20’

tall masonry wall panels.

To test this assumption, a series of partially reinforced masonry walls were constructed

and tested under a uniform out-of-plane loading (no axial loading). Two different block

sizes were used in the construction of the wall panel systems, which were 8’-8” wide

and 20’-0” high, and consisted of six 8” CMU running bond specimens, one 8” CMU

stack bond specimen, and one 6” CMU running bond test specimen. Each wall system

was provided with two bond beams, one at the top of the wall and the other 7’-2” above

the foundation, each containing two #4 horizontal reinforcement bars. The strip

foundation was attached to the walls by 5/8” dowels (grouted 2’-0” high), which were

placed at the center and either side of the wall in the last cell. The quantity of vertical

reinforcement used in each panel was equal even though five separate spacings were

used in the specimens, which were grouted using the high lift method (6 foot lifts with

mechanical consolidation). The wall specimens were configured to replicate actual field

conditions as closely as possible.

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The measured load and deflection data were recorded. The deflections sampled at

mid-height from the vertical centerline and the outer vertical edges were very close to

one another suggesting the reinforced and unreinforced wall sections, at least at this

aspect ratio, behave as a unit. It was also observed that with all of the running bond

specimens, a horizontal measurement wire at mid-height remained straight the full width

between the vertical reinforcement, suggesting again that that the wall deformed

essentially as a unit.

In addition, calculations were made using classical techniques, in which the response of

the masonry wall was divided into uncracked and cracked behavior. In the above

calculations, the face shells of the masonry units were assumed to be acting in

compression with the flange/web portions, where applicable. The elastic material

constants used in the design strength and deflection calculations were based on tests of

the reinforcing steel, masonry units, grout, and mortar. The predicted response was

plotted against the measured results in order to determine if the effective width used in

the calculations (calculations were based on total width being effective) produced

accurate predictions of behavior. For the majority of the specimens, good agreement

was seen between measured and predicted results. Performance of the stack bonded

wall specimens suggested that these specimens had an effective wall width of only

around half that of the running bond specimens.

The authors concluded that for 20’ tall masonry walls constructed from 8” and 6” CMU’s

in running bond, the vertical reinforcement performed essentially the same at 8’-0”

spacing as it did at a vertical bar spacing of only 2’-0”. This suggests that, for the 8’

configuration tested, the effective width of masonry balancing the vertical reinforcement

is equal to the total width of the specimen, or 13 t (104”/8”). It appears that the current

code provision of 6t for effective width may be unnecessarily conservative for out-of-

plane flexural behavior of partially reinforced masonry walls constructed using running

bond. For the stack bond configurations, even with joint reinforcing, the effective width

of masonry for each of the vertical reinforcing bars was approximately half of that

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observed for the running bond (roughly 52”, or a reinforcement spacing to thickness

ratio of 6.5). In this case, the code provisions appear to be acceptable.

Additional text and code documents were reviewed, including the Masonry Designers'

Guide [TMS, 2004], Reinforced Masonry Design [Schneider and Dickey, 1994], The

MSJC Code Commentary [MSJC, 2005], Reinforced Masonry Engineering Handbook,

Clay and Concrete Masonry [AMRHEIN, 1998], and the UBC 1991 Commentary to

Chapter 24 [TMS, 1992]. Generally, the authors of these documents simply quote the

code provisions relative to the effective width of masonry. Amrhein [AMRHEIN, 1998]

does also include a segment in his book talking about how research conducted by the

Masonry Institute of America (MIA) [Dickey and Mackintosh, 1971] had shown that the

entire width of masonry may be used as the effective width with a bar spacing of up to 8

feet. The UBC 1991 Commentary to Chapter 24 [TMS, 1993] also cites the research

done by Dickey and Mackintosh and further points out that for stack bonded masonry

the MIA research showed that some stress does transfer across the head joint, even

though the code currently has no provision for such stress transfer. Section 2.3.3 of the

MSJC Code Commentary [MSJC, 2005] states that limited research is available on this

subject while giving reference to the Dickey and Mackintosh document. It appears all

these documents reference the same research [Dickey and Mackintosh, 1971], if they

give any references at all.

Another aspect to consider relative to reinforcement spacing in partially grouted

masonry, is how out-of-plane loads are transferred from the unreinforced masonry to

the reinforced masonry sections. As was discussed previously, it is typically assumed

that unreinforced masonry wall sections span horizontally between vertically reinforced

sections, even though this assumption may be theoretically inconsistent if flexural

mechanisms are assumed to be the sole mechanism of transfer. It was further

postulated that this mechanism of load transfer may include both flexure and arching

action. For a partially reinforced masonry wall, this theory suggests that each portion of

the wall that spans between the vertically reinforced wall sections can be regarded as

unreinforced masonry infill panels spanning between two semi-rigid vertical supports.

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At each end of the infill, thrusting forces are developed in the plane of the wall and are

resisted by an equal and opposite thrusting force developed by adjoining panels on

either side. For discontinuous panels, the horizontal reinforcing in the walls, in bond

beams and dowelled foundations act to tie this shallow arch.

Arching action has been applied to the unreinforced masonry walls loaded out-of-plane

on more than one occasion. McDowell et al. [McDowell, 1956] explored this arching

action concept in great depth in a paper titled, “Arching Action Theory of Masonry

Walls”. In this investigation it was shown that masonry walls can resist much greater

loads than what would be expected if one were to compare it to standard analysis

techniques, under specific conditions. Their analysis was based on the theory that the

resistance of masonry walls to out-of-plane loads was completely derived from the in-

plane thrusting forces that are developed and the observation of the wall panel’s

tendency to be compressed to the point of crushing at the mid-span and support edges.

In this investigation, masonry wall specimens were idealized with a solid masonry

element spanning between constrained supports on two sides. It was assumed that

upon first loading, a tension crack was initiated along the center and edges of the wall

panel. As loading is increased, it was assumed that the wall panel begins behaving as

two separate rigid elements connected by a hinge at the mid-point and ends. The

resistance to the rotation of these hinged elements is produced by the compression

strut in the masonry material formed at the inner contact faces and the in-plane thrusts.

The in-plane compression force that is developed in the masonry segments is a

representation of the deflection dependent stress dispersal over the contact areas.

Strain along the block contact areas initially increases linearly with the center deflection

of the wall. At the point in which the crushing stress is reached, the stress at the

support contact areas will become constant and will continue to do so even as the strain

continues to increase. At a large enough deflection, the compression strains will begin

to decrease and the stress will become zero at those locations. The compression block

contact areas will continue to decrease until failure (this is where the maximum thrust

force is reached prior to failure). The theoretical behavior was compared to test results

and, the test results were found to be in general agreement after the initial cracking

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stage. The authors concluded that masonry walls could resist considerably higher load

levels than what obtained from elastic or elastic-plastic flexural strength analysis when

the wall panels outer vertical edges are restrained from in-plane displacement. Also,

the predictions based on the arching theory, which includes the assumptions made

regarding the masonry stress-strain properties, have a good correlation with tests.

Other investigators have also investigated arching action in masonry walls. Using a

methodology similar to that of McDowell et al [McDowell, 1956], Anderson [Anderson,

1984] discusses the effects of the aching action in masonry walls loaded out-of-plane.

This investigation discussed that, although guidance is not generally given by most

codes for the arching action of unreinforced masonry walls spanning between vertical

supports, the 1978 BS 5628 proposes designing these panels as a three hinged arch.

The theories proposed by this research were separated into pre-cracking and post-

cracking conditions, which are affected by factors such as elastic shortening strain of

the wall due to the arching thrust, and deformations of the abutments. For the

stiffnesses of the supports, it was assumed that for interior panels, the stiffness was

infinity since the thrust forces from the surrounding panels balanced each other. Figure

2.1 represents the pre-cracked arching effect of the wall including the location of the

thrust forces and the profile of the wall deflection prior to the consideration of the

arching action.

Figure 2.1 [Anderson, 1984]

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Post-cracking theory suggests that at the point when cracking initiates, the wall behaves

as two separate rigid wall elements connected by hinges at the supports and at mid-

span. The center point of the wall is used for the location of the third hinge not only

because it is a likely occurrence, but also because it can be proven that the minimum

strength of the wall occurs for this condition. Figure 2.2 shows how the masonry wall

system is modeled as a segmental arch after cracking.

Figure 2.2 [Anderson, 1984]

This research defines a failure criteria based on a parabolic compression block at the

contact surfaces of the block wall hinges. Using these assumptions, equations were

developed to predict the behavior of wall systems based on arching action. These

theories were used to predict the behavior of unreinforced test specimens. The testing

apparatus was designed to be used with walls with adjustable end restraint and heights.

The wall systems were loaded with four and eight point loads respectively and the

deflections were measured by eight displacement transducers. Comparison of

measured and predicted behavior suggested that post-cracking arching behavior does

not lend itself to simple span to thickness ratio term descriptions for up to 3 m spans. It

is important to note that a switch from crushing failure to instability was found to occur

with a ratio of around 35 to 40. When crushing is the mode of failure, the thrust force

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developed by the arching action is a function of the compressive strength of the

masonry and the thickness of the wall, but when instability becomes the issue, the

prediction equations become much more complex. In addition this comparison showed

that although deflection prediction was not very reliable, the prediction of ultimate

capacities using arching theory was quite reasonable and that this potential is notably

greater than the theoretical flexural strength of the wall. The ultimate strength

comparison was based on the difference in the cracking load capacity to that of the

failure capacity. It is important to also note that the load required to initiate cracking in

the restrained system was around 3 times the level necessary for a comparable wall

system without end restraints.

The out-of-plane behavior of infill masonry panels was also investigated by Abrams et-al

[Abrams et-al, 1994]. This investigation looked at the out-of-plane behavior of

unreinforced masonry panels contained within concrete frames and clearly showed that,

even when damaged by in-plane forces, infill panels have significant post cracking out-

of-plane strength as a result of arching action. This investigation also developed an

analytical model based on a simple three hinged arch mechanism and used their

results, and that of a Canadian investigation on infill panels in steel frames, to show that

confinement flexibility has a significant effect and arch instability, or “snap through”, is

often the critical failure mode.

There were also a number of documents reviewed that related to the behavior of

unreinforced and reinforced masonry walls systems loaded out-of-plane. These came

from a variety sources (the US, Canada, Australia and New Zealand), although most

were not specifically related to the subject of this investigation since they investigated

unreinforced walls, or walls with vertical reinforcement at spacing equal to or less than 4

ft. However, a few of these investigations are summarized in the following sections

since they give a representative sample of the research that has been conducted in this

general area, or have some aspects that may be peripherally related to the

investigation.

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The technical report by Abboud, Hamid, and Harris [Abboud, Hamid and Harris, 1996],

which was part of a joint research program between the United States and Japan,

presents results of an experimental study that covered the elastic and inelastic behavior

and flexural strength of vertically spanned reinforced concrete masonry walls subject to

out-of-plane loading. Six, simply supported wall specimens were constructed and

tested to examine the effects of quantity and location of vertical reinforcement, block

size, and degree of grouting used on out-of-plane behavior. The analysis incorporated

cracking patterns and moments, load vs. deflection data graphs, and the ductility of the

system in regards to displacement. The six wall specimens were constructed of 4 in., or

6 in., CMU’s, 48 inches wide by 104 inches high, and were either fully grouted or

partially grouted. Two vertical reinforcement spacing patterns were used, 24 inch

spacing centrally positioned about the wall and 8 inches on center staggered.

Horizontal reinforcement was also used at every fourth course (bar spacing is much

more narrow than spacing for the proposed research). Figure 2.3 shows the reinforcing

bar locations.

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Figure 2.3 [Abboud, Hamid and Harris, 1996],

The test data illustrated that, the lower the percentage of reinforcement used, the higher

the ductility. It was also concluded that the quantity and location of vertical

reinforcement (centrally located versus staggered) considerably affected the wall

strength, deflections, and ductility. It was found, however, that an increase in the

percentage of vertical reinforcement does not have a significant affect on the initial

crack load but has a considerable influence on the ultimate loading capacity (higher the

percentage represents larger capacity). Conversely, the quantity of grouting increases

the cracking moment but does not greatly change the flexural strength of the wall

system.

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Work conducted by Drysdale and Essawy [Drysdale and Essawy, 1988] tested twenty-

one full-scale unreinforced concrete masonry wall specimens at McMaster University in

Ontario Canada. The primary focus of the research was on cracking patterns and

failure modes of unreinforced concrete masonry walls and therefore did not address

effective width. This investigation evaluated unreinforced masonry walls subjected to a

uniformly distributed out-of-plane load with simple horizontal and vertical supports.

Three wall panel lengths were tested, 19 feet 8 inches, 17 feet 1 inch, and 11 feet 10

inches. One of the configurations included axial compression. The test results show

that pre-compression of the wall specimens increased capacity. Typical crack patterns

propagated through head joints, rarely passing through the units themselves. The

reaction of the wall systems indicated, that they responded in a flexural ductile mode,

even though they were unreinforced. Load vs. deflection plots indicated that at the

onset of cracking, the load-carrying capacity of the wall panel is reduced to roughly 90

to 95 percent of the load realized prior to cracking. It was found that the cracking load is

affected considerably by the degree of grouting used.

In a further study of the current British, Australian, and North American design

procedures, investigators [Essawy and Drysdale, 1987] evaluated the appropriateness

of the code provisions analytical models through a comparison with existing

experimental data. Thier study showed that unreinforced masonry walls can carry load

in two way bending and that elastic plate theory appears to be the most appropriate

modeling technique. The authors also expressed a need for additional out-of-plane

flexural bending research for masonry wall systems, specifically the influence of support

conditions.

Research conducted by Lawrence [Lawrence, 1995], examined the out-of-plane

horizontal flexural strength of clay brick masonry with stresses parallel to the bed joints.

