Note: Descriptions are shown in the official language in which they were submitted.
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SURFACE REINFORCED CONCRETE MASONRY UNITS
FIELD OF THE INVENTION .
The present invention relates to concrete masonry units for use with
elongate reinforcement members in the construction of a masonry wall, and more
particularly the present invention relates to concrete masonry units arranged
to
receive the reinforcement members recessed into the exterior sides of the
units.
BACKGROUND
Existing Concrete Masonry Units (CMUs) have two hollow cores and are
fabricated with two exterior flat surfaces. When constructing a wall using
CMUs they
are typically assembled by placing reinforcement and grout in the center of
each core.
The reinforcement is introduced into the assembly to enable the wall to resist
tension
stress while the grout is necessary to create a bond between the reinforcement
and
the concrete blocks. The reinforcement is placed near the centre axis of the
block
which is also the neutral axis on the wall as a flexural member. When the
reinforcement in a flexural member is placed close to the neutral axis it does
very little
work as the tension stress is zero at the neutral axis. Placing the
reinforcement at the
centre of the wall also allows the wall to crack at the tension side before
the
reinforcement begins to work. Cracking of a concrete block wall considerably
reduces
its durability and increases the operations and maintenance costs while also
reducing
the design life of the structure. To summarize the issues with the existing
system is
as follows: i) Tension reinforcement has to be placed at a location where
there is little
or no tension stress; and ii) In order to create a bond between the
reinforcement and
the block the core has to be filled with grout increasing material use and
self-weight of
the structure. This directly increases the cost of the building and carbon
footprint of
the construction.
SUMMARY OF THE INVENTION
According to one aspect of the invention there is provided a masonry
unit arranged for use with elongate reinforcement members in construction of a
masonry wall, the masonry unit comprising:
a concrete body which is elongate in a longitudinal direction between
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two opposing ends of the body, the concrete body further comprising:
a top and a bottom which are arranged for stacking with other
masonry units of identical configuration to form the masonry wall;
a first exterior side wall and a second exterior side wall which are
parallel and spaced apart from one another to extend in the longitudinal
direction
between the two opposing ends along opposing sides of the concrete body such
that
the first and second exterior side walls are arranged to define respective
portions of
opposing surfaces of the masonry wall; and
at least one hollow core extending through the body between the
top and the bottom of the concrete body;
wherein at least one of the exterior side walls includes a reinforcement
channel formed therein which extends between the top and the bottom of the
body,
the reinforcement channel being arranged for vertical alignment with the
reinforcement channels of said other masonry units, and the reinforcement
channels
being arranged for receiving a portion of a respective one of the elongate
reinforcement members therein in forming the masonry wall.
According to a second aspect of the present invention there is provided
a masonry wall comprising:
a plurality of masonry units as described above which are arranged in
stacked rows with mortar between the rows such that the reinforcement channels
of at
least some of the masonry units are vertically in alignment with the
reinforcement
channels of other ones of the masonry units;
a plurality of reinforcement members received within respective ones of
the reinforcement channels such that the reinforcement members each span
across a
plurality of the stacked rows at a location recessed laterally inwardly from a
respective
surface of the masonry wall defined by respective ones of the exterior side
walls of
the masonry units; and
a bonding material received within the reinforcement channels so as to
bond the reinforcement members to the masonry units.
According to a third aspect of the present invention there is provided a
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method of constructing a masonry wall comprising:
providing a plurality of masonry units as described above and stacking
the masonry units in rows with mortar between the rows such that the
reinforcement
channels of at least some of the masonry units are vertically in alignment
with the
reinforcement channels of other ones of the masonry units;
providing a plurality of reinforcement members and placing the
reinforcement members within respective ones of the reinforcement channels
such
that the reinforcement members each span across a plurality of the stacked
rows at a
location recessed laterally inwardly from a respective surface of the masonry
wall
defined by respective ones of the exterior side walls of the masonry units;
and
applying a bonding material to the reinforcement channels so as to bond
the reinforcement members to the masonry units.
By providing reinforcement channels in the exterior surfaces of the
masonry units, the reinforcement members can be relocated from a central
location
within the wall towards the surfaces of the wall. The reinforcement channels
thus
accommodate placement of reinforcement near the extreme tension surface where
it
is most needed, thereby increasing the loadbearing and flexural capacity of
walls
constructed using the masonry units, and reducing materials used in
constructing the
wall. The resulting masonry units are accordingly referred to herein as
Surface
Reinforced Concrete Masonry Units (SRCMU).
The masonry unit of the present invention is unique in its fabrication as it
has vertical channels or grooves on one or both exterior surfaces. The grooves
will
line up both in running bond and stack bond formation. The continuous groove
on the
surface of the wall will enable designers and engineers to specify the
placement of the
reinforcement on the surface of the tension side of the wall. Therefore, the
reinforcement is placed near the extreme fiber on the tension side where it is
most
efficient or "works" the most. Placing the reinforcement on the tension side
reduces
the tension cracking of the wall therefore increasing the design life of the
structure.
The masonry unit of the present invention may be reinforced with Fibre
Reinforced Polymer (FRP) rods or specially fabricated glass fibre that can be
applied
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with resin directly or traditional steel reinforcement. FRP reinforcement can
be
applied with resin containing fire retardant. Traditionally, steel reinforcing
has been
used in concrete masonry unit construction; however, the masonry unit of the
present
invention will give the designers the option of using traditional or more
efficient
reinforcement such as FRP in concrete block masonry construction.
SRCMU can be manufactured using the same fabrication and curing
technology as for CMU. The mold has to be modified to accommodate the channels
of SRCUM. SRCMU would have the same percentage solid and effective loadbearing
area as traditional CMU. Examples of possible dimensions and variations of
SRCMU
are shown in the accompanying drawings.
The details and the general construction procedure for constructing a
wall using SRCMU has also been modified from the traditional concrete block
wall
system. Grouting the cores are not required since there are no reinforcement
in the
cores; as noted earlier, grouting facilitates the bond between the
reinforcement and
the rest of the wall in conventional CMU construction. Elimination of grout
will result
in many benefits such as reduction of material (rendering the wall assembly
and the
concrete block wall construction more sustainable), reducing the self-weight
of the
wall which in turn facilitates the reduction of more construction materials
and
foundation requirements, and reduces thermal bridging of the wall assembly.