The authors indicated that there is currently insufficient understanding of how masonry

carries load in this direction, resulting in overly simplified assumptions, or empirical

relationships, applied to the design codes. This research contained both analytical and

experimental elements designed to examine how the behavior of a wall can be

17

expressed in terms of the constituent material properties (311 vertical beams and 310

horizontal beams were tested). Specimens were constructed and tested for flexure

across the head joints using simple supports spaced at 900mm and distance between

the loading points of 400mm. Comparison tests for flexure across the bed joints used

support spacing of 690mm and load spacing of 320mm. The results these tests showed

that the majority of the failures followed at straight line pattern through the head joints

and brick elements. The variation of ultimate stress was evaluated as a function of

cracking stress and it was found that both characteristics were dependent on different

factors. Although, the data suggests that the horizontal cracking stress is related to

bond strength (indicating the influence of the mortar in the head joints), it was also

noted that the stresses produced by flexure parallel to the bed joints are distributed to

the adjacent brick elements through a torsion that is produced on the connecting

portions of the bed joints through friction. The analysis procedures presented in this

report were found to give reasonable predictions of the distribution of moments between

brick elements and the head joints.

This investigator also conducted tests to evaluate effects that workmanship has on this

type of behavior [Lawrence, 1995]. It has been found that in the field, where much of

the time the head joints are not properly filled with mortar, this behavior is affected but a

significant horizontal (parallel to the bed joint) flexural capacity is still present though the

torsional action of the bed joints.

Al-Manaseer and Neis [Al-Manaseer and Neis, 1987], investigated the flexural behavior

of post-tensioned masonry wall systems and evaluated the effects where uplift forces

completely removed the bed joint friction that would ordinarily be developed when an

axial load is applied. The investigation showed that bed joint friction assists with the

overall strength of the wall system and is affected by uplift.

Currently the MSJC Code [MSJC, 2005] provides a table of allowable flexural tensile

stresses (and Modulus of Rupture strengths) for unreinforced masonry elements

subjected to flexure. These tabulated values vary with a number of factors including

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mortar type and the direction in which the stress is oriented relative to the mortar bed

joint. Russell Brown and John Melander (Brown and Melander, 2003] investigated this

anisotropic behavior to determine whether masonry cement based mortars produce

lower flexural capacities, as defined by code. The results from this investigation and

that conducted by Hamid and Drysdale [Hamid and Drysdale, 1988] suggested that the

failure mode of masonry wall panels that were loaded in a manner that produced stress

parallel to the bed joints, had a much more complex behavior than walls that were

loaded to produce flexural stresses normal to the bed joints. Concrete masonry

specimens evaluated in these investigations with stresses parallel to the bed joints

showed two failure patterns; one that zigzagged between the head and bed joints

vertically up the center of the wall panels and one that had a straight crack that followed

the line of the head joints and went through the masonry units. This latter type of failure

resulted from a combined unit and mortar tensile failure and illustrates yet another form

of lateral load transfer mechanism for out of plane loads that is more susceptible to unit

strength variations than that of the mortar, or mortar/unit bond. The investigation also

found that walls subjected to flexure about vertical end supports, have a much greater

strength capacity than what is currently accounted for in the code.

Samarasinghe and Lawrence [Samarasinghe and Lawrence, 1994] also investigated

unreinforced masonry walls loaded out-of-plane using an energy based approach. This

approach assumed that if you can consider an unreinforced masonry wall panel

subjected to out-of-plane loads, the load energy applied to the wall is counteracted by

the energy that is developed within the vertical and diagonal cracks that form in the wall.

As the wall panel deflects and continues to crack under the loading, the energy that the

wall absorbs is a function of the moments along the crack lines and incremental

rotations of the cracks. By setting the work done on the wall equal to the energy

absorbed incrementally by the cracks, the ultimate wall capacity can be obtained. The

authors indicated that the Australian masonry design code, AS 3700 bases its horizontal

and diagonal moment capacities on the principles just described but with the inclusion

of some empirical steps. New expressions for these moment capacities were

19

developed from research by Willis et al.[Willis, 2004], [Willis et –al, 2006], in order to

improve the applicability of the equations and to give them a more rational basis.

Based on the load-deflection response of the unreinforced masonry walls subjected to

out-of-plane biaxial bending by Willis and others [Willis et-al, 2006], [Lawrence, 1995],

[Drysdale and Assawy, 1988] it is clear that there was a gradual reduction in the

stiffness in these wall systems as the load is increased However, even after cracking

has occurred, a level of frictional resistance is still maintained at the head joints prior to

the failure of the bed joints. Most of this post cracking resistance is likely due to the

torsional mechanism developed in the bed joint, but some capacity may also be due to

the arching across the head joint and the overlapping unit acting at the tension tie. This

issue needs to be explored further.

Based on the literature survey, the following conclusions relative to the performance of

widely spaced vertical reinforcing bars in masonry walls loaded out-of-plane can be

made:

1. Only one published investigation appeared to be directly related to the

performance of concrete masonry walls with widely spaced vertical reinforcing

under out-of-plane loading. (They tested a maximum reinforcement spacing of

approximately 8 ft for a 20 ft span).

2. This one investigation showed that larger reinforcement spacing appeared to

produce larger effective widths and these wall specimens appear to be able to

transfer the loads horizontally without distress to vertically reinforced sections (At

least if the walls were constructed with two bond beams and a dowelled

reinforced footing).

3. Work on arching of unreinforced masonry infill panels between structural frames

suggest that significant resistance to out-of-plane loads can be developed using

this mechanism. This mechanism can be used to transfer significant load from

unreinforced masonry wall sections to vertically reinforced sections if sufficient

horizontal reinforcing bars are present to act as a tension tie for the arching

20

mechanism, at the perimeter of the panel or within the panel itself. This

horizontal reinforcing can be provided in bond beams and dowelled footings.

4. Investigations of the out-of-plane load deflection behavior of unreinforced

masonry walls suggest that there are a number of mechanisms present that help

to transfer out-of-plane loads horizontally in running bond masonry.

5. None of the work found looked at the effect of vertical uplift force on the out-of-

plane load carrying capacity of partially grouted reinforced masonry walls. This

needs to be evaluated further, and is one of the areas that will be addressed by

this investigation.

21

3.0 TEST PROGRAM

3.1 INTRODUCTION

In support of the development of a methodology that describes the mechanism of

horizontal load transfer in partially reinforced masonry walls, a series of six full scale

wall specimens were tested in the structural laboratory at North Carolina A&T State

University (NC A&T SU) in Greensboro, NC. In addition, material tests were conducted

on a set of masonry prisms, samples of the grout and mortar used for construction, and

of the steel reinforcing bars. The following sections of this chapter describe the

techniques and procedures used in the construction and testing of the wall specimens

and representative construction materials.

3.2 SPECIMEN CONSTRUCTION Six concrete masonry wall specimens were constructed by a crew of experienced

masons using 8” hollow concrete masonry units (CMU’s). The CMU’s were standard 8”

ASTM C90 concrete units and were laid in running bond, 16 courses high and 8 units in

length. As shown in Figure 3.1, the overall dimension of the walls were 10’-8” x 10’-8”,

and were constructed with face-shell mortar bedding using ASTM C270 Type S

Masonry Cement mortar. All six walls were constructed over two days and allowed to

cure for at least a week in ambient lab conditions. During construction, a single #5

reinforcing bar was placed in the center of the base bond beam and wired in place.

Knockout bond beam units were used for the bond beams at the top and bottom of the

wall. Vertical reinforcing was placed in the center of the outer cores of the wall panels

and held in position by bar positioners.

22

#5 OR #7 REBAR INGROUTED CELL

#5 REBAR INBOND BEAM

8" CMU UNITS

12" ANCHOR BOLTS

8" 2'-0" 4'-0" 2'-0"8" 8"8"

10'-8"

10'-0"

4" 4"

10'-0"

4"

4"

10'-8"

934"

2'-1"

2'-1"

STANDARD HOOK (MIN. EXTENSION 12db)

Figure 3.1 Full Scale Wall Specimen

Three wall specimens had a #5 reinforcing bar placed in the outer vertical cores and

three had a #7 reinforcing bar placed in the outer vertical cores. A #5 reinforcing bar

was then placed into the center of the bond beam on the top of the wall specimens.

The bond beam reinforcing was bent down a minimum of 25” into the end vertical cores

so that they formed a lap splice with the vertical reinforcing.

Once the reinforcement was placed, the walls were grouted using a high lift grouting

procedure. A coarse ready-mixed grout was used to grout the vertical bars and the top

bond beams. The lower bond beams were grouted with a fine grout mixed to the

23

proportion specifications of ASTM C426 (3 parts sand to 1 part cement). The walls

were allowed to cure for at least twenty-eight days in the lab environment before testing.

Samples of representative mortar batches, grout batches, units, and reinforcing bars

were taken throughout the wall construction as described in the following sections.

The wall specimens were constructed on three courses of dry stacked masonry block as

shown in Figure 3.2. This was done to allow the embedment of ½” anchor bolts in the

lower bond beam. The identical bolt configuration was also used in the top bond beam

so that a structural tube could be attached to the wall system. These tubes were later

used to apply a compression load to the specimens for transport and the to exert an

uplift force during testing. The raised block allowed clearance to attach the lower

structural tube.

A nut and washer were secured on the end of the ½” threaded anchor rods that were

embedded in grout to ensure a solid attachment.

24

934"

1'-158"

WALL SPECIMEN

758"

758"

758"

EMBEDDED 12

4"

12" OSB

8" CMU's DRY STACKED

412"

LAB FLOOR

Figure 3.2 Base Configuration for Construction of Wall Specimens

The threaded anchor rods were attached with glue to and through a piece of ½” thick

oriented strand board (OSB), to maintain the desired position during grouting. The OSB

board was not only used to hold the rods in place, but was also used to provide a level

surface to construct the specimens on (shown in Figure 3.2). Section 3.4.2 provides

further discussion on the wall specimen design and development of testing procedures.

3.3 MATERIAL TESTING

All materials used in the construction of the walls, excluding the anchor rods, were

tested using the applicable ASTM standard test method. It was not necessary to test

the anchor rods because the rods were not loaded near their capacities and will not

affect the results. The masonry prisms were tested for compressive strength, the rebar

for tensile yield and ultimate strength, and the grout and mortar were tested for

25

compressive strength as well. The prisms were also used to determine the wall weight,

both grouted and ungrouted.

3.3.1 Masonry Prism Testing

Six masonry prism specimens were constructed at the same time as the walls using the

same block and mortar as was used for the walls. The masonry prisms were fabricated

using standard half block (8” x 8”) CMU’s, two courses high with full mortar bedding.

Three of the prism specimens were grouted, one from each of the grout batches.

Compression tests were carried out on each of the six prisms using the procedures

outlined by ASTM C1314 (Standard Test Method for Compressive Strength of Masonry

Prisms). Specimens were allowed to cure in the lab air for at least 28 days.

3.3.2 Grout Testing

Grout was sampled during construction of the wall specimens. A total of eleven

specimens were prepared using the procedures in ASTM C1019 (Standard Test Method

for Sampling and Testing Grout). Compressive strength testing was performed on the

grout after curing at least twenty-eight days in accordance with ASTM C1019.

3.3.3 Mortar Testing

The ASTM C270 Type S Masonry Cement Mortar used in the construction of the full-

scale wall specimens and the corresponding prisms were sampled at different times

throughout the building process to provide a representative mortar sample. A set of two

2” cubes were made for each double batch mixed, giving a total of sixteen cubes. The

cubes were kept in their forms for 24 hours then were stripped, marked, and placed in a

lime bath solution to cure in the lab environment for at least 28 days. After the cure

period, compressive tests performed as per ASTM C 109 (Standard Test Method for

Compressive Strength of Hydraulic Cement Mortars).

3.3.4 Reinforcement Testing

The yield and ultimate tensile strength of the bars used for the horizontal and vertical

reinforcement in the wall specimens was determined using the procedures defined by

26

ASTM A370 (Standard Test Methods and Definitions for Mechanical Testing of Steel

Products).

3.4 SET-UP AND TESTING PROCEDURES FOR WALL SPECIMENS

3.4.1 Wall Specimen Measurements and Labeling

Following the construction of the full-scale walls, all specimens were labeled in

accordance with the reinforcement configuration used. Measurements were taken for

the wall dimensions after the twenty-eight days curing period was complete to allow for

any shrinkage during the cure process.

The series of specimens that had #5 horizontal and #5 vertical reinforcing bars were

constructed on the left side of the lab and were numbered from 1 to 3. On the right side

of the lab, the series corresponding to the reinforcement configuration that utilized #5

horizontal and #7 vertical bars were numbered 4 through 6.

3.4.2 Test Setup and Procedures

In order to move the wall specimens from where they were constructed (vertically) to the

final horizontal position in the testing frame, a compressive loading was applied to the

top and bottom of the wall prior to moving. This was done to prevent the mortar joints

from cracking under the self weight of the system. Anchor rods were provided in each

of the bond beams for the attachment of a hollow structural tube that was used to apply

a pre-compression load to the specimen during moving and then an uplift load during

testing.

To aid in the development of the testing apparatus, testing procedures, and test

specimen design, a linear elastic finite element model (FE model) of the partially

reinforced masonry wall specimens subjected to an axial compression load and out-of-

plane self-weight was developed using ANSYS, version 10.0 (see Figure 3.3). A rough

27

estimate of the load required to keep the entire system in compression while being

moved was determined using the net cross-sectional area of the wall (An) and setting

the desired maximum compression stress level to around 100 psi. Several loading

combinations were modeled.

Figure 3.3 Finite Element Model of Partially Reinforced Wall

The best results were obtained with three load application points combined with a HSS

8 x 4 x ½ steel tube. The final total compressive load was 39000 lb, with 9000 lb on

each end and 21000 lb at the middle. Figures 3.4 through 3.7 show the stress

distributions in the wall specimen, on the front and backside, in both the vertical and

horizontal direction (orientation used refers to the directionality of the wall if it were in

the vertical position, the axes are labeled in the diagrams).

28

Figure 3.4 Axial Stress Distribution of Partially Reinforced Wall (Front View)

The axial stress levels were higher on the front side of the walls than 100 psi, but are

well below the compressive strength of the masonry. Anomalies in the stress

distribution shown in Figure 3.4 and 3.5 are localized and are likely to be a product of

the modeling. These were ignored since they are not likely to occur.

29

Figure 3.5 Lateral Stress Distribution of Partially Reinforced Wall (Front View)

The middle section on the backside of the wall was the critical stress location in both

directions. It should be noted that maintaining all of the wall section in compression was

not practical using only three load application points. However, the predicted tensile

stresses were well below the modulus of rupture (fr) of the mortar joints (see Figure 3.6

& 3.7).

30

Figure 3.6 Axial Stress Distribution of Partially Reinforced Wall (Back View)

Figure 3.7 Lateral Stress Distribution of Partially Reinforced Wall (Back View)

Using the configuration described previously, compression load was applied using four

threaded rods that spanned between the top and bottom HSS tubes (one rod at each

end and two located in the middle). The 1” diameter rods were equipped with load cells

31

to monitor the load applied (see Figure 3.8). Figure 3.9 shows the front and side view of

the wall specimen with the hollow tubes and rods attached.

Figure 3.8 Load Cell Configuration for Compression Loading

1" THREADED ROD

8" CMU RUNNING BONDWALL SPECIMEN

HSS8x4x12 RECTANGULAR TUBE

STEEL PLATE12" ANCHOR RODS

1" THREADED ROD

STEEL PLATE

HSS8x4x12 RECTANGULAR

TUBE

FRONT VIEW SIDE VIEW

12" OSB

12" OSB

Figure 3.9 Specimen Configuration for Wall Repositioning

32

Once the compression load was applied, the test specimens were lowered with a crane

onto the 3 in. diameter roller supports positioned 4 in. from the outer edge directly under

the horizontal reinforcement location. The walls, shown in Figure 3.10, were seated on

the rollers using gypsum capping mixture meeting ASTM C 1552 (Standard Practice for

Capping Concrete Masonry Units, Related Units and Masonry Prisms for Compression

Testing) to reduce the unevenness of the bearing area. Relatively rigid HSS 12 x 8 x ½

were placed underneath the rollers for support. A wiffle tree apparatus was placed at

the center of the wall specimen to apply an out-of-plane point load to four locations.

Round tubes were used as rollers between the wiffle tree beams and the wall specimen

(the rollers were welded to the beams to prevent shifting during testing).

Figure 3.10 Typical Testing Configuration for Wall Specimens

The compression force was kept on the walls during the placement of the specimen,

and after they were placed in the testing apparatus. The compression load was

monitored until after all displacement sensors were in place and the computerized data

acquisition program was prepared to record the data. This was done because the self-

weight of the masonry was likely to crack the wall specimen in absence of the

compression force.

33

Each wall specimen had three String Potentiometer Position Transducers (String Pots)

positioned to record the out-of-plane movements along the center span of the

specimen, 4” from either edge and in the center of the specimen. These locations were

chosen to obtain an understanding of how the wall deflects at the center relative to the

outer edges. The String Pots were placed on a support surface directly underneath the

specimen with the strings attached to screws embedded in the wall using wall anchors.

Five Linear Variable Differential Transformers (LVDT) were positioned to measure the

strain perpendicular and parallel to the wall span, across specific mortar joint locations

on the tension side of the wall. The strain parallel to the span was taken at center span

4” in from outer edge directly under the vertical reinforcement location, and the strains

perpendicular to the span were sampled along the specimen centerline, at two quarter

points 32” in from outer edge and at center span. All of the LVDT’s used 8” gauge

lengths and were placed in sensor mounts attached to aluminum L-brackets. The

brackets were attached to the wall using wall anchors. Figures 3.11 and 3.12 show

the sensors used for each wall specimen, along with a close-up view of two LVDT

sensors and two string pots located on the underside of the walls, respectively.

Once all of the sensors were attached and the capping mixture had fully hardened, the

computer data acquisition system was set to start recording data and the compression

loading was incrementally released from the wall. The two central tension rods were

completely removed from the testing assemblage because they were only needed for

the compression loading and would be interfere with the application of the point loads.

34

CLOSE-UP DETAIL

STRING POT

LVDT

Figure 3.11 Displacement Sensor Configuration

Figure 3.12 Close-up View of LVDT and String Pot Sensors at the Center Span of Wall

Specimen

1" THREADED ROD


ROUND HSS3.00x0.250 TUBE


STEEL PLATE


STRING POT

LVDTSTRING POT

STRING POT

LVDT

LVDT

LVDT

LVDT

SEE DETAIL BELOW

STRAIN GAUGE

ISOMETRIC VIEW

Rods were removed after the compression force was incrementally decreased

35

After the compression load was released, the anchor bolts attaching the tubes to the

walls were loosened so that the stiffness of the tubes would not affect the bending

behavior of the wall during testing. The end tubes were also slotted where the rods

were attached to further reduce any effect on the wall specimen behavior.

A round tube was slid over each of the two exterior tension rods, along with two

additional nuts and plate washers. These nuts were tightened down firmly against the

ends of the plate washers creating a compression load in the tubes and applying an

uplift forced to the HSS tube attached to the wall specimens. The nuts were tightened

until a total axial uplift of 1000 lb was applied to each of the wall specimen bond beams.

The uplift load was measured using load cells placed between the rods and beam.

With the output from all the sensors being recorded by the computerized data

acquisition program, an additional out-of-plane load was applied to the wiffle tree

mechanism by the MTS loading system (The total applied point load was measured

using a load cell inline with the actuator ram). These additional out-of-plane point loads

were applied in a gradual, uniform, manner until failure of the specimens was observed.

Failure was defined as the point when there was a significant loss in load capacity.

Figures 3.13 and 3.14 show the side and end views of the wall specimen in the testing

apparatus.

36


W24x117 TESTING MACHINE GIRDER


TUBE

LVDTLVDT

2'-8"

STRING POT


MTS LOADING SYSTEM


TUBE10'-0"

4"2'-8"

4" 2'-8"

ROUND HSS2.375x0.125 TUBEHSS4x4x

12 RECTANGULAR

TUBE

1" THREADED ROD


Figure 3.13 Wall Specimen Testing Set-up (Side View)

W24x117 TESTING MACHINE GIRDER


2'-8"

MTS LOADING SYSTEM

4'-0"

12" ANCHOR RODS

HSS12x8x12

TUBE



TUBE

1" THREADED ROD


10'-8"

Figure 3.14 Wall Specimen Testing Set-up (End View)

37

4.0 TEST RESULTS 4.1 INTRODUCTION A total of six full-scale wall specimens were tested under combined uplift and out-of-

plane loading. In addition, thirty-three small-scale compression tests and six tension

tests were conducted on the materials used for the construction of the walls. This

chapter focuses on the test results.

4.2 GROUT COMPRESSION TESTS

The grout, which was poured in three stages, was tested periodically throughout the

wall specimen testing (testing was conducted for six consecutive days). The average

strength for pours 1 through 3 was 4749 psi, giving a coefficient of variance (COV) of

18.4 %. The grout strength was consistently greater than the minimum of 2000 psi

required by ASTM C476 (Standard Specification for Grout for Masonry). Table 4.1

shows the compressive test results for the grout specimens.

Table 4.1 Grout Compression Test Results

Specimen Age Net Area Load Net CompressiveDesignation Days (in2) (lb) Strength (psi)

1 28 9.45 36070 38172 28 9.48 35951 37923 28 9.49 35022 36924 29 9.44 56023 59375 29 8.95 47362 52946 29 9.06 49319 54467 30 9.33 50387 54028 30 9.66 57328 59329 30 9.54 43169 452310 31 9.16 39669 433111 31 10.19 41528 4075

Average 4749COV 18.4%

38

4.3 MORTAR COMPRESSION TESTS

Table 4.2 summarizes the results of the mortar compression tests. As with the grout,

the mortar was tested periodically during the testing of the wall specimens. The

average compressive strength for all eight cubes is 3295 psi with a COV of 8.0%.

These values suggest that the mortar mixing was relatively consistent.

Table 4.2 Mortar Compression Test Results

Specimen Age Net Area Load Net CompressiveDesignation Days (in2) (lb) Strength (psi)

1 28 4.0 12953 32382 28 4.0 12646 31623 30 4.0 13823 34564 30 4.0 14337 35845 30 4.0 12982 32466 32 4.0 14624 36567 32 4.0 11351 28388 34 4.0 12725 3181


4.4 PRISM COMPRESSION TESTS

The masonry prisms were tested in pairs of two (one grouted and one ungrouted), on

the same day that wall specimens 1, 3, and 5 were tested. The average net area

compressive strength for the grouted units is 2343 psi , with a COV of 9 2. % . For the

ungrouted prisms, the average unit strength is 2341 psi , having a COV of 9 9. % . The

overall variation of compressive strengths for the prisms was relatively low. Tables 4.3

and 4.4 summarize the compression test results for the grouted and ungrouted masonry

prisms.

39

Table 4.3 Grouted Prism Compression Test Results

Specimen Designation Net Area Load Net Compressive

Strength 1 58.5 150900 25812 58.4 133680 22903 58.4 126160 2159


( )in2 ( )lb ( )psi

Table 4.4 Ungrouted Prism Compression Test Results

Specimen Designation Net Area Load Net Compressive

Strength 4 38.8 82166 21205 38.6 99786 25836 38.7 89800 2322


( )in2 ( )lb ( )psi

In addition, the average weight of the 7-5/8 in x 7-5/8 in. x 15-5/8 in prisms was 28.0 lb

for the ungrouted and 55.8 lb grouted prisms, respectively.

4.5 REINFORCEMENT TENSION TESTS

Three tension tests for each of the two reinforcement sizes used in the construction of

the wall specimens were performed. The average yield strength for the #5 and #7 bars

were found to be greater than the 60 ksi specified yield strength. The variation from

specified yield strength was most significant for the #5 bars, and this strength increase

appears to have a noticeable effect of the wall test results. The summarization of the

tension tests conducted on the reinforcement is shown in Table 4.5.

40

Table 4.5 Reinforcement Tension Test Results

4.6 WALL SPECIMEN TEST RESULTS

4.6.1 Wall 1 Test Results

During the testing of wall Specimen 1, deflections initially occurred in a symmetric

manner at mid-span as the 39000 lb compression load was removed, showing

approximately the same deformations on all three sensors. The strains recorded at

mid-span were in agreement with the string pot measurements, indicating that under the

self-weight of the system, the wall was deforming essentially in single curvature (the

strain perpendicular to the span at this load level was at, or around zero). Once the

entire compression load was removed, the uplift force of 500 lb applied, and the out-of-

plane point load was incrementally placed on the wall, tension cracks along the bed

joints of the block increased in width and larger deflections were observed. As the load

approached the ultimate strength of the specimen, small cracks began to form in some

of the head joints creating significant stair step patterned cracks that propagated from

each corner, following the head and bed joints toward the center. When the head joint

cracks began to occur, horizontal strains started to show a considerable level of

bending perpendicular to the span, more so at the center than at the symmetrically

placed LVDT’s at quarter points of the wall height. The applied load reached a

maximum value of 3139 lb, with a centerline and edge deflection of 2.99 in. and 2.06 in.,

Reinforcement Size

Net Area( in2)

Yield Stress(psi)

Ultimate Stress(psi)

#5 0.31 85610 102000 #5 0.31 84780 100700 #5 0.31 81590 99070

Average 83990 100600 COV 2.5% 1.5%

#7 0.6 68630 103500 #7 0.6 65670 106230 #7 0.6 70680 114830

Average 68330 108200 COV 3.7% 5.5%

41

respectively. After the peak load was reached, additional deformation was imposed on

the wall to test the stability of the specimen. No “snap through” (stability failure of the

crack separated masonry) was observed over an additional inch of deformation. This

suggests that significant confinement was provided by the horizontal reinforcement,

tying the wall together. Figure 4.1 and 4.2 show the stair step crack pattern that formed

at each corner and the overall curvature of the wall at failure.

Figure 4.1 Stair Step Crack Pattern Typical for Each Corner of Wall 1

42

Figure 4.2 Curvature of Wall 1 at Failure

Since there were two different types of out-of-plane loads applied to the wall specimens

it was difficult to plot a load-deflection history for each wall. However, an attempt was

made to produce an approximation of this history by converting the out of plane loading

due to the self weight of the wall into an equivalent total point load, P. The self-weight

of the wall was determined using the weight of the prisms and a weighted average

based on wall areas, grouted and ungrouted. This calculation resulted in a uniform

average weight for the wall specimens, w, of 41.7 lb/ft2. The total applied point load, P,

(applied as shown in Figures 3.13 and 3.14) that would produce the same peak moment

as a uniform load of 41.7 lb/ft2 was calculated to be 2370 lb. To provide a smooth graph,

and since the compression load was reduced uniformly, the total equivalent point load

(2370 lb) was divided by the number of deflection data points that were recorded up to

the application of the uplift force and this load was assigned to each deflection point.

The additional applied total point loading was then added to the self-weight value.

The resulting load deflection response is shown in Figure 4.3. It is clearly shown by the

change in slope of the plot that the wall cracked at an equivalent point load of

approximately 1500 lb (total load at this level was only due to self-weight since the

compression load had not been completely removed). It is also shown in the plot that

deflection at mid-span, near the edges and middle, did not diverge until significant

additional loads were applied.