Optionally, neoprene or polystyrene spacers can be placed between two
side by side blocks as the wall is being constructed, which means the head
joints
between each block does not have to be mortared; thereby, reducing material
requirement and reducing thermal bridging, while increasing construction
speed.
Various embodiments of the invention will now be described in
conjunction with the accompanying drawings in which:
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1A is a top plan view of a first embodiment of the masonry unit
with channels on both sides. This unit can be used for the following
condition: i) for
doubly reinforced wall for additional capacity; ii) when both sides of the
wall is
exposed and the designers require the same look on both sides; or iii) for
when the
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designers want to have the channels exposed on one side to create a scored
look.
Figure 1B is a sectional view along the line A-A of Figure 1A.
Figure 1C is a sectional view along the line B-B of Figure 1A.
Figure 2A is a top plan view of a second embodiment of the masonry
5 unit with channels on one side only. This unit can be used for the
following
conditions: i) additional capacity of doubly reinforced wall is not required;
ii) when the
wall is exposed and the designers require a traditional look of concrete block
wall; or
iii) when used in an addition to an existing structure and the new addition
has to
match the existing.
Figure 2B is a sectional view along the line A-A of Figure 2A.
Figure 20 is a sectional view along the line B-B of Figure 2A.
Figure 3A is a top plan view of a third embodiment of the masonry unit
for use as a corner unit in which the unit is exposed at corners of concrete
block walls.
This unit can also be fabricated one side smooth (without channels) that can
be used
in the same conditions as indicated for the one side smooth stretcher unit.
This unit
can also be fabricated as a bullnose block both channel both sides and channel
on
one side only to accommodate reinforcement.
Figure 3B is a sectional view along the line A-A of Figure 3A.
Figure 3C is a sectional view along the line B-B of Figure 3A.
Figure 4A is a perspective view of a wall assembly using the masonry
blocks units according to Figures 1A to 10.
Figure 4B is a top plan view of the wall assembly of Figure 4A.
Figure 4C is an enlarged view of the highlighted portion of Figure 4B.
Figure 5, Figure 6, and Figure 7 show the relative compressive and
moment resistance of various configurations of fully grouted masonry walls.
Figure 8 and Figure 9 show the relative compressive and moment
resistance of various configurations of partially grouted masonry walls.
Figure 10 shows the relative compressive and moment resistance of
various configurations of ungrouted masonry walls.
Figure 11 and Figure 12 show the strain reaction along the height (z
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direction) of the SRCMU and CMU masonry prisms, respectively.
Figure 13 and Figure 14 show the strain reaction along the length (x
direction) of the SRCMU and CMU masonry prisms, respectively.
Figure 15 and Figure 16 show the strain reaction along the thickness (y-
direction) of the SRCMU and CMU masonry prisms, respectively.
Figure 17 shows the maximum stress supported by the prisms
constructed from the SRCMUs, LPCMUs, and CCMUs.
Figure 18 shows a test set-up for testing SRCMU units.
Figures 19 and 20 shows the distribution of stresses along the steel
reinforcing bars at 50%, 75%, and 100% of the failure load as well as at the
point
where the steel bar began to yield.
Figures 21 and 22 show the distribution of stresses along the FRP
reinforcing bars at 50%, 75%, and 100% of their failure load.
Figure 23 illustrates a test set-up to simulate the behaviour of an
SRCMU system under flexural loading conditions.
Figure 24 shows the tensile stresses in the GFRP reinforcing bar on the
tension side with little stress being transferred to the reinforcement on the
compression side of the prism.
Figure 25 shows the tensile stresses in the steel reinforcing bar on the
tension side with little stress being transferred to the reinforcement on the
compression side of the prism.
Figures 26 and 27 show the deflection at mid-span and crack width at
mid-span, respectively, for a typical steel reinforced specimen and a typical
GFRP
reinforced specimen.
In the drawings like characters of reference indicate corresponding parts
in the different figures.
DETAILED DESCRIPTION
Referring to the accompanying figures, there is illustrated a masonry
unit generally indicated by reference numeral 10. The masonry unit 10 is
particularly
suited for use in the construction of a masonry wall 12 as shown in Figures 4A
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through 4C. The masonry units 10 permit reinforcement members 14, for example
conventional rebar or other forms of elongate reinforcement, to be recessed
into one
or both exterior surfaces of the assembled wall.
The wall 12 is typically constructed in a manner similar to the use of
conventional concrete masonry units by abutting the units longitudinally end
to end in
rows with the rows being stacked one above the other. Each unit may be
vertically
aligned directly above a corresponding unit in the previous row therebelow, or
more
preferably each masonry unit 10 is offset longitudinally by half of the length
of the unit
relative to a corresponding unit of the previous row so that each masonry unit
is
engaged upon a portion of two additional masonry units therebelow in a
conventional
brick pattern.
Although various forms of the masonry unit 10 may be provided for
various applications, such as at an intermediate location within a wall, at
one end of a
wall, in a wall reinforced at a single side, or in a wall reinforced on both
sides. A
common double-sided stretcher unit as shown in Figures 1A through 10 for use
at
intermediate locations within the wall 12 of Figures 4A through 40 will first
be
described herein.
Each masonry unit 10 according to Figures 1A through 10 comprises a
concrete body such that the body is seamless, unitary and integral as a single
body.
The body is generally rectangular in shape including a flat top 20 and a flat
bottom 22
so as to be suitably arranged for vertical stacking in the masonry wall
construction.
Each body is also elongate in a longitudinal direction between two opposing
ends 24.
A first exterior side wall 26 and a second exterior side wall 28 extend
longitudinally along laterally opposed sides of the body between the two
opposing
ends while spanning the full height between the top and bottom of the body.
The
exterior side walls define respective portions of the two opposing surfaces of
the
finished wall 12.
The body includes two hollow cores 30 formed therein at longitudinally
spaced positions to extend fully through the body between the top and bottom
thereof.