43

0

1000

2000

3000

4000

5000

6000

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Deflection (in)

Out

-of-P

lane

Loa

d (lb

)

Deflection at Center Deflection at Edges

Figure 4.3 Wall Specimen 1 – Load vs. Out-of-Plane Deflection

Significant deflections were observed after the reinforcement reached yield stress (at

around P = 5400 lb), giving a maximum recorded deflection at the center and edges of

3.12 in. and 2.09 in., respectively. The overall wall response was quite ductile; and it

appeared that the wall failure was governed by the yielding of the reinforcement parallel

to the wall span.

After the testing was completed and the wall was removed from the testing machine,

openings had to be made in the wall at four corner locations so that the reinforcement

could be cut because the bars were still effectively holding the wall together. Once the

cuts had been made, the wall fell apart. Note that this was typical for all the wall

specimens.

44

As summary of the load and deflection data for each wall configuration is given in Table

4.6 at the end of Section 4.3.


Using the procedures described for Wall Specimen #1, an out-of-plane load- deflection

history was produced for Wall Specimen #2 and shown in Figure 4.4. The behavior

exhibited by the Wall #2 (also with #5 reinforcing bars parallel to the span) was similar

to that described for Wall Specimen #1, with a few exceptions. The stair-step cracks

that formed from the corners toward the center initially only occurred at three locations,

which caused the edge deflections to vary. However, upon further loading, the

difference in the edge deflections reduced to an insignificant amount. Cracking of the

wall first initiated in the bed joints at an equivalent point load of approximately 1100 lb,

during the compression unloading stage. Deflections indicate that the walls act stiffer at

the edges in comparison to the center (this is also found for Wall Specimen 1). The

maximum out-of-plane load (equivalent self-weight load of 2370 lb plus applied load)

was 4824 lb. The corresponding mid-span deflections, at the center and the average of

the edges were 1.39 in. and 0.80 in, respectively. The observed deflections are

considerably smaller than Wall Specimen 1

After the reinforcement parallel to the span appeared to reach yield, the wall continued

to perform in a ductile manner producing roughly an additional inch of deflection at the

center before the loads began to drop off. At the point when the load was removed, the

stability of the system did not appear to be an issue, and it is believed that the wall

could have carried further deformations. The maximum deflection at the center was

1.81 in. and an average of 0.89 in. at the edges, much stiffer than Wall Specimen 1.

Figure 4.4 shows a side view of the specimen after the ultimate load was reached. The

two-way action creates a bulge in the wall about the center, which is where the

maximum deflection is observed. The load deflection performance of this wall specimen

is also summarized in Table 4.6 at the end of this section.

45

0

1000

2000

3000

4000

5000

6000

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Deflection (in)

App

lied

Loa

d (lb

)

Deflection at Center Average Deflection at Edges

Figure 4.4 Wall Specimen #2 – Load vs. Out-of-Plane Deflection

Figure 4.5 Curvature of Wall #2 at Failure

46


Using the procedure described previously, the approximate equivalent load-deflection

history for Wall Specimen #3 (also reinforced with #5 rebar in vertical cores at the panel

edges) was developed and is shown in Figure 4.6. During this test, initial bed-joint

cracking and some minor head joint cracking occurred at an equivalent point loading of

approximately 1300 lb, with mid-span center and average edge deflections of 0.044 in.

and 0.020 in., respectively. Apparent yielding of the reinforcement occurred at P load of

approximately 4500 lb, giving a mid-span center and average edge deflection of 0.114

in. and 0.55 in, respectively.

One of the primary differences between the behavior of this specimen compared to the

others is that the ultimate load was reached very shortly after the point of yield.

Additionally, the load dropped abruptly by approximately 1500 lb after a maximum of

equivalent point of 5327 lb was reached. This lower applied load was then maintained

for more than an additional inch of deflection at the center of the wall. The mid-span

deflections that were measured at the maximum load were 0.35 in. and 0.15 at the

center and edges, respectively.

As with the other walls constructed with #5 reinforcing bars parallel to the span,

significant strains perpendicular to the span did not develop until the formation of the

stair-step cracks, which occurred close to ultimate load. On the lower end of the loading

spectrum, the deflections were relatively even across the centerline, with the low or no

strains perpendicular to the span. The overall load-deflection behavior of Wall

Specimen #3 indicated that it was much stiffer than either of the other specimens for

most of the loading. However, the maximum deflections of Wall Specimen #3 were

close to that measured for Wall Specimen 2.

As shown In Table 4.6, even with the differences described, the overall strength

behavior of the three walls specimens constructed with #5 reinforcing bars parallel to

the span was quite consistent (the COV is 6.8%).

47

0

1000

2000

3000

4000

5000

6000

-0.5 0 0.5 1 1.5 2Deflection (in)

App

lied

Loa

d (lb

)


Figure 4.6 Wall Specimen 3 – Load vs. Out-of-Plane Deflection

Figure 4.7 shows the underside of Wall Specimen #3 in the test apparatus at ultimate

load. The LVDT that is shown in the photo is located at the center where the stair–step

cracks that propagated from all four corners meet. The crack pattern shown was typical

for all specimens tested.

48

Figure 4.7 Curvature and Stair Step-Crack Pattern of Wall Specimen # 3 at Failure

In general, for all these wall tests (Specimens #1, #2, and #3), bed joint cracks first

appeared near center span, usually during removal of the compression loading. It was

not clear at what stage the head joint/stair-step cracks first formed, but after the

reinforcement yielded and the deflections increased, these cracks opened significantly

more than the continuous bed joint cracks at mid-span.

From the crack formations, it appears that the crack isolated triangular segments of

wall may be forming an arch during the latter stages of loading, demonstrating a form of

horizontal load transfer between widely spaced reinforcement not accounted for in the

MSCJ 2005 Code. Further comparison of the test data to the analytical models is

discussed in Chapter 5.


Initial load-deflection behavior of this wall specimen did not vary significantly from the

previous wall specimens, even though #7 reinforcing bars were used parallel to the wall

49

spans. Deflections remained relatively uniform at the mid-span of the wall for more than

half of the total load.

Using the procedures described previously and an equivalent self weight total point load

of 2370 lb, an approximate load deflection history was developed and shown in Figure

4.8. As shown in this plot, a noticeable difference in edge and center deformations

does not occur until P is approximately 3250 lb. The LVDT’s measuring the strain

showed little to no bending deformation perpendicular to the span at the top and bottom

locations but there were significant deformations in the same direction at the center of

the wall, near the ultimate load.

Cracking of the bed joints first occurred at a P load of roughly, 1200 lb. This is similar to

the load levels observed for this cracking in Walls Specimens #1, #2, and #3. However,

these bed-joint cracks did not open as wide as these other specimens when additional

loading was applied

0

1000

2000

3000

4000

5000

6000

7000

-0.5 0 0.5 1 1.5 2 2.5 3 3.5Deflection (in)

App

lied

Loa

d (lb

)



50

As additional loads were applied, stair-step-cracks formed from the center of the wall

outward to all four corners, following head and bed joints near the load that yielded the

reinforcement. An increase in strains perpendicular to the span at all three sensors

was found once the significant cracking had occurred.

The load deflection plot suggests that the reinforcement (likely that perpendicular to

span) began to yield at a total equivalent load (P) of 5337 lb, with a corresponding

maximum mid-span deflection of 1.34 in.

The ultimate equivalent P load of 5794 lb was reached at a deflection of 1.78 in.and the

specimen continued to carry approximately the same load for an additional inch of

deflection. Maximum deflections at the center and edges are shown in Table 4.6.

When the test was terminated, and the additional applied loads were removed, the

majority of the vertical edge deformations were regained suggesting that the

reinforcement parallel to the span remained in the elastic range. Figure 4.9 gives an

overall view of the specimen at failure.

Figure 4.9 Curvature of Wall # 4 at Failure


Wall Specimen #5 exhibited many of the same behaviors observed in the previous wall

specimens. One characteristic that is shared by all specimens, regardless of the

51

reinforcement configuration, is the stair-stepped cracking patterns. Figure 4.10

illustrates the size and location of cracks occurring in the diagonal direction for the

specimen, which is typical for walls with #7 vertical reinforcement bars.



4.11. As shown in this plot, Wall Specimen #5 was much stiffer than Wall Specimen

#4, although the load deformation curve had a similar shape. The behavior was quite

ductile and significant bending perpendicular to the span did not occur until extensive

stair step cracking was evident.

Figure 4.10 Tension Crack Pattern of Wall #5 at Failure

52

In addition to the tension cracks observed on the underside of the wall, small

compression cracks also formed directly above some locations of the stair-step cracks,

and occurred in the units themselves.

0

1000

2000

3000

4000

5000

6000

7000

8000

-0.5 0 0.5 1 1.5 2 2.5Deflection (in)

App

lied

Loa

d (lb

)



Maximum deflections and loads are shown in Table 4.6. As with Wall #4, most of the

elastic deformations in the vertical reinforcement were recovered when the applied

loading was removed.


Wall Specimen #6 exhibited similar load-deflection characteristics to the previous walls.

The one noticeable difference was the level at which initial cracking occurred. The first

cracks occurred at an equivalent point load, P of approximately 600 lb, which was less

than half the cracking load of all the other specimens.

53



4.12. As shown in this plot the load deformation curved had a similar shape to Wall #5.

The behavior was quite ductile and significant bending perpendicular to the span did not

occur until extensive stair step cracking was evident.

0

1000

2000

3000

4000

5000

6000

7000

-0.5 0 0.5 1 1.5 2 2.5Deflection (in)

App

lied

Load

(lb)

Deflection at Center Average Deflection at Edges Figure 4.12 Wall Specimen #6 – Load vs. Out-of-Plane Deflection

Figure 4.13 shows the underside of the wall at failure, at the center LVDT and String Pot

location.

54

Figure 4.13 Center Head and Bed Joint Crack Pattern of Wall 6 at Failure

The photo demonstrates the size of separations that occurred; yet the wall still

maintained stability. The vertical crack at the center of the photo was the meeting point

for the four stair step cracks.

Compression cracking, found also with the previous specimen, was observed on the

topside locations above the stair step cracks. Figure 4.14 shows the compression

cracks on the topside of the wall at the center.

Figure 4.14 Center Compression Crack Pattern of Wall 6 at Failure

55

The summary of maximum loads and deflections for this wall specimen is shown in

Table 4.6.

Table 4.6 Wall Specimen Test Results

Specimen Designation Ultimate Load Center Defl. at Ult. Edge Defl. at Ult. Max Defl. at Center Max Defl. at Edge

1 5509 2.99 2.06 3.12 2.092 4824 1.39 0.80 1.81 0.893 5327 0.35 0.14 1.84 0.41

Average 5220 1.57 1.00 2.25 1.13COV 6.8% 84.5% 97.1% 33.2% 76.6%

4 5794 1.78 1.39 2.90 1.595 6918 1.09 0.81 1.95 0.886 6063 0.68 0.55 2.20 0.74

Average 6258 1.18 0.92 2.35 1.07COV 9.39% 46.84% 46.44% 20.84% 42.44%

( )in( )lb ( )in ( )in ( )in

Note: Ultimate Loads are Equivalent P Load = 2370 lb (due to 41.7 psf self-weight) + total applied load.

56

5.0 DISCUSSION 5.1 INTRODUCTION

One of the prime objectives of this research was to develop a design methodology for

partially reinforced walls with widely spaced reinforcing bars that accounts for the actual

behavior of the walls. The walls specimens were analyzed using two hand calculation

methods, and a Finite element model. These analyses and the comparison of predicted

to measured results are presented in the following sections.

5.2 WALL ARCHING ACTION

5.2.1 Arching Action in Continuous Walls

A theory presented by researchers at the Polytechnic of the South Bank in London

[Anderson, 1984], regarding arching action of solidly grouted masonry infill panels

loaded out-of-plane, was used to suggest that the unreinforced sections of masonry

spanning horizontally between vertical reinforcement may be transferring load through

some sort of tied arch mechanism.

Anderson [Anderson, 1984] derived equations describing the uniform out-of-plane load

masonry infill panels could carry in terms of an ultimate thrusting force using statics and

assumptions about the abutment contact areas, compression core shape, and masonry

crushing strength. It is proposed that an analysis of partially reinforced walls is

fundamentally the same as arching of infill panels, with differences only in the contact

area and compression core assumptions. It was also assumed that the thrusting forces

that the arching produces in-plane will be balanced by the thrust forces produced by the

adjoining wall segments, except at locations where discontinuities in the wall occur such

as a control joint or door opening (this issue of discontinuous wall segments is

examined in Section 5.2.2).

For a continuous, partially reinforced, masonry wall with vertical reinforcing bars, it can

be assumed that the unreinforced masonry segments span horizontally between

57

locations of vertical reinforcement. If, at the ultimate, a three pin arch is assumed to

form due to cracking at the location of the reinforcing and at the center of the horizontal

span, then in-plane thrust forces can be assumed to develop at the inner contact points

of these cracks (hinges). The ultimate compressive stress in the masonry at the hinges

can be defined as 08. 'f m (as in Strength Design Method in the MSJC Code) and can be

assumed to be uniform over and effective depth of 08. times the CMU block face-shell

thickness ( 08. t fs ). The thrusting force per unit height at ultimate loading ( Pu ) is

therefore given by:

P f tu m fs= 0 64. ' (Eq. 5-1)

Figure 5.1 shows the positioning of Pu relative to the wall thickness ( t ) for half a wall

segment that makes up one side of the three-pinned arch subjected to uniform out-of-

plane loading ( w ). The arch was assumed to span the distance equal to the vertical

rebar spacing ( s ).

CL

t-0.8t

are being summed

tfs

(t/2)-0.4t

CL

s/2

w

w s2

Pu

Pu

Figure 5.1 Segmental Arch Loading Configuration (Continuous Walls)

An expression for w can be derived using equilibrium and summing the moments about

the center hinge location shown in Figure 5.1.

58

( )M ws s ws s P t tu fs= = ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟−⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟− −∑ 0

2 2 2 408.

( )08

082

= − −ws P t tu fs.

Solving the expression for w gives an approximation of the uniform out-of-plane load a

partially reinforced concrete masonry wall can carry in terms of vertical reinforcement

spacing, block size, and compressive strength.

( )w

P t t

su fs

=−8 08

2

. (Eq. 5-2)

Equation 5-1 includes an allowance for a triangular stress distribution at the joints.

However, Anderson [Anderson, 1984] suggests that it is possible that w may reach a

maximum value before Pu is large enough to cause crushing failure. This may occur

when the ratio of the bar spacing to the wall thickness is relatively high. In this case

there will be a change of eccentricity of Pu and a reduced contact area due to

deformations. The increase of the eccentricity and reduction of effective stress area will

intensify the chances of localized crushing of the outer faces of the joints [Anderson,

1984]. Under these conditions, the wall failure would be a combination of local crushing

and arch instability, occurring much earlier than predicted by Equation 5-2.

For masonry with low unit strength, the post-cracking model presented by Anderson

[Anderson, 1984] showed that there is a changeover from crushing to instability with λ

(horizontal span/wall thickness) between 30 and 40. Abrams et al in their investigation

[Abrams et-al, 1994] also predicted instability of infill masonry wall panels confined by

relatively stiff structural fames. For 8” CMU walls their model would predict arch

instability near span to thickness ratios of approximately 28. Since the level of grouting

of the masonry does not greatly change the post-cracking out-of-plane strength of the

wall [Abboud, Hamid and Harris, 1996] and the effective compression area at the joints

is less than the face shell thickness for either fully grouted or partially grouted walls, it is

59

reasonable to conclude that for continuous 8" CMU walls with a moderate f m' and a

vertical bar spacing of 120" , instability should not govern ( Pu should develop fully giving

a maximum w defined by Equation 5-2). In general, the out-plane wall strength defined

by a continuous shallow arch model will be likely be governed by masonry crushing for

λ less than, or equal to20 .

Using the above arching model, a comparison of the uniform out-of-plane load carrying

capacity can be made with grouped bars at 12 t and at a standard spacing of 6 t . In

this analysis, the following assumptions were made:

h in= 120

B= 48 in. and 96 in. vertical spacing (6 t and 12 t )

As = 0.31 in2 at 6t or 0.62 in2 at 12t (one or two #5 bars- used vertically)

F psiy = 60000

f’m = 2000 psi

The nominal moment capacity for a reinforced masonry wall is given in Section 3354. . . of

the MSJC 2005 Code by,

M A f d an s s= −⎛

⎝⎜⎞⎠⎟2

MSJC 2005, (3-27)

Where the equivalent depth of the compression block at nominal strength is,

a A ff bs s

m

=08. '

MSJC 2005, (3-28)

Equating Mn to the applied moment, assuming simple supports, uniform loading,

reinforcing bars in the center of the wall, and solving for w generates the following

expression:

2

)(4Bh

atfAnw ysb −= (Eq. 5-3)

For Equation 5-3, the length of the wall ( B ) is taken as the vertical bar spacing. For

the material property values listed, and assuming a bar spacing of 6 t , the out-of-plane

load, w , can be determined as:

60

2120)48()48)(2000(8.0

)60000(31.0626.760000)31.0(4 ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=w = 0.795 lb/in2 = 114.4 psf

Examining the previous calculation, it can be seen that, if double the vertical spacing

were used, with two bars grouped together, the same moment capacity, and therefore

wall capacity, would result since the effective width of the bar is limited to 6t. However,

the uniform load that can be transferred horizontally, as defined by arching action

(Equation 5-2) for bars spaced at 96" , is around ten times that defined by the out-of-

plane reinforced moment capacity of the wall as shown below.

( )( )( ) ( )( )

( )w

psi in in in

inlb

in=−

=8 0 64 2000 125 7 625 08 125

969 22 2

. . . . ..

( ) ( )w inft

lbin

lbft=

⎛

⎝⎜

⎞

⎠⎟ =9 2 12 1324 82 2

2

2. .

Even if the number of bars is increased significantly, it is likely that the masonry stress

will start to govern, limiting the vertical moment capacity to values below the horizontal

span capacity of the arch, even with a larger number of bars. Arching action in a

continuous, partially reinforced, masonry wall appears to be able to transfer substantial

loads horizontally between vertical reinforcing bars for most practical spacing limits for

reinforcing.

5.2.2 Arching Action in Discontinuous Walls

As mentioned in Section 5.2.1, the in-plane arching thrusts are balanced in continuous

masonry by the surrounding masonry on each side of the vertical reinforcing bars.

However, the need for control joints, and door or window openings, creates a condition

that invalidates the above assumption. In these locations, it was postulated that the

arch will be confined by the horizontal reinforcement in bond beams and doweled

foundations rather than the surrounding masonry. This model uses the same principals

61

as the continuous walls, except that the horizontal reinforcing resists the in-plane

thrusting force. Figure 5.2 shows half a wall segment that makes up one side of the

proposed three-pinned arch confined along the centerline of the wall by the horizontal

reinforcement.

s/2CL

W

t

Compression Force Strut

4"

Tension Force Tie Member(Horizontal Reinforcement)

t2

t fs

B/2

WB2

Location in which moments are being summed

t t fs20 4− .

Pu

TT

Figure 5.2 Segmental Arch Loading Configuration (Discontinuous Walls)

The maximum confining force provided by the horizontal reinforcement (TT ) is the total

number of bars (nb ) multiplied by the area of steel and the yield strength (the analysis

assumes cracks are formed as before and W is given in terms of unit wall length). The

location of Pu was assumed to be applied at a depth of t t fs2 0 4− . from the centerline of

the wall, which is consistent with position used for continuous walls. Because the

components of the arch thrust along the centerline are sensitive to the level of rotation

of the wall segments, it is better representative of the wall strength to sum the moments

about the point indicated on the diagram.

.

M WB s WB B T t tT fs= = ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟− ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟− −⎛

⎝⎜⎞⎠⎟∑ 0

2 2 2 4 20 4.

04 2 8

0 42

= − − +WBs T t WB T tT

T fs.

62

Simplifying the equilibrium equation and solving for w , results in an expression for a

discontinuous wall segment in terms of vertical and horizontal reinforcement, block size

compressive strength, and the geometry of the wall.

( )( )

wT t t

Bh s BT fs

=−

−

4 08

2

. (Eq. 5-4)

Unlike the arch model developed for continuous walls, for typical horizontal reinforcing

configurations, the compressive stress generated in the discontinuous masonry is well

below the strength of the materials used, which indicates that the masonry will remain in

the elastic range. Localized crushing of the joints should generally not be an issue. If

one #5 bar were used in the foundation and one #5 bar was in a bond beam at the top

of the wall with a vertical spacing of 96 in, the compressive stress in the masonry

needed to balance yielding of the bars would be 387 5. psi , which is approximately 20%

of the masonry compressive capacity assuming an f m' of 2000 psi . This value

assumes that the stress is applied uniformly over between the horizontal bars and over

80% of the face shell depth. (see the calculation below).

( )( )( )( )

f Tcompression area

n A Ft b

psiin in

psimT b s y

fs

inbar

= = = =08

2 0 31 6000008 125 96

387 52

... .

.

Using the same material property assumptions from the continuous arch strength

analysis in Section 5.2.1 with a wall with a length ( B ) of 96" and a vertical bar spacing

of 88" (centered in the corner block cores), the uniform out-of-plane load that would

produce horizontal tie bar yielding can be obtained using Eq. 5-4:

( )( )( ) ( )( )

( )( ) ( )( )wpsi in in

in in in in

inbar

lbin=

−

−=

4 2 0 31 60000 7 625 08 125

96 120 2 88 96107

2

2

. . . ..

( ) ( )w inft

lbin

lbft=

⎛

⎝⎜

⎞

⎠⎟ =107 12 1542 2

2

2.

The ultimate strength of the continuous and discontinuous walls is quite different for the

configurations evaluated. The significant reduction in out plane load carried by the tied

63

arch in discontinuous walls indicates that the magnitude of the confinement affects how

well the system performs. For design purposes, it is desirable that the level of load that

the arch can transfer horizontally should be greater than or equal to that defined by the

bending strength of the wall spanning vertically.

Comparing the bending strength of the grouped bars spaced at 12 t , calculated in

Section 5.2.1, to the value given by the tied arch, the horizontal reinforcement just does

provide sufficient tie force for the wall to reach its full bending capacity.

However, there is another action of the arch segments that must be accounted for in the

analysis. Since the wall segments that form the arch are tied by the horizontal

reinforcement at the top and bottom of the wall, and the in-plane thrust force Pu is

applied along the height of the wall, the arch segment must act like an in-plane beam

spanning between the horizontal reinforcing tie supports under a uniform load This

requires the vertical reinforcement to act to resist not only out-of-plane bending moment

(for which it was designed), but also the in-plane bending stresses from the arch

segments. The combined stress in the vertical reinforced bars must be limited to the

steel yield, thus reducing the out-of-plane load that the wall can carry before the steel

yields. It should be noted that arching action will not occur until the masonry cracks

parallel to the span and will not add to the stress in the vertical reinforcing until this

happens.

The in-plane bending action described above was analyzed by conservatively assuming

that the thrusting force was distributed uniformly over a vertical wall crack at mid-width

over the entire wall height. Using this configuration, each wall segment was assumed to

act as a uniformly loaded simply supported beam, spanning between the horizontal

reinforcement as shown in Figure 5.3

The increase in tensile stress in the vertical reinforcement can be determined by first

finding the in-plane moment produced by the thrust force ( M Pu).

64

( )M

P h s hP

uu=

−28

(Eq. 5-5)

A ratio of the M Pu

to the out-of-plane nominal strength based moment capacity gives

the percentage of the vertical bar capacity used by the arching action horizontal load

transfer. This can be represented by the following equation.

4" s/2

h

B/2

Pu

VERTICAL REINFORCEMENT

HORIZONTALREINFORCEMENT

4"

4"

Figure 5.3 Thrusting Force Generated In-plane Beam Action

65

( )( )

%.

CapP h s h

A f su

s sa

=−

−12 5 2

2

(Eq. 5-6)

In the analysis of the combined wall system, a check must be performed iteratively to

account for both the tension stress in the vertical bars produced by the in-plane

bending, and the stress produced by out-of-plane bending. The out-of-plane load and

the trust forces are reduced until the stress from horizontal bending and arching action

just reaches the yield stress of the vertical reinforcement.

In conditions where the same reinforcement configuration is used in both the horizontal

and vertical directions for a wall with an aspect ratio of one and a rebar spacing of 10' ,

the horizontal arching capacity will exceed the out-of-plane load that will produced

yielding in the vertical reinforcing bars. It can also be shown that this can occur for

other combinations of wall geometry and reinforcement configurations. An example of

this calculation is shown in Section 5.2.4.

5.2.3 Flexural Bending in Partially Reinforced Walls Arching action may not be the only mechanism of horizontal load transfer present in

partially grouted masonry walls loaded out-of-plane. To assist in the development of a

predictive model that correctly describes the out-of-plane strength behavior of partially

reinforced walls, flexural bending theory was also examined as a possible mechanism

of horizontal load transfer. The two strength mechanism theories (arching action and

flexural bending) are compared in Sections 5.2.4 and 5.2.5.

It was shown by past research, on the out-of-plane bending capacity of unreinforced

masonry walls, that masonry wall out-of-plane bending strength is much greater than

what current theory suggests [Brown and Melander, 2003]. The unaccounted for

strength is believed to be derived from friction produced by torsion of the head and bead

joints ([Drysdale and Essawy, 1988] and [Lawrence, 1995]). The torsional friction

continues to transfer stress horizontally through the unreinforced sections of wall after

cracking has occurred. This was used to suggest that the torsion of the head and bed

66

joints transfer load over a much further distance than the standard effective width given

by the MSJC 2005 Code.

In a similar manner it is suggested that the horizontal reinforcement in the bond beam

and doweled foundations may be acting in flexure over a much larger effective width

than allowed by the code and may be providing horizontal load transfer in bending.

Examining just horizontal bending, an expression for the maximum out-of-plane load

that a wall can carry under flexural conditions was derived from Figure 5.4 by summing

the moments about the point indicated on the diagram. As with the arching action

analyses, the reinforcement was assumed to be at the center of the block, in the outer

cores on either side of the wall and in the top and bottom bond beams. The out-of-

plane support reactions were assumed to act at the location of the vertical

reinforcement for horizontal span and at the horizontal reinforcement for the vertical

span. Bending about the horizontal and vertical axes was analyzed independent of each

other (bi-axial bending will be discussed later in Section 5.3). This was considered to

be conservative because the masonry will actually benefit from additional confinement

provided on the concave side of the wall by the compressive stresses from the opposite

direction.

67

s/2

WB2

CL

Location in which moments are being summed (t/2)-(a/2)

TTt

a

0.8f'm

B/2

V

TC

TC

W

Horizontal Reinforcement

Vertical Reinforcement

Figure 5.4 Vertical Bending Configuration - Uniform Loading

A simplified expression for W in terms of wall geometry and reinforcement (units are

load per unit wall length) can be written as shown by Equation 5-7 on the following

page.

( )( )

WT t a

B s BT=

−−

42

(Eq. 5-7)

The equation can be expressed as a uniform pressure loading by dividing Equation 5-7

by the height of the wall.

( )( )

wT t a

Bh s BT=

−−

42

(Eq. 5-8)

Using the wall geometry and material properties shown below, (which are the same as

used for the arching action example for discontinuous wall segments), a comparison of

peak out plane load predicted by flexural theory and by arching action can be made.

The difference in load that is predicted by the two methods establishes a range

observed behavior and can be used to determine which mechanism is present.