The two hollow cores 30 are separated longitudinally by a web portion 32 which
is
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connected between the first and second exterior side walls at a longitudinally
centered
location. The web portion thus extends in a lateral direction between the two
opposing
side walls. The web portion spans the full height between the top and bottom
of the
body.
Two end walls 34 are provided for enclosing the two opposing ends of
the body such that one of the hollow cores is defined between the web portion
32 and
each one of the two end walls 34.
Inner surfaces of the web portion, the end walls, and the exterior side
walls may be formed with a slight inclination from vertical to aid in
releasing the
concrete body from a respective concrete mold.
The body of each masonry unit further includes a reinforcement channel
36 formed in each one of the two exterior side walls. Each reinforcement
channel is
longitudinally centered between the opposing ends of the body and spans the
full
height between the top and bottom sides of the body. Each channel is a
generally U-
shaped and is opened to the exterior of the body.
By being longitudinally centered, each reinforcement channel aligns
laterally with the web portion 32. The web portion increases in thickness as
measured
in the longitudinal direction of the block from the center, laterally outward
towards
each of the two exterior side walls locating the reinforcement channels 36
therein to
provide additional reinforcement of material about each channel.
Each end of the block further includes a partial channel 38 along the
exterior sidewall at the end of the body. The partial channel is located at
the
intersection of the end wall and the exterior side wall so as to be open to
both the end
and the exterior side of the block. The partial channel 38 spans the full
height
between the top and bottom. The shape and depth of the partial channel 38 is
arranged such that when two masonry units of identical configuration are
abutted end
to end using mortar (or a spacer element described further below) between the
units,
the resulting combination of two adjacent partial channels 38 defines a whole
reinforcement channel of identical configuration to the reinforcement channels
36 at
the intermediate location along each exterior side wall.
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Each of the reinforcement channels, including integral channels 36 or
channels formed by the abutment of two partial channels 38, is vertically
aligned with
corresponding reinforcement channels of masonry units stacked above and below
the
respective unit to form respective portions of a vertical recess spanning the
height of
the assembled masonry wall. In this manner, the reinforcement channels are
arranged to receive the reinforcement members 14 therein such that the members
span across several rows within the channels so as to be recessed inwardly
relative
to the resulting exterior face of the assembled masonry wall. The
reinforcement
channels 36 are accordingly suitably sized to receive the reinforcement
members
therein as well as additional bonding material 40 to bond the reinforcement
members
to the masonry units across several rows of units.
Each of the end walls 34 is further shaped to define a recessed channel
42 at a central location in the lateral direction such that the channel 42
spans the full
height of the unit between the top and bottom thereof. The recessed channel 42
is
recessed longitudinally inward relative to adjacent portions of the end face
44 defined
by the end wall. Each end face 44 spans the full height and spans in the
lateral
direction from the recessed channel towards the respective exterior side wall
of the
body. When partial channels 38 are provided the end faces 44 span between the
recessed channel and a respective one of the partial channels 38 at the end of
the
body.
In the illustrated embodiment, the masonry units 10 are used in
combination with spacer members 46 in which each spacer member is abutted
between the two ends of two adjacent masonry units within a respective row of
the
masonry wall. The spacer member comprises a body of rigid insulation having a
profile which mates with the corresponding exterior profile of the end wall 34
of the
body of the masonry unit 10.
More specifically, each spacer member comprises two side portions 48
and a central portion 50 located between the two side portions in the lateral
direction
such that all three portions span the full height of a single masonry unit.
The central
portion 50 is suitably sized to be received within the recessed channels 42 of
two
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adjacent masonry units abutted on either side of the spacer member. The two
side
portions are reduced in thickness in the longitudinal direction of the masonry
units so
as to be suitable for abutment with the corresponding end faces 44 on either
side of
the recessed channels 42.
5 The overall width of the spacer member in the lateral direction
between
opposing exterior sides of the masonry units is arranged to be less than the
body of
the masonry units such that the opposing ends of each spacer member are
recessed
inwardly relative to the exterior surface of the exterior side walls in the
finished
masonry wall construction. More particularly the spacer member terminates at
10 opposing ends adjacent the innermost portion of the partial channels 38
such that the
spacer member does not protrude into or obstruct the resultant reinforcement
channel
36 formed by the abutment of two partial channels 38. In this manner, the
reinforcement channel assembled from two partial channels remains unobstructed
to
allow the respective portion of the reinforcement member to be received
therein while
also permitting the spacer body to be hidden within the wall when covered by
the
reinforcement member and/or corresponding mortar or other finishing bonding
material at the exterior or the masonry wall.
Construction of a masonry wall using the unit 10 typically involves
initially applying a layer of levelling grout upon which a first row of
masonry units are
positioned in a longitudinally end-to-end abutted relationship with spacer
members 46
or mortar being received between each adjacent pair of masonry units. Each
subsequent row of masonry units is stacked on the previous row by first
applying a
layer of mortar across the tops of the masonry units of the previous row
followed by
another row of longitudinally aligned end-to-end abutted masonry units.
In the preferred arrangement, each masonry unit is offset by half the
length of a unit relative to corresponding units of the previous row such that
each
reinforcement channel 36 is vertically aligned with a corresponding
reinforcement
channel formed by two partial channels 38 in the previous row therebelow.
Likewise
each reinforcement channel formed by the abutment of two partial channels in
the
current row is vertically aligned directly above a corresponding integral
reinforcement
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channel of the previous row therebelow. The hollow cores are similarly
vertically
aligned with the hollow cores of units of the previous rows.
Subsequent to the stacking of the masonry units in the form of the
masonry wall, the reinforcement members are recessed into one or both exterior
faces of the masonry wall by being received within respective reinforcement
channels
with each reinforcement member spanning across multiple rows of units. The
reinforcement members are retained within the respective reinforcement
channels
using the bonding material 40, which is also recessed into the channels
relative to the
exterior surface of the assembled wall structure. In this manner, the bonding
material
covers the reinforcement members within the interior of the assembled wall
structure
as well as covering any spacer members 46 which were used in abutment between
adjacent masonry units.