68

h in= 120

B in= 96

s in= 88

Asin

bar= 0 31 2. (#5 bars used both horizontally and vertically)

F psiy = 60000

f psim' = 2000 (8in Standard CMU Block)

The uniform load predicted by Equation 5-8 for a wall spanning horizontally becomes,

( )( )( ) ( )( )( )( )

( )( ) ( ) ( )( )w

in psi inin psi

psi in

in in in inlb

in=

−⎛

⎝⎜⎜

⎞

⎠⎟⎟

−=

4 2 0 31 60000 7 6252 0 31 60000

08 2000 88

96 120 2 88 96119

22

2

. ..

..

( ) ( )w

inft

lbin

lbft=

⎛

⎝⎜⎜

⎞

⎠⎟⎟ =119

1217112 2

2

2. .

This creates a difference of approximately 17 2lb

ft between the out-of-plane load

predicted by the two methodologies for the example values given. Since the

assumptions remain the same for both axes of bending, Equation 5-8 can be rewritten

to find the horizontal bending strength by rearranging the height and the length.

( )( )

wT t a

Bh s hT=

−−

42

(Eq. 5-9)

The only difference in the governing equations for bending and arching is the equivalent

width over which the compressive stress in the masonry is distributed.

The major difference in the wall behavior predicted by the two models will be that, if

arching action is present, the additional stresses produced by in-plane bending of the

arch segments will reduce the out-of plane wall load at which the vertical rebar will yield.

5.2.4 Analysis of Wall Specimens

69

During testing the wall specimens were not just subjected to a uniform load. In addition

to the uniform self-weight over the entire surface of the wall, the walls were also

subjected to an applied out-of-plane point load ( PT ), which is applied to four evenly

spaced points in a square pattern about the center of the wall (See Chapter 3). In

addition, an uplift force was applied to the top of the walls. Because of the combined

loading applied to the specimens, the analysis presented previously was revised. This

revision is summarized in the following sections.

5.2.4.1 Flexural Bending Analysis of Wall Specimens The analysis was separated between the horizontal and vertical directions because the

vertical reinforcement was subject to an axial tensile force during the out-of-plane

loading. This generates additional tensile stress in the vertical bars that is not present

in the horizontal direction. Figure 5.5 shows the loading configuration of the horizontally

spanning arch segment with the uniform load as well as two, inline, concentrated loads

at a total of ½ PT.

70

s/2

CL


t

a

0.8f'm

PT

2

t a2 2−

TT

W

B/2

PT

2WB

2

B/8

V

TC

TC

Horizontal Reinforcement

Figure 5.5 Vertical Bending Configuration - Combined Loading

The same procedures used for the flexural bending analysis in Section 5.2.3 were used

to develop the expression for PT . In this analysis, W was not an applied load but rather

the self-weight of the masonry and PT is the applied point load. Summing the moments

about the point indicated in Figure 5.5 gives,

M WB P s WB B T t a P BTT

T= = +⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟− ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟− −⎛

⎝⎜⎞⎠⎟− ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟∑ 0

2 2 2 2 4 2 2 2 8

( )0

4 2 8 2 16

2

=+

− − + −s WB P T t WB T a P BT T T T

Simplifying the equilibrium equation and solving for PT results in the following

expression.

( )

PWBs T t WB T a

s BTT T

=− − − +

−

2 2 4 4

4

2

(Eq. 5-10a)

71

It is sometimes easier to compute the PT formula in its expanded form which can be

written as,

P T ts B

WBs B

T as B

WBTT T=−

+−

−−

−8

4 48

4

2

(Eq. 5-10b)

An interaction diagram must be utilized in the development of the PT expression for the

vertical direction because of the addition of the vertical axial loading. The total point

load that can be applied to the wall system, in addition to the self-weight of the wall can

be obtained by equating the vertical moment capacity of the wall, given by the

interaction diagram for a given uplift load, with the peak moment that is applied to the

wall spanning vertically by the out-of-plane loading configuration. The peak vertical

span moment that is produced by the applied load and self-weight of the masonry is,

( )M s Wh P h Wh P

peakT T= +⎛

⎝⎜⎞⎠⎟−

+4 4

216

(Eq. 5-11)

The interaction diagram was set-up using an Excel spreadsheet using Strength Design

equations given by the MSJC 2005 Code. For the purpose of this analysis, the load

factor φ was left off of the vertical moment capacity equation ( Mcap ) to give nominal

strength. Setting Mcap in Equation 5-11 to the value given by the interaction diagram,

and solving for PT results in an expression for the combined out-of-plane and axial load

configuration as shown:

( )P

Whs Wh M

s hTcap

=− − −

−

2 2 8

4

2

(Eq. 5-12)

Where the unfactored moment capacity used in the interaction diagram is,

M c f b t cn A f d t

cap m b s s= −⎛⎝⎜

⎞⎠⎟− −⎛

⎝⎜⎞⎠⎟

08 082

082 2

. . '. (Eq. 5-13a)

Since the reinforcement is located at in the center of the block core, the d is equal to

half the block thickness; therefore, the second half of the equation cancels out leaving,

M c f b t ccap m= −⎛

⎝⎜⎞⎠⎟

08 082

082

. . ' . (Eq. 5-13b)

72

5.2.4.2 Arching Action Analysis for Wall Specimens

The vertical span flexural capacity of the wall is reduced by the axial tensile force

applied to the bond beams. Similarly, the confinement of the arch is also affected by

the additional stress in the vertical bars, but in a less direct manner. It was shown in

Section 5.2.2 that arching behavior in discontinuous wall segments is affected by the

spacing and size of the vertical and horizontal reinforcement due to the in-plane beam

action produced by the thrusting force. Uplift forces reduce the usable tensile capacity

of the vertical bars, thus reducing the in-plane confinement of the arch and out-of-plane

load resistance. Figure 5.6 shows the modified loading configuration accounting for all

of the assumptions described previously.

Using simple statics, the equilibrium equation described in Section 5.2.2 and solving

for PT , results in an expression that is very similar to Equation 5-10 for flexural bending.

The only difference is the area over which the compression stress in the masonry is

applied.

( )

PWBs T t WB T t

s BTT T fs

=− − − +

−

2 2 4 32

4

2 . (Eq. 5-14a)

PT

2B/8


t t fs20 4− .

Pu

TT

s/2CL

W

t


4"

Tension Force Tie Member(Horizontal Reinforcement)

t2

t fs

B/2

PT

2WB

2

73

Figure 5.6 Arching Action Configuration - Combined Loading

The expanded form of the equation is,

P T ts B

WBs B

T ts B

WBTT T fs=−

+−

−−

−8

4 46 44

2 . (Eq. 5-14b)

The additional stress in the vertical reinforcement caused by the in-plane bending from

the arching thrust was determined using a five step iterative calculation method using

the flexural and arching action equations that were previously derived in Section 5.2.2.

In order to establish a starting point for the iterative process, the PT defined by out-of-

plane bending strength (Equation 5-12) was computed and used for the initial PT value.

This value was used as PT in the horizontal arching equation (Equation 5-14) and the

stress in the horizontal reinforcement caused by this load was computed. The

horizontal bar stress was then used to determine the uniform in-plane thrusting force

( Pu ) using f s in the following equation.

PTh

n A fhu

T b s s= = (Eq. 5-15)

Since the original vertical bar stress was set to yield, any additional stress beyond this

level was not possible since strain hardening was ignored. The in-plane moment

produced by the Pu , described by Equation 5-5, was then set equal to the nominal

moment in-plane moment capacity of the arch segment (given by Equation 3-27 in the

MSJC 2005 Code). The equation was then used to determine the additional stress in

the vertical reinforcement created by the Pu . The stress input used in Equation 5-12

was reduced so that the sum of the stresses produced out-of-plane (and uplift) and in-

plane flexure were equal to the yield stress of the vertical bars, or when yield stress is

reached in the horizontal reinforcement, whichever occurred first.

74

In all the previous analyses, a behavioral characteristic of shallow arches that has not

been discussed for discontinuous wall segments is the overall arch stability. Arch

instability occurs when a combination of the elongation of the horizontal reinforcement

and the in-plane deformation of the wall segments are sufficient to produce a snap

through of the arch.

If it is assumed that the stress and strain in the horizontal reinforcement is constant

throughout the entire length, and only the in-plane deflection of the wall segments near

the center of the wall is of concern, then an approximate stability analysis can be

conducted.

Figure 5.7 shows the components of the arching mechanism used for the stability

analysis. The figure shows a top section view of the wall, for half of the arch. It was

assumed that when the outer mid-point of the wall at mid-span moved enough so that

the compression strut became horizontal, the arch becomes unstable and portions of

the wall will fall through. It was also assumed that the deformation of the compression

strut is small compared to the other deflection and can be ignored. The movement of

the compression strut is thus a combination of the elongation of the horizontal

reinforcing bars and the in-plane bending deformation of the arch segment (maximum

near the center span of the wall).


Tension Force Tie Member

Vertical Reinforcing Bar

Outer Mid-Point of Wall

2s

2ty =

2

22 tsz +=

Figure 5.7 Components of the Arching Mechanism Relative to Stability

The premise of this analysis suggests that arch snap through will occur when the

deformations, plus the original depth of the arch segment, are greater than the length of

75

the compression strut of the arch (z). Assuming a uniform loading for the beam

deformation and simple supports, this produced the equation,

L s s P sE I

zfs u

m eff

= + + ≤2 2

5384

4ε (Eq. 5-16)

The small portions of wall that extend beyond the spacing of the horizontal

reinforcement were neglected in the deflection calculation. Also, the effective moment

of inertia, typically about one-half of the gross moment of inertia ( I g ), was determined

by Section 3.1.5.3 in the MSJC 2005 Code Commentary as:

I IMM

IMM

I Ieff ncr

acr

cr

an g=

⎛⎝⎜

⎞⎠⎟ + −

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥≤ ≤

3 3

1 05.

The net moment of inertia ( In ) in the Ieff formula (using face shells only) ignores the

effect of the grouted cores since this will have a negligible effect on the overall

deflection. The cracked moment of inertia ( Icr ) was found using the method of

transformed sections as follows:

ρ**

*=A

bds n E

Es

m

= ( ) ( )k n n n* * * *= + −ρ ρ ρ2

2

In the above formula, d * is the distance from the centerline of the wall to the center of

mass of the reinforcement in tension, and k d* * is the transformed location of the neutral

axis. The nominal moment cracking strength of the mortar joints ( Mcr ) was found by

multiplying the net section modulus ( Sn ) with the appropriate modulus of rupture for the

mortar type as given by Table 3.1.8.2.1 in the MSJC 2005 Code. The applied moment

( Ma ), was set equal to M Pu (Equation 5-5). In a manner similar to that used to find the

stress in the vertical reinforcement (described previously), the stability analysis was

conducted by an iterative approach. This was required since several variables that

make up the Lf equation are dependent on the applied load and vary accordingly. A

spreadsheet was used to iteratively compute Ieff , Pu , εs , along with the Lf for

comparative examples presented in Section 5.2.4.3.

76

5.2.4.3 A Comparative Analysis Between Arching and Flexural Models

The two wall specimen configurations described in Chapter 3 were analyzed using both

the flexural and arching models. The wall specimens were initially designed so that the

walls with the #5 vertical bar arrangement would fail by out-of-plane bending

perpendicular to the span, or by arching action. The remaining specimens (with the #7

vertical bars) were expected to fail by horizontal flexural bending or arching action

(there is also the possibility of a combination of flexural bending and arching action

occurring). These configurations were initially analyzed using nominal material

properties as described in the following discussion. These analyses were redone with

the measured material properties in later sections.

The self-weight of the wall was set equal to w and assumed to be 338 2. lbft . This was an

assumed value for the wall weight and was used for comparison purposes before the

actual wall weight was measured. These calculations were redone later using the

average measured wall weights (later in Chapter 5). For PT calculations, this loading

was converted a load over the wall height (W - lb/in of width). The maximum out-of-

plane point load that can theoretically be applied to the wall specimens, assuming

flexural bending about the vertical axes (Equation 5-10), with #5 horizontal bars and

assuming an f m' of 2000 psi becomes,

( )( )( )( )( ) ( )

( )( )( ) ( )

( )( )( )( )( ) ( ) ( )( )

Pin psi in

in inin

in in

in psi in

in inin lb

T

lbin

lbin

=−

+−

−−

− =

8 2 0 31 60000 7 625

4 120 12830 128

4 120 128

8 2 0 31 60000 019375

4 120 12830 128 3839

2 2

2

. .

. .

The equivalent depth of the compression zone at nominal strength was given by

Equation 3-28 of the MSJC 2005 Code using the entire width of the specimen between

the bars as the effective width. All material strengths used in the calculations are

nominal values since they are presented for comparative purpose only.

( )( )( )( )

ain psi

psi inin= =

2 0 31 60000

08 2000 120019375

2.

..

77

Since only one horizontal bar configuration was used, the out-of-plane load resistance

based on bending strength perpendicular (horizontal) to the span is the same for both

wall specimen configurations. In contrast, the two out-of-plane load resistances, based

bending strengths parallel to span (vertical) (Equation 5-12), for the #5 and #7 vertical

bars are 3675 lb and 9264 lb , respectively . Note that these values are the total applied

concentrated loads, in addition to the self weight. Sample calculations for the #5

vertical bar configuration are shown below.

( )( )( ) ( )

( )( ) ( ) ( )( )P

inin in

lb inin in

in lbT

lbin lb

in=−

+⋅

−− =

30 1284 120 128

16 1345994 120 128

30 128 3674 52

.

In the calculation above Mcap was determined using a Strength Design interaction

diagram that was developed using an Excel spreadsheet. If Equation 5-12 were

considered without an uplift force applied, the out-of-plane load resistance is the same

as what is found using Equation 5-10 for bending parallel to the span. The axial tensile

force reduces the wall capacity by approximate 4.3% for the configuration investigated.