The reinforcement members may take various forms including steel
rods, glass fiber rods, fiber reinforced polymer rods or any other suitable
elongate
member having sufficient tensile strength to reinforce the assembled masonry
wall
structure.
Similarly, the bonding material may take various forms. For example,
the bonding material may comprise mortar, epoxy, or other curable resins and
the
like.
The reinforcement members may be provided in all reinforcement
channels at one or both sides of the assembled wall, or alternatively only at
selected
channels longitudinally spaced apart as required to meet strength
requirements.
The masonry unit described above with regard to Figures 1A through 1C
is particularly suited for use at an intermediate location within a wall where
the option
of reinforcement at both sides of the wall is desired.
Alternatively, if it is clear the reinforcement is only required at one of the
two surfaces of the masonry wall, a single-sided masonry unit as shown in
Figures 2A
through 20 may be provided. The masonry unit 10 shown in Figures 2A through 2C
is identical to the first embodiment with the exception of one of the first or
second
exterior sides comprising a flat side 70 spanning the full length of the body
in the
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longitudinal direction so as to be uninterrupted by any reinforcement
channels, either
whole or partial.
In yet a further consideration, where it is desired for the finished
masonry wall to terminate at a free end, a bullnose masonry unit may be
provided as
shown in Figures 3A through 3C. The masonry unit 10 shown in Figures 3A
through
3C is identical to the first embodiment with the exception of one of the two
opposing
ends comprising a flat surface 80 spanning the full height and width of the
end of the
body so as to be free of any recessed channel or partial channels described
above.
In this instance, a plurality of half blocks 90 are also typically provided,
as shown in Figure 4A, which are half the length of a typical masonry unit so
that all of
the rows terminate at a common location even when the blocks are offset by
half a
length relative to adjacent rows in a conventional brick pattern.
Relationship between Compressive Resistance and Moment Resistance
The following sections illustrate the potential strength of walls
constructed of surface reinforced masonry units compared to those made from
conventional hollow masonry units. Figures 5 to 10 show the Compressive
resistance
vs. Moment resistance diagrams (Pr-Mr diagrams) for walls with the same
thickness
and reinforcement ratio. The curves seen in Figures 5 to 10 were developed
using the
methodology described in CSA S304.1-04 as prescribed by the National Building
Code of Canada. The model used to determine the stress in the masonry units
and
grout was the equivalent rectangular stress block (S304.1-04 10.2.6). Table 1
shows
the variables used for the application of CSA S304.1-04 for the purposes of
this
document. It was assumed that the surface reinforced units would behave in the
same
way as conventional hollow masonry units, the only difference being the
location of
the reinforcing steel.
Table 1
Variable Value Value justification
Ae (effective cross sectional area of varies Varies according to the
masonry per 1m length of wail) percentage of cores that
are
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grouted
As (total cross sectional area of steel 300 mm2 Dictated by the
reinforcement
rebar per lm length of wall) ratio (p)
Asf (cross sectional area of steel rebar 150 mm2 Dictated by the
reinforcement
near the tension face of the wall per lm ratio (p)
length of wall)
Ase (cross sectional area of steel rebar 150 mm2 Dictated by the
reinforcement
near the compression face of the wall ratio (p)
per lm length of wall)
b (effective width of the test wall 1000 mm Typically used for analysis
section)
bw (effective width of the grouted cores 400 mm Consistent with 2 grouted
in partially grouted walls per width b) cores per meter width of wall
c (depth from the compression face of varies Varies from 0 to infinity in
the wall to the neutral axis) order to construct the Pr-Mr
diagrams
Cm (compression force from masonry varies Varies depending on the
rectangular stress block) design and the depth to
neutral axis (c)
Cmff (compression force from masonry varies Varies depending on the
rectangular stress block in the face shell design and the depth to
near the compressive face of the wall) neutral axis (c)
Cmf2 (compression force from masonry varies Varies depending on the
rectangular stress block in the face shell design and the depth to
near the tension face of the wall) neutral axis (c)
Cmw (compression force from masonry varies Varies depending on the
rectangular stress block in the grouted design and the depth to
cores of the wall) neutral axis (c)
Cs (force in the steel rebar near the varies Varies depending on the -
,
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compression face of the wall) design and the depth to
neutral axis (c)
d (depth to reinforcing steel for 95 mm Centre of masonry unit
conventional units)
di (depth to reinforcing steel on the 10 mm Varies depending on design
compression face of the surface
reinforced units)
d2 (depth to reinforcing steel on the 180 mm Varies depending on design
tension face of the surface reinforced
units)
Es (Modulus of elasticity of steel rebar) 200,000 S304.1-04 6.5.1
MPa
rn (masonry compressive strength) 10 MPa Typical value for general use
masonry
fy (yield strength of steel rebar) 400 MPa S304.1-04 10.2.3
fat (stress in steel rebar at centre line or varies Varies according to the
strain
near the tension face of the wall) in the steel (Eat)
fac (stress in steel rebar near the varies Varies according to the strain
compression face of the wall) in the steel (Esc)
Mr (moment resistance of a masonry varies Varies depending on the
wall, per width b) design and the depth to
neutral axis (c)
Pr (compressive resistance of a varies Varies depending on the
masonry wall, per width b) design and the depth to
neutral axis (c)
t (wall thickness) 190 mm Typical block type for general
use
T (force in the steel rebar in the varies Varies depending on the
centreline of the wall or near the tension design and the depth to
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face) neutral axis (c)
tr (thickness of the masonry unit face 32 mm Typical (Hatzinikolas 2005)
shell)
pi (ratio of depth of rectangular 0.8 5304.1-04 10.2.6
compression block to depth of neutral
axis)
Ern (maximum usable masonry strain) 0.003 S304.1-04 10.2.2
Est (strain in steel rebar at centreline or varies Varies depending on the
near the tension face of the wall) design and the depth to
neutral axis (c)
csc (strain in steel rebar near the varies Varies depending on the
compression face of the wall) design and the depth to
neutral axis (c)
p (reinforcement ratio) 0.158 ''/0 Arbitrary amount allowed
by
S304.1-04
(1)s (steel rebar resistance factor) 0.85 S304.1-04 4.3.2.2
(lh-n (masonry resistance factor) 0.6 S304.1-04 4.3.2.1
x (factor used to account for direction of 1.0 For out of plane vertical
compressive stress in a masonry bending S304.1-04 10.2.6
member relative to the direction used for
the determination of fin)
Table 2 explains the shorthand used to identify the various configurations of
masonry
walls analysed for the purposes of this section of the text.
Table 2
SR Surface reinforced masonry units
C Conventional masonry units
UT Steel reinforcement not tied
T Steel reinforcement tied
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UR Unreinforced (no steel reinforcement)
G Fully grouted cores
PG Partially grouted cores
UG Ungrouted (no cores grouted)
Example: SR/UT/G means the wall is composed of surface reinforced masonry
units (SR)
reinforced with steel rebar that is not tied (UT) and fully grouted (G).
First will be discussed configurations in which all the cores in the wall
are filled with grout (SWUT/G, C/UT/G, SFITT/G, C/T/G and C/UFi/G). For the
cases
where the reinforcing steel is not tied and when no reinforcing steel is used,
the
maximum factored compressive resistance (Pr(max)) is calculated as:
Pr(max)=0.80 (0.85(pmf`mAe) S304.1-04 10.4.1/7.4
For the cases where the reinforcing steel is tied, Pr(max) is calculated as:
Pr(max)0.80 (0.85(Pmfm(Ae-As)+(psfyAs) S304.1-04 10.4.2
Factored compressive resistance (Pr) and moment resistance (Mr) must
satisfy conditions of equilibrium and compatibility of strain (S304.1-04
10.1.1). For
grouted CMU walls to satisfy conditions of equilibrium of forces, the
following equation
must be satisfied:
Pr=Cm-T
Where:
Cm=cpm0.85fiffixbpic is the compressive force in the masonry (S304.1-04
10.2.6).
and
T=9sfstAs is the tension force in the steel rebar. Where fst=min{EstEs;fh is
the tension stress in the steel rebar and As is the cross-sectional area of
the steel
rebar (S304.1-04 10.2.3).
For grouted CMU walls to satisfy conditions of equilibrium of moments
the following equation must be satisfied:
Mr=Crn*(t/2-431c/2)-T*(t/2-d)
For grouted CMU walls to satisfy conditions of compatibility of strain the
following equation must be satisfied:
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cm/c=Est/(c-d)
For grouted SRCMU walls to satisfy conditions of equilibrium of forces
the following equation must be satisfied:
Pr=Cm+Cs-T
Where:
Cm=vm0.85fmxbr3ic is the compressive force in the masonry (S304.1-04
10.2.6).
Cs=cpsfscAsc is the compressive force in the steel rebar. Where
fsc=min{EscEs;fy} is the compressive stress in the steel rebar and Aso is the
cross-
sectional area of the steel rebar near the compression face (S304.1-04
10.2.3).
and
T=TsfstAst is the tension force in the steel rebar. Where fst.min{EstEs;fy} is
the tension stress in the steel rebar and At is the cross-sectional area of
the steel
rebar near the tension face (S304.1-04 10.2.3).
For grouted SRCMU walls to satisfy conditions of equilibrium of
moments the following equation must be satisfied:
Mr.Cm*(t/2-131c/2)+Cs*(t/2-d1)-T*(t/2-d2)
For grouted SRCMU walls to satisfy conditions of compatibility of strain
the following equation must be satisfied:
Em/c=csci(c-d 1 )=Est/(c-d2)
Figure 5, Figure 6, and Figure 7 show the relative compressive and
moment resistance of various configurations of fully grouted masonry walls.
The
maximum compressive resistance of the wall made from surface reinforced
masonry
units is no greater than that of conventional masonry units, however the
moment
resistance of the wall is greatly improved by the use of surface reinforced
units. This
can be seen by comparing SWT/G to C/T/G and SR/UT/G to C/UT/G. As expected,
the unreinforced wall has the lowest moment resistance and shows the same
behaviour for both types of masonry.
Considering partially grouted configurations in which only a portion of
the cores in the wall are filled with grout (SR/UT/PG, C/UT/PG, SR/T/PG and
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Cfr/PG), for the cases where the reinforcing steel is not tied and when no
reinforcing
steel is used, Pr(max) is calculated as:
Pr(max)=0.80 (0.85(pmfmAe) S304.1-04 10.4.1/7.4
For the cases where the reinforcing steel is tied, Pr(max) is calculated as:
Pr(max)=0.80 (0.85(pmfrn(Ae-As)+TsfyAs) S304.1-04 10.4.2
Factored compressive resistance (Pr) and moment resistance (Mr) must
satisfy conditions of equilibrium and compatibility of strain (S304.1-04
10.1.1). For
partially grouted CMU walls to satisfy conditions of equilibrium of forces,
the following
equation must be satisfied:
Pr=Cmf1+Cmw+Cm12-T
Where:
Cnif1=min{(pm0.85frnxbr31c ; (pm0.85fmxbtf) is the compressive force in the
face shell near the compressive face of the wall (S304.1-04 10.2.6).
Cmw=min{pm0.85frnxbw(t-2b) ; max {0 ; 9m0.85fmxb(31c4t)}} is the
compressive force in the grouted cores of the wall (S304.1-04 10.2.6).
Cmf2.max{0 ; 9m0.85frnxb(Pic1+tf)} is the compressive force in the face
shell near the tension face of the wall (S304.1-04 10.2.6).
T.(psfstAs is the tension force in the steel rebar. Where fst=min{EstEs;fy}
is the tension stress in the steel rebar and As is the cross-sectional area of
the steel
rebar (S304.1-04 10.2.3).