The arching model is more complicated and has more checks to ensure an accurate

prediction of the wall behavior. Using Equation 5-14 to determine PT for arching action

limited by yielding of the horizontal tie reinforcing only, initially produces the following

result:

( )( )( )( )( ) ( )

( )( )( ) ( )

( )( )( )( )( ) ( ) ( )( )

Pin psi in

in inin

in in

in psi in

in inin lb

T

lbin

lbin

=−

+−

−−

− =

8 2 0 31 60000 7 625

4 120 12830 128

4 120 128

6 4 2 0 31 60000 125

4 120 12830 128 3158

2 2

2

. .

. . .

A preliminary comparison shows that there is a difference in the predicted out-of-plane

load capacity from the flexural model and the arching model (approximately a 17 8. %

difference). However, there are other limit states for the arch model and these must be

checked as well.

78

To evaluate the combined stresses on the vertical reinforcing the following procedures

were used:

1. The stress observed in the horizontal reinforcement was determined by equating the

out-of-plane bending strength parallel to the span with the arching action expression, as

follows:

( ) ( )( )

fs WB P B WB P

n A t tsT T

b s fs

=+ − +

−

4 28 08.

(Eq. 5-17)

2. PT was initially given by Equation 5-12, but was reduced to ensure the stress in the

vertical bars is less than or equal to yield. The final stress in the horizontal bar

becomes,

( ) ( )( )( ) ( ) ( )( )( )

( )( ) ( )( )f

in in lb in in lb

in in in

f psi

s

lbin

lbin

s

=+ − +

−

=

4 120 30 128 1594 2 128 2 30 128 1594 2

8 2 0 31 7 625 08 125

43254

2

. .

. . . .

3. Substituting the horizontal stress into Equation 5-15 gives the thrusting force that was

produced by the applied out-of-plane load.

( )( )

Pin psi

inulb

in= =2 0 31 43254

128209 5

2..

4. The additional stress that was induced in the vertical bars, due to the arching thrust,

was found by taking the moment produced by the Pu , equating it with the nominal in-

plane moment capacity, then solving for f s :

f f sbA

b f f s b P h s P hAs

m

s

m m u u

s

= −− +08 08 125 0 6252 2. ' . ' ' . .

(Eq. 5-18)

5. A computer program was used for the iterative process and the total predicted

vertical bar stress was the sum of the stress given by Equation 5-18 and the stress

produced by the horizontal bending. Equation 5-19 represents the initial stress in the

vertical bars due horizontal bending.

79

( ) ( )

fb f s Wh P f b t h Wh P

n Af bt

n ATn A

sm T m T

b s

m

b s

PT

b s

=− + − − +

+ +

0141421 20 8 5 2

0 4

2. ' '

. ' (Eq. 5-19)

The uplift force is represented by TPT . Portions of the expression become non-real

solutions, but the final result is a real solution. If the program being used to compute

these values does not understand imaginary numbers, than Equation 5-19 must be

derived in a different form. For example, Equation 5-18 can be used to define some of

for the assumed material values.

( )

fP

n ATn As

T

b s

PT

b s

=− − −

+29065443393 60982 5 251845461273. . .

The total tensile stress in the vertical reinforcing bars, given by the sum of Equations 5-

18 and 5-19 then becomes,

( )( ) ( ) ( )( )( ) ( )( )

( ) ( )( )( )

( )( ) ( )

f

psi in in in in inin

in psipsi in in

in

lb

inlbin

psi

s

lbin

lbin

=−

− +

× +

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

+− − −

+⎡

⎣

⎢⎢

⎤

⎦

⎥⎥=

2000 120 120 125 209 5 128 120 0 625 209 5 1280 31

08 120 200008 2000 120 120

0 31

29065443393 60982 5 1594 2 251845461273

2 0 311000

2 0 3160000

2 2

2

2

2 2

. . . ..

..

.

. . . .

. .

For the specimens having #5 vertical reinforcing bars, the additional stresses induced in

the vertical reinforcement by the in-plane bending of the arch segments drives the

stresses in the vertical bars up high enough to reach yield at a load 49 5. % lower than

predicted by the confinement reinforcing yielding, from 3158 lb to a PT of 1594 lb . For

this configuration, the out-of-plane load capacity predicted by the arch model was

controlled by the strength of the vertical bars. At the point when yield stress was

reached in the vertical bars (based on an assumed 60000 psi yield strength), the stress

in the horizontal reinforcement had only reached approximately 3 4 of their yield

strength ( f psis = 43254 ). The stress values were obtained using an Excel spreadsheet

using the iterative method prescribed in Section 5.2.4.2.

80

The final check required in the arch model is an evaluation of stability at the load level

defined by strength limits. This was done by examining the stability of the arch to see if

the final PT value was enough to cause a premature failure by the snap through.

In this evaluation, the net moment of inertia for each wall segment that forms the

shallow arch, can be written as

( )( )I bh in in

inn = = =3 3

4

122 5 64

1254613

. (ignoring the grouted cores -face shell bedding)

After cracking, a reduction of approximately 76% in the moment of inertia occurs

( I incr = 12849 4 ). The new location of the neutral axis ( k d* * ) was found by the method

of transformed sections (the method is described in Section 5.2.4.2), which was used to

calculate Icr .

( )( )

ρ* ..

.= =0 31

2 5 600 0020667

2inin in

( )n psi

psi= =

29 10900 2000

161116* .

( ) ( ) ( )k * . . . .= + − =0 0332963 2 0 0332963 0 0332963 0 22692

( )k d in in* * . .= =0 2269 60 136

The in-plane moment that must be exceeded before cracking will take place was

obtained by multiplying the modulus of rupture for Type S mortar, given by Table

3.1.8.2.1 in the MSJC 2005 Code, with the net section modulus and produced a

moment of 64854 lb in⋅ . The moment produced by the thrusting force (given by

Equation 5-5) exceeds the cracking moment by roughly six times.

( )( ) ( )( )M M

in in inlb inP a

lbin

u= =

−= ⋅

209 5 128 2 120 1288

375424.

Substituting the computed values into the Ieff expression gives,

81

( ) ( )I in lb in

lb inin lb in

lb in

I in I o k

eff

eff n

=⋅⋅

⎛⎝⎜

⎞⎠⎟ + −

⋅⋅

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

= <

5461364854375424

12849 164854375424

13064

43

43

4 . .

At the limiting out-of-plane PT for the number #5 vertical reinforcing configuration, the

arch will not become unstable because the total deformations of arch segments will not

produce snap through as defined by Equation 5-16 (see below).

( ) ( )( )

( )( )( )L

inin

psipsi in

psi in

L in z in o k

f

lbin

f

= +

⎛⎝⎜

⎞⎠⎟+

= < =

1202

12043254

290000002

5 209 5 120384 900 2000 13064

60114 60121

4

4

.

. . . .

The same calculations were executed using an In that included the effects of the

grouted cores and resulted in a change of less than 3%.

An analysis was also conducted for the wall configuration with #7 vertical reinforcing

bars and nominal material values. The final PT value governed by stability

( P lbT = 2266 ) was found to be lower than the value defined by the arch model strength

checks. This specimen configuration was not governed by the strength (yield) of the

horizontal or vertical reinforcement, but by the stability of the arch. The bar stress was

highest in the horizontal direction but only reached 841. % of its yield strength. It was

concluded, by a comparison of the horizontal bending and arching action capacities that

the specimens that have #7 vertical bars will fail in the horizontal direction due

instability of the arch. Similarly, the specimens with the #5 vertical reinforcing bars

appear to be also governed by arching action, but through yielding of the vertical steel

reinforcing due to the additional in-plane bending stressed, rather than stability.

These analyses were repeated with similar results with the measured material

properties, with similar results. Please see Section 5.4 for a discussion of these results

and a comparison with the measured wall specimen behavior.

82

5.3 ELASTIC FINITE ELEMENT ANALYSIS

As a parallel analysis to the hand calculation methods described in the previous

sections, an elastic finite element (FE) model, using ANSYS 10.0, was developed to

examine the stress levels within the masonry and the effects of bi-axial bending under

the support conditions and the loading configuration used in the testing program.

5.3.1 Finite Element Model Development

The masonry walls were modeled using a 3-D – 8 noded solid element, with three

degrees of freedom at each node (translations in the nodal x, y, and z directions). The

reinforcement was modeled using a 3-D uniaxial elastic beam element. The beam

element has six degrees of freedom at each node consisting of translations in the x, y,

and z directions along with rotations about each of the axes listed.

The FE model mesh described in Chapter 3 was used in this analysis (see Figure 3.3).

The bond beams and outer cores where the reinforcement was located, was modeled

with solid units, with the reinforcement elements located along the centerline of the wall,

4" in from the outer edge of the block. The remaining portions of the wall were

modeled as hollow units. Figure 5.8 shows a cutout segment of the left side of the FE

model illustrating the solid and hollow units.

Figure 5.8 Isometric Cutout View of Element Model Configuration

83

Since the analyses was conducted prior to the testing of the wall specimens, the

strength of the masonry used to calculated the elastic modulus was assumed to be

2000 psi , yielding an Em of 18 106. × psi (the same f m' was used for hand calculation

analyses). The yield strength of the steel was assumed to be 60000 psi . The self-

weight of the block was applied as a surface pressure to the outer face of the elements

and was varied to account for the differences in the weight of the hollow and solid units.

To simulate an applied uplift load on the walls, an axial tensile force of 1000 lb was

applied to two points at the ends of the HSS x x8 4 1 2 beams attached to the anchor bolts

at the top and bottom of the walls. The HSS x x8 4 1 2 beams were modeled using the a

beam element with the appropriate properties given by the Manual of Steel Construction

published by the American Institute of Steel Construction (AISC). A gap of half an inch

was allowed between the top/bottom of the wall and the HSS x x8 4 1 2 beams to prevent

compression being applied to the center of the wall due to the bending of the beam.

The wall specimens had anchor bolts attached to the steel beams in a manner that only

accepted tensile load. For this reason, the anchor bolts were modeled using a 3-D spar

element that allowed tension only loading.

Similarly, the contact between the wall and the HSS x x12 8 1 2 support beams that span

the length of each of the bond beams, were modeled with a spar element using the

compression-only option to simulate a roller support between that wall and beam.

Four equal out-of-plane point loads were applied to nodes on the outer face of the

elements in a square orientation with a spacing of 32 in., positioned about the center of

the wall. The magnitude of loading corresponded to the values predicted by the flexural

hand calculation analyses presented in Section 5.2.4.3. The models were run for pre-

cracked and post-cracked behavior to show how the distribution of loads change after

Mcr was exceeded.

84

5.3.2 Pre-cracked Behavior The modulus of rupture of the masonry assembly, given by Table 3.1.8.2.1 in the MSJC

2005 Code, is significantly greater when the direction of flexural tensile stress is parallel

to the bed joints. Since the walls were constructed using face shell bedding, the section

modulus is essentially the same in both directions. This causes the theoretical moment

required to initiate cracking of the walls to be nearly twice as high in the horizontal

direction as the vertical direction, for Type S mortar in ungrouted walls. Approximately

12 5. % of the wall is grouted in the horizontal bending direction giving an interpolated

modulus of rupture corresponding to flexural tensile stress normal to the bed joints of

52 4. psi . The Mcr in the horizontal direction is still approximately 14. times that for the

vertical direction ( f psir = 75 for stress parallel to the bed joints in running bond for

either ungrouted or partially grouted masonry).

As load is applied to the wall specimens, cracking will occur first in the bed joints near

mid-span (where the maximum moment is). This crack will propagate until the crack

spans the entire width of the wall. As the walls were subjected to additional load, and

Mcr was reached in the horizontal direction, cracks formed near mid-width, in the

vertical direction.

Examining the moment produced by the wall self-weight shows that the theoretical Mcr

is exceeded before any additional load is applied to the wall. This suggests that the wall

specimens will crack when the compression loading is removed. A look at the vertical

stress distribution for the wall specimens with the #5 vertical reinforcing bars subjected

to self-weight only, confirms this result (see Figure 5.9). The maximum vertical tensile

stress exceeds the modulus of rupture for Type S mortar in regions located near the

outer edges of the wall, along the horizontal centerline. At the middle of the wall, the

tensile stress is around 62 3. psi which also exceeds the cracking stress. The minor

difference between the stress at the outer edges and at the middle along the centerline

85

of the wall suggests that the masonry is effective at transferring load evenly, at least

prior to cracking, over the entire width of the walls.

Figure 5.9 Vertical Stress Distribution; #5 Vertical Bar Configuration

Self-weight Loading (Back View)

The stress in the horizontal direction (stress parallel to the bed joints) was influenced

significantly by the support conditions. The stress levels illustrated by Figure 5.10 (the

horizontal stress distribution under self-weight) are well below the cracking limit,

indicating that when the axial compression is released, the specimens should not crack

vertically.

86

Figure 5.10 Horizontal Stress Distribution; #5 Vertical Bar Configuration

Self-weight Loading (Back View)

Hand calculation models assumed that the walls transferred load horizontally between

vertical reinforcement. Away from the supports, the stress distributions shown in Figure

5.9 and 5.10 suggest that this assumption is reasonable. However, the low level of

horizontal stress suggests that the FE model indicates that the majority of the load is

transferred directly to the supports through single curvature bending. The pre-cracked

behavior is almost identical for the FE model of the walls with #7 vertical bars with less

than 1 psi difference in stress levels, and is therefore not shown.

To examine whether the testing apparatus and wall configurations may be affecting the

results, another FE model was developed. This model was uniformly loaded with an

out-of-plane load equal to the wall self-weight but with a pinned foundation and a roller

connection to a rigid diaphragm at the top of the wall. As with the actual specimen

loading configuration, an uplift of 1000 lb was applied to the top of the wall. The vertical

stress distribution (and level of stress), shown in Figure 5.11, was very similar to the

specimen stresses shown in Figure 5.9, suggesting that the testing configuration does

not cause abnormal stresses in the vertical direction.

87

The horizontal stress was found to be affected to some extent by the testing

configuration for the masonry self-weight. Figure 5.12 shows the horizontal stresses are

lower and have a slightly different pattern than the previous analysis.