For partially grouted CMU walls to satisfy conditions of equilibrium of
moments the following equation must be satisfied:
Mr=Crnii*(t/2-min{pic/2 ; tf/2})+Cmw*(max{t/2-(13-ic-tf)/2 ; 0})+Cmf2*(P1c4f/2
)+Cs*(t/2-d1)-
T*(t/2-d2)
For partially grouted CMU wall to satisfy conditions of compatibility of
strain the following equation must be satisfied:
Ern/c.Est/(c-d)
For partially grouted SRCMU walls to satisfy conditions of equilibrium of
forces the following equation must be satisfied:
Pr=Cmf1+Cmw+Cmf2+Cs-T
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Where:
Crnfi=nnin{cpm0.85fmxbpic ; 9m0.85rmxbtf) is the compressive force in the
face shell near the compressive face of the wail (5304.1-04 10.2.6).
Cmw=nnin{cpm0.85fnixbw(t-2tt) ; max {0 ; (prn0.85fmxb(131c-tt)}} is the
compressive force in the grouted cores of the wall (5304.1-04 10.2.6).
Cmf2=max{0 ; Trn0.85fnnxb(131c-t+tf)} is the compressive force in the face
shell near the tension face of the wall (S304.1-04 10.2.6).
Cs=qhfscAsc is the compressive force in the steel rebar. Where
fse.min(EscEs;fy) is the compressive stress in the steel rebar and As0 is the
cross-
sectional area of the steel rebar near the compression face (5304.1-04
10.2.3).
T=TsfstAst is the tension force in the steel rebar. Where fst=min{estEs;fy} is
the tension stress in the steel rebar and At is the cross-sectional area of
the steel
rebar near the tension face (S304.1-04 10.2.3).
For partially grouted SRCMU walls to satisfy conditions of equilibrium of
moments:
Mr=Cmfilt/2-nnin{r3ic/2 ; tf/2})+Cmw*(max{t/2-(131 c-tf)/2 ; 0})+Cmf2*((131c-
tt)/2 )+Cs*(t/2-
d1)-T*(t/2-d2)
For partially grouted SRCMU walls to satisfy conditions of compatibility
of strain:
Em/c=E8c/(c-di)=Est/(c-d2)
Figure 8 and Figure 9 show the relative compressive and moment
resistance of various configurations of partially grouted masonry walls.
Similar to the
fully grouted walls, the maximum compression resistance of the wall does not
change
with the type of masonry unit (conventional or surface reinforced). By
comparing
SR/T/PG to Cl/PG and SR/UT/PG to C/UT/PG, once again an appreciable gain in
moment resistance can be observed for the surface reinforced masonry walls as
compared to the conventional masonry walls.
Considering ungrouted configurations in which none of the cores in the
wall are filled with grout (SR/UT/UG, SR/T/UG and C/UR/UG), for the cases
where
the reinforcing steel is not tied and when no reinforcing steel is used,
Pr(max) is
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calculated as:
Pr(max)=0.80 (0.85(pmf 'mAe) S304.1-04 10.4.1/7.4
For the cases where the reinforcing steel is tied, Pr(max) is calculated as:
Pr(max)=0.80 (0.85(pmfrn(Ae-As)+TsfyAs) S304.1-04 10.4.2
5 Factored compressive resistance (Pr) and moment resistance (Mr)
must
satisfy conditions of equilibrium and compatibility of strain (S304.1-04
10.1.1). For
ungrouted CMU walls to satisfy conditions of equilibrium of forces, the
following
equation must be satisfied:
Pr=Cmf1+Cmf2
10 Where:
Cmfi.min{(pm0.85frnxbi3ic ; cpm0.85frnxbtfl is the compressive force in the
face shell near the compressive face of the wall (S304.1-04 10.2.6).
Cmf2=maxf0 ; wm0.85firnxb(131c-t+tf)} is the compressive force in the face
shell near the tension face of the wall (S304.1-04 10.2.6).
15 For ungrouted CMU walls to satisfy conditions of equilibrium of
moments
the following equation must be satisfied:
Mr=Cmfilt/2-min{Pic/2 ; tf/2})+Cmf21(131c-tf)/2)
There is no need to check compatibility of strain for C/UR/UG since
there is only one material. For ungrouted SRCMU walls to satisfy conditions of
20 equilibrium of forces the following equation must be satisfied:
Pr=Cmfi +Cmf2+Cs-T
Where:
Cmfi=min(pm0.85frnxbi3ic ; cpm0.85frnxbtf) is the compressive force in the
face shell near the compressive face of the wall (S304.1-04 10.2.6).
Cmf2=max{0 ; Trn0.85finixb(lic-t+tf)} is the compressive force in the face
shell near the tension face of the wall (S304.1-04 10.2.6).
Cs=cpsfscAse is the compressive force in the steel rebar. Where
fsc=min{cscEs;fy} is the compressive stress in the steel rebar and Asa is the
cross-
sectional area of the steel rebar near the compression face (S304.1-04
10.2.3).
T=TsfstAst is the tension force in the steel rebar. Where fst=miniEstEs;fy) is
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the tension stress in the steel rebar and At is the cross-sectional area of
the steel
rebar near the tension face (5304.1-04 10.2.3).
For ungrouted SRCMU walls to satisfy conditions of equilibrium of
moments the following equation must be satisfied:
Mr.Cmte(t/2-nn i n {Pic/2 ; tt/2})+Cm12*((131c-tt)/2)+Cs*(t/2-d )-T*(t/2 -d2)
For ungrouted SRCMU walls to satisfy conditions of compatibility of
strain the following equation must be satisfied:
Em/c=Esc/(c-di) =est/(c-d2)
Figure 10 shows the relative compressive and moment resistance of
various configurations of ungrouted masonry walls. In conventional masonry
construction, grout is used to bond the reinforcing steel bars to the masonry
assemblage, conventional masonry practices therefore do not allow ungrouted
masonry walls to be vertically reinforced. Using surface reinforced masonry
units it is
possible to vertically reinforce ungrouted masonry walls, greatly increasing
the wall's
moment resistance without the added weight of grout.
Distribution of Strain Under Axial Loading
It is common practice to test the strength of masonry units by testing
prisms made from two masonry units stacked one on top of the other with a
single
mortar bed between them. The figures 11 to 16 illustrate the strain reaction
of
conventional hollow masonry units as well as surface reinforced units. Since
the
purpose is to verify the behaviour of the unit itself, both prisms are left
ungrouted and
unreinforced. The ANSYS Mechanical finite element modeling package was used to
model the prisms because of its versatility and because it is commonly used in
industry.
A linear elastic material model was used to represent both the masonry
unit and the mortar. The material properties of the masonry units and mortar
bed are
shown in Table 3. Typical values were obtained from Drysdale (2005). The
effect of
self-weight of the units and mortar was neglected.
Table 3
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Masonry unit Mortar
Young's 8500 MPa Young's 4250 MPa
modulus modulus
Poisson ratio 0.2 Poisson ratio 0.18
Specifications of the numerical model are shown in Table 4. Both prism
models were subjected to an axial pressure of 10MPa with the prisms confined
at the
top and bottom surfaces (typical of laboratory conditions).
Table 4
Specification Value
Number of nodes Approx. 18,000
Number of elements Approx. 13,000
Boundary conditions Displacement x,y,z:
at z=0 (prism base) fixed
Rotation x,y,z: fixed
Boundary conditions Displacement x,y:
at z=390 mm (top of fixed
prism) Uniform pressure:
MPa
Interface condition Fully bonded
between masonry
and mortar
5
Figure 11 and Figure 12 show the strain reaction along the height (z
direction) of the SRCMU and CMU masonry prisms, respectively. As expected, the
more flexible mortar joint reacts with much higher strain levels than the
masonry units.
Both types of masonry unit react with very similar patterns of strain.
10 Figure 13 and Figure 14 show the strain reaction along the length (x
direction) of the SRCMU and CMU masonry prisms, respectively. Here some
differences exist between the two types of masonry units. Tension strain is
higher in
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the middle section of the surface reinforced unit (near the centre web)
because of the
reduced cross section as compared to the conventional unit. However, both
types of
units exhibit higher strains near the cored sections of the unit than near the
centre
web.
Figure 15 and Figure 16 show the strain reaction along the thickness (y-
direction) of the SRCMU and CMU masonry prisms, respectively. Here the
geometry
of the surface reinforced unit appears to relieve some of the strain near the
centre
web of the unit. No additional strain concentrations appear to exist in the
surface
reinforced prism when compared to the conventional prism.
Physical Testing Axial Compressive Behaviour
Testing of physical specimens were conducted to compare the
behaviour of stack bonded masonry prisms constructed of conventionally shaped
hollow concrete masonry blocks to those constructed of SRCMUs under axial
compressive stresses. 5 masonry prisms were constructed using SRCMUs produced
in laboratory, 3 prisms were constructed of conventionally shaped masonry
blocks
produced in laboratory (LPCMU), and 3 prisms were constructed from
commercially
available conventional hollow concrete blocks (CCMU). All specimens (four
blocks
high each) were constructed on the same day by a skilled mason.
To ensure that they had reached their maximum load-carrying capacity,
all eleven specimens were tested to failure, more than 28 days after they had
been
produced.
Figure 17 shows the maximum stress supported by the prisms
constructed from the SRCMUs, LPCMUs, and CCMUs. The average strength for the
three different populations of prisms varied by less than 22% from the global
average,
and the coefficient of variation of the entire population of masonry prisms
at, 9.7%, is
well within the 15% limit set by Annex D of S304.1 for small samples of
prisms. The
coefficient of variation of elastic modulus measured for the prisms was 8.1%.
Together, these results suggest both that the blocks manufactured in the
laboratory
have similar compressive properties to those that were commercially produced
and
that blocks with the SRCMU cross-section have similar compressive properties
to
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those that have the conventional hollow block cross-section.
An analysis of the modes of failure observed during the compression
testing of masonry prisms has yielded three different modes of failure;
vertical splitting
of the web, vertical splitting of the face shell, and diagonal splitting of
the face shell.
These three modes of failure were observed to some extent in all eleven
masonry
specimens tested.
Neither the analysis of the strength of the masonry prisms nor their
modes of failure suggest that a significant difference in compressive
behaviour exists
between conventional hollow masonry blocks and SRCMUs.
Physical Testing Development of Reinforcement Stresses
In order for a reinforcing bar to allow a masonry system to develop its
required flexural strength, the reinforcing bars must be properly anchored. In
order for
a reinforcing system to be practicable, adequate anchorage of reinforcing bars
must
be achievable within a short distance.
A pull out test was devised in order to determine the bond
characteristics as well as the modes of failure of SRCMU systems reinforced
with
steel rebar or with Fibre Reinforced Polymer (FRP) reinforcing bars. For this
test,
reinforcing bars were mechanically pulled out from three-high stack-bonded
SRCMU
prisms into which they had been installed using epoxy grout. The reinforcing
bars
were fitted with instrumentation to determine the distribution of forces
within the bars
as they were being pulled out.
Six specimens were constructed for this test; 3 specimens were
reinforced using 10M steel rebar, and 3 specimens were constructed using
9.5nnm
FRP reinforcing bars. Each reinforcing bar was fitted with six strain gauges
at
intervals of 100mm in order to accurately quantify the distribution of forces
within the
bars during loading.
The full test set-up is shown in figure 18. The masonry specimen (101)
is restrained against the loading platens (102) with four steel angles (103)
and four
threaded rods (104). A sheet of fibre board (105) and a steel plate (106) are
used to
distribute the loads from the restraining device to avoid stress
concentrations in the
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blocks which would cause premature failure. The free end of the reinforcing
bar (107)
is anchored into the restraining block (108) of the testing frame.
Figures 19 and 20 shows the distribution of stresses along the steel
reinforcing bars at 50%, 75%, and 100% of the failure load as well as at the
point
5
where the steel bars began to yield. Figures 21 and 22 show the distribution
of
stresses along the FRP reinforcing bars at 50%, 75%, and 100% of their failure
load.