Simulation of Field Supports and Loading (Back View)

88


Simulation of Field Supports and Loading (Back View)

It was concluded from the results of both FE models that, for both reinforcement

configurations, the walls will initially crack in the bed joints near mid-span, and that the

supports may slightly affect the pre-crack bending behavior of the wall systems.

5.3.3 Post-cracked Behavior The previously discussed FE models, were modified using a reduction of the element

elastic modulus (reduced to a negligible value relative to the elastic modulus of the

block) to simulate the regions of block that had cracked. The point loads were applied

in the four-point arrangement described earlier using increments of 500 lb until the total

PT load was reached. The stresses were examined normal and parallel to the bed

joints, at each load interval. The elements that reached the tensile cracking stress were

modified and a new run was conducted to verify if the cracking affected other elements

in the surrounding regions (this process was repeated for all load increments).

89

5.3.3.1 Finite Element Model For #5 Vertical Bar Configuration

The regions that were cracked prior to the PT loading (having tensile stresses that

exceeded the modulus of rupture in a given direction), under self-weight of the wall

system was applied, were identified and the moduli modified accordingly. Following the

revaluation of the model, the axial tensile stress in the vertical and horizontal bars was

examined to see how well the stresses correlated to the hand calculation models. In the

vertical direction, good correlation was found between the theoretical stress values

given by the interaction diagram and the FE model prediction (approximately a 2%

difference). A significantly lower stress level was observed in the horizontal bars, which

was believed to be a result of the masonry not being cracked in those locations at this

load level.

The final out-of-plane point load applied to the FE model was 3675 lb (as predicted by

the analysis shown in Section 5.2.4.3). A total of seven load increments were used

excluding the initial cracking due to self-weight. As shown in Figure 5-13, the

distribution of stress normal to the bed joints curved near the vertical reinforcement.

Near the center of the wall, outside of the standard effective compression width set by

the MSJC 2005 Code (48" for an 8" CMU wall), the masonry is carrying as high a level

of compressive stress as the locations close to the reinforcement. This suggests that

the entire masonry width may be effective around the reinforcement for flexural

analyses. The hyperbolic curvature in the compressive stress also shows how the point

load is transferred to the vertical and horizontal reinforcement.

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Combined Loading (Front View)

The distribution of stress parallel to the bed joints changed in shape from vertically

arranged parallel lines under the uniform self-weight, shown by Figure 5.10, to form an

x-type pattern that stretches from the location of the point loads outward toward to the

corners of the wall. Stresses parallel to the bed joints in close proximity to the

centerline are approximately 25% of the values normal to the bed joints (see Figure

5.14).

91



Based on the stresses in the masonry and reinforcement, the FE model of the wall with

#5 vertical bars suggests that the specimen failure will occur in the vertical

reinforcement when PT is approximately equal to the value given by Equation 5-12

(bending about the horizontal axis). The best correlation between the FE model for

ultimate capacity, failure type, and stress distributions, was found to be with the flexural

bending theory developed in Section 5.2.4.1.

5.3.3.2 Finite Element Model For #7 Vertical Bar Configuration

The FE analysis described previously was repeated for the wall specimens with the #7

vertical bar configuration. The final crack pattern and shape of the stress distributions,

about the horizontal and vertical axes, was very similar to those predicted by the

previous model. However, a different type of failure was predicted. Stresses normal to

the bed joints were found to reach the compressive strength of the masonry before the

reinforcement was yielded, causing the wall capacity to be less than approximately two

thirds the expected reinforced flexural capacity. It is believed that the premature

compressive failure may be the result of the modeling technique used to simulate the

92

cracking of the masonry. In some instances, this method can alter the validity of the

results given, and may not be a true representation of the wall behavior.

The deformations predicted by the FE model suggest that walls behaved more stiffly at

the vertical reinforcement locations than with the other model. This can also be

observed by the increase in horizontal stress values, approximately twice the value as

the #5 vertical bar configuration with a maximum compressive stress in the masonry of

1362 psi . Figure 5.15 shows the vertical stress distribution and demonstrates the load

path to the supports.



A comparison of the FE analyses and the hand calculation models, indicates that hand

calculation methods predict the #7 vertical bar configuration may be governed by the

strength of the wall in the horizontally spanning direction for both arching action and

flexural bending. However, the FE model predicted the failure to occur in the opposite

93

direction at a higher load than the hand calculations, but at a lower level than the full

horizontal bending capacity. However, the finite element model is affected by the

support modeling and further investigation should be conducted before a definite

conclusion can be made on this issue.

5.4 A COMPARISON OF PREDICTED AND MEASURED PERFORMANCE

In the following subsections, the previous analyses were revised using measured

quantities and compared to wall test behavior to determine whether any of the proposed

analytical models matched actual wall behavior.

5.4.1 Wall Specimens with #5 Vertical Reinforcement

From Table 4.6, the total average measured ultimate out-of-plane load for the wall

specimens with vertical #5 reinforcing bars was5220 lb . This value includes the

equivalent load due to the uniform self-weight of the wall of 2370 lb , leaving an applied

PT load of 2850 lb . The equivalent point load for the wall self-weight was obtained by

taking the moment that was produced by the uniform load and equating it with that

which would be produced by a point load

Calculations were conducted for horizontal bending, vertical bending, and arching action

using the measured material strengths. The self-weight of the wall used was the

average weight of the grouted and ungrouted sections giving a uniform weight of

417 2. lbft .

The predicted PT values limited by vertical and horizontal flexure was 5571 lb and

5734 lb , respectively. These values are much greater than the measured wall capacity.

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The arching models predicted a yielding of the vertical rebar due to the combined

tensile stress at a PT of 2775 lb . This is within 2 6. % of the measured load and

appears to match the observed wall behavior.

An arch stability analysis was conducted using the iterative method describe in Section

5.2.4.3, and the predicted out-of-plane load required to cause a failure due to instability

was 2370 lb, about 17% below the measured strength. It should be noted that this

could be considered reasonable agreement since the stability analysis is conservatively

based on uniform loading and uses an approximation for the effective stiffness of the

masonry arch segments that is likely quite conservative.

The FE analysis was not rerun using the measured material strengths. However, the

stress distribution in the horizontal direction, shown by Figure 5.14 in Section 5.3.3.1,

follows a similar pattern to the cracks observed in all the wall specimens. This suggests

that the pattern of these cracks is affected by horizontal load transfer.

Based on the overall behavior of the wall specimens with #5 vertical reinforcing bars,

both predicted and observed, it appears that the mechanism of load transfer found in

walls with widely spaced vertical bars may be a combination of bending and arching

action. However, at the ultimate load, failure appears to be governed by arching action

since the measured wall strength was approximately 50% of the wall capacity defined

by the theoretical bending capacity in the vertical span direction (as predicted by the

arch model).

It appears that the arching action model shows promise and may form the basis of a

reliable model for design purposes. Further refinement of the model may be necessary

and further research with a wider range of wall sizes and reinforcement configurations is

required to confirm the general applicability of this model, however.

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5.4.2 Wall Specimens With #7 Vertical Reinforcement

Table 4.6 shows that the average ultimate load resisted by the wall specimens with #7

vertical reinforcing bars, including the 2370 lb equivalent point load from the masonry

self-weight, was 6258 lb . The average PT for this wall specimen configuration was

therefore 3888 lb .

Calculations were conducted as described previously using the measured material

properties tabulated in Chapter 4. Horizontal bending capacities described by Equation

5-10, produce the same out-of-plane load capacities as before, since this wall specimen

configuration used identical reinforcement in the bond beams. The predicted load

capacity, PT , was 5734 lb . In the vertical direction, the larger bars produced a produced

a predicted capacity, PT , of 10356 lb , based on flexure in the vertical direction only

(Equation 5-12).

For this wall configuration, strength limits for the arching model are defined by yielding

of the horizontal reinforcing at the top and bottom of the wall, resulted in a predicted PT

of 4824 lb . The stress in the vertical reinforcement did not reach yield before the

horizontal bars. This value was determined using Equation 5-14.

Using the iterative method describe in Section 5.2.4.3, the applied out-of-plane load

theoretically required to cause a failure due to arch instability for this wall configuration

was 2390 lb . Since the average measured wall strength (3888 lb) fell between the arch

strength limits and stability limits, it was concluded that an instability failure was indeed

occurring. This was supported by the large deformations of the wall specimens near

mid-width and mid-span, at failure.

96

As with the previous analysis, the FE model was not a good predictor of the failure

loads or mechanism, but the test specimen crack patterns appeared to generally follow

the stress patterns given by the FE model.

The comparison between the two theoretical prediction methods, the FE analysis, and

the measured behavior of the test specimens, showed that arching action was present

and was the controlling the mode of wall failure. It was found that when #7 vertical bars

were used with #5 horizontal bars in the tested configuration, stability of the arch begins

to play a role in the strength of the system (regardless of variations in material

strengths, see Section 5.2.4.3).

5.4.3 Summary Comments

It is clear from the previous discussion that the proposed arch model predicts the

behavior of the wall specimens reasonably well. In addition, the postulated in-plane

bending of the arch segments did appear to be present, as evidenced by the reduction

in expected vertical flexural capacity of the specimens on the wall specimens with #5

vertical reinforcing bars.

It is important to note that the reduction in out-of-plane load capacities (as defined by

vertical flexural capacities) observed in these wall tests will only occur in discontinuous

locations of the wall, such as corners or control joints (were lower loading typically

occurs). Furthermore, additional horizontal reinforcing can significantly increase the

horizontal spanning capacity of the walls, and greatly reduce the vertical bending

capacity reduction. It is likely that joint reinforcement that is present in most concrete

masonry will act to help tie the arch formed by the masonry segments over a much

shorter distance, greatly reducing any additional stress that is placed on the vertical

reinforcement.

97

It is interesting to note that, if we assumed that the unreinforced hollow 8 in. CMU wall

simply spanned horizontally between the vertical reinforcements at 10 ft. spacing, a

maximum uniform wall load could be determined based on the maximum flexural tensile

stresses in the uncracked masonry. This calculation was done and is shown below

using the modulus of rupture listed in the MSJC code [MSJC, 2005] for Type S Masonry

Cement mortar and hollow units with stresses parallel to the bed joints:

Mr = S x Fr = 81 in3/ft x 75 psi /12 = 506.2 lb.ft

The maximum uniform load that could be applied to the tested 8 in. CMU walls, based

on this capacity and a 10 ft span is

W = 506.2 x 8/(10)2 = 40.5 psf

This result would suggest that the test specimens should have failed under their own

weight when the compression load was removed. Clearly the conventional analysis

assumption that the unreinforced masonry spans horizontally between reinforcement

would significantly underestimate the capacity of continuous masonry walls and even

underestimate the horizontal spanning capacity of masonry in discontinuous wall

sections.

Even though the arching model and analysis techniques give reasonable results for

both reinforcement configurations, a refinement of the equations relative to the assumed

shape of the cracked wall segments, the distribution of the thrust force, and effective

arch segment stiffness needs to be conducted. The central vertical crack assumption

and in-plane load distribution, used in the development of the prediction equations, does

not match observed behavior exactly. In addition, the effect of distributed reinforcing

(such as joint reinforcing) needs to be investigated. However, this relatively simple

method does appear to predict ultimate behavior reasonably well, and is conservative.

98

6.0 CONCLUSIONS

Based on the results of this investigation the following conclusions can be made.

1. The tests and analyses clearly showed that the masonry walls spanned in the

principal (vertical) bending direction in single curvature even after significant bed

joint cracking occurred. This bed joint cracking was generally limited to the mid-

span region. At higher load levels, after cracks formed parallel to the span (in the

head joints), an arch mechanism appeared to form that allowed significant loads

to be transferred horizontally between the vertically reinforced sections.

2. The shallow arch model for continuous masonry walls appears to suggest that

significant loads can be transferred over bar spacings sufficiently large to ensure

that flexural capacity of the vertically reinforced masonry will govern before

failure of the lateral load transfer mechanism, at least for the 8 CMU wall

configurations examined. From work by others, arch instability/crushing will not

likely to be an issue until spans exceed 28 times the wall thickness.

3. Under high lateral loads and after sufficient cracking occurs to form a horizontal

tied arch, it appears that in discontinuous masonry walls, a portion of the tensile

capacity of the vertical reinforcement is required to resist the in-plane thrusting

forces of the shallow arch, reducing the amount of reinforcement remaining to

resist the out-of-plane lateral loads. If these arches form, conventional flexural

capacity and loading analysis can overestimate the capacity of the walls with

widely spaced reinforcing, if arching action is not accounted for. If other

horizontal reinforcement is present, the effects of arching on the vertical flexural

capacity may be significantly diminished.

4. At ultimate loads levels, elastic Finite Element modeling does not appear to be a

reasonable analytical/design method for these wall systems and can greatly over

estimate the capacity of walls and incorrectly predict failure modes, although the

99

horizontal stress distribution patterns, do appear match the crack pattern

observed in the wall tests.

5. The arching model appears to give a reasonably good prediction of the specimen

ultimate capacities, although further refinement of the arch model may be

necessary after a greater variety of wall configurations are evaluated.

7.0 ACKNOWLEDGMENTS

The author would like to acknowledge the significant contributions of Mr. Neils Andresen

to this investigation. Much of the work described here (including the testing, analysis,

figures, etc.) formed the bulk of his Masters thesis [Andresen, 2006].

The author would also like to thank the NCMA foundation for its funding this

investigation, along with Dennis Graber who provided excellent support as the project

monitor. The advice and guidance of Robert Thomas and Jason Thompson from NCMA

are also gratefully acknowledged.

Finally the contributions of materials from the membership of The Carolina Concrete

Masonry Association and their Director Paul LaVene were greatly appreciated.

100

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spacing of reinforcing bars in partially ... spacing of reinforcing bars in partially grouted...

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