Note that figures 19 and 21 show specimens for which the mode of failure was
the
rupture of the bar and figures 20 and 22 show specimens for which the mode of
failure was the pulling out of the bar from the channel. Given the
similarities in
10
behaviour apparent in figures 19 and 20 and figures 21 and 22, it appears that
both
10M steel bars and 9.5mm GFRP bars are near the limit of strength which may be
developed by the SRCMU system used for this experimental programme. Further
examination of Figures 19 to 22 indicate that there was a high likelihood for
progressive debonding of the bars to occur for all specimens, since high
stress levels
15
in the bars could be observed in the lower portion of specimens. This theory
is
supported by the observation that 50% of the specimens tested failed by
progressive
debonding of the reinforcing bar before the bar ruptured.
The lower force at which the GFRP bars pulled out of the masonry
specimens is due to the lower modulus of elasticity (higher flexibility) of
the material,
20
which causes stresses to concentrate more near the free end of the bar on
which the
force is applied; this causes the bond between the bar and the concrete to
fail
progressively away from the applied force.
Also of note is that the yield stress (value used for engineering design)
of the steel bars was achieved with no significant damage to the specimens. It
can
25
therefore be said that the yield strength of the 10M steel bar was developed
within
600mm (the height of the pull-out specimens). This compares well with the
length
required to develop the strength of steel rebar with masonry grout from CSA
S304.1,
which for a common grout strength of f'gr=1 OMPa and no modification factors
would
be.
Id= 0.45*ki k2k3(fy/f9r-2)db
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Id=0.451*1*1*(400MPa/(10MPa)-2)10nnm
Id=570mm
Physical Testing, Flexural Behaviour
To simulate the behaviour of an SRCMU system under flexural loading
conditions, six specimens were constructed to be tested in four-point loading
conditions. The configuration of the specimens is illustrated in figure 23;
each
specimen is constructed of six SRCMUs (101) bonded vertically, and reinforced
in
compression and tension with reinforcing bars (102). The specimens are
supported at
points (103) and loaded at points (104). Strain gauges are located at points
(105)
along the length of each reinforcing bar in order to determine the stress at
those
locations. Other data collected includes crack width and deflection at mid-
span of the
prism.
Using the approach from CSA S304.1 and removing the material
factors, the failure load of the specimens can be estimated:
Assumptions:
= Equilibrium of forces Cr=Tr
= Sufficient development length is provided to develop the full tensile
strength for
the reinforcing materials.
For steel reinforced specimens:
Tension resistance:
Tr=Asfy
Compression resistance:
Cr4'm0.85ab+fsA's
Symbol Value Source
f'm Masonry compressive strength=20MPa Compression testing
fy Steel yield strength=400MPa Material data sheet
fs Stress in compression steel=variable
As Steel reinforcement cross sectional Material data sheet
area=100mm2
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A's Compression steel reinforcement cross- Material data sheet
sectional area=100mrn2
Width of rectangular stress Measured
block=180mm
a Depth of rectangular stress -
block=variable
Mr Moment resistance of the prism=variable -
d Distance from top of prism to tension Measured
reinforcement=170mm
Cr.Tr
fm0.85ab+fsA's=Asfy
a.(Tr-fsA's)/(fm0.85b)
a=14.7mm
Mr=Tr*(d-a/2)
Mr=6.5kNm
Total load = 2*Mr/0.33m
Total load = 39.4 kN
For FRP reinforced specimens:
Tension resistance:
Tr=Afrpfr
Compression resistance:
Cr=fm0.85ab+fsA'frp
Symbol Value Source
fm Masonry compressive strength=20MPa Compression testing
fr FRP rupture strength=1100MPa Material data sheet
= ,
fs FRP compression stress=variable
Afrp FRP reinforcement cross sectional Material data sheet
area=71.3mm2
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A'frp Compression FRP reinforcement cross Material data sheet
sectional area=71.3mm2
b Width of rectangular stress block=180mm Measured
a . Depth of rectangular stress -
block=variable
Mr Moment resistance of the prism=variable -
d Distance from top of prism to tension Mesaured
reinforcement=170mm
Cr=Tr
fm0.85ab+fsA'frp=Tr
a=(Tr-fsA'frp)/(fm0.85b)
a=24.4mm
Mr=Tr*(d-a/2)
Mr=12.3kNm
Total load = 2*Mr/0.33m
Total load = 75.0 kN
The high flexural resistance of the specimens being tested resulted in all
6 specimens failing in diagonal tension (also known as shear). However, the
observed
strength of the specimens nonetheless compare well with anticipated results.
Figure
24 shows the increase in tensile stresses in the GFRP reinforcing bar on the
tension
side (strain gauges 201 to 203) with little stress being transferred to the
reinforcement
on the compression side of the prism (strain gauge 204). The higher tension
stress in
strain gauge 202 compared to gauges 201 and 203 is due to its location within
the
central mortar joint of the specimen; this location is most likely to crack,
forcing the
reinforcing bar to withstand the entire tensile stress at that location.
A similar behaviour can be observed in the steel reinforced specimens
as shown in Figure 25. The main difference in behaviour between the steel
reinforced
specimens and the GFRP reinforced specimens is the higher stiffness of the
steel
reinforcing bars, which causes much lower strain values under similar stress
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conditions.
Figures 26 and 27 show the deflection at mid-span and crack width at
mid-span, respectively, for a typical steel reinforced specimen and a typical
GFRP
reinforced specimen. As expected, deflections and crack width are
significantly lower
for the steel reinforced specimens compared with the GFRP specimens. However,
all
specimens exhibited roughly linear behaviour up to approximately 50% of their
strength, followed by an increased rate of deflection until total failure
occurred. This
type of behaviour is beneficial in engineering design as it allows for
conspicuous signs
of deterioration in a building system before total failure occurs.
The following references referred to in the above description are
incorporated herein by reference.
CSA (2004) CSA S304.1-04 (R2010) Design of Masonry Structures,
Canadian Standards Association, Mississauga, Ontario
Drysdale RG, Hannid AA (2005) Masonry Structures Behaviour and
Design Canadian Edition. Canadian Masonry Design Centre, Mississauga, Ontario
Hatzinikolas MA, Korany Y (2005) Masonry Design for Engineers and
Architects. Canadian Masonry Publications, Edmonton, Alberta
Since various modifications can be made in my invention as herein
above described, it is intended that all matter contained in the accompanying
specification shall be interpreted as illustrative only and not in a limiting
sense.
