Classnotes for ROSE School Course in:

Masonry Structures

Lesson 2 and 3: Properties of Masonry Materials

Introduction, compressive strength, modulus of elasticity
condition assessment, movements

Notes Prepared by:

Daniel P. Abrams
Willett Professor of Civil Engineering
University of Illinois at Urbana-Champaign
October 7, 2004

Masonry Structures, Lectures 2-3, slide 1

Historical Use of Masonry
as a Structural Material

Masonry Structures, Lectures 2-3, slide 2

The First Building Material

 The first masonry structures

were constructed of mud, sun-
dried brick.
 The people of Jericho were
building with brick more than
9000 years ago.
 Sumerian and Babylonian
builders covered brick walls
with kiln-baked glazed brick.
 Mesopotamian builders
Etemenanki Ziggurat constructed temple towers from
height 91 meters 4000 BC to 600 BC.

Masonry Structures, Lectures 2-3, slide 3

The First Building Material

 Stone masonry was used for

Egyptian pyramids c. 2500 BC.
 Pyramid of Khufu at Giza
measured 147 m. high and 230
m. square.
 Pyramid of Khafre at Giza was
constructed without cranes,
pulleys or lifting tackle. No
mortar or adhesive was used.
 Ancient examples of Cyclopean
Pyramid of Khafre at Giza masonry found throughout
Europe, China and Peru.
 Egyptian houses made of mud-
brick walls.

Masonry Structures, Lectures 2-3, slide 4

Greek and Roman Architecture

 Early Greek architecture

(3000 to 700 BC) used
massive stone blocks for
walls, and early vaults and
domes.
 Greeks constructed with
limestone and marble.
 Romans constructed with
concrete, terra cotta and
El Puente Aqueduct
fired clay bricks.
near Segovia Spain
1st Century AD  Romans refined arch, vault
two tiers of arches 28. 5m tall and dome construction to
construct great aqueducts,
coliseums and palaces were
built with clay brick.
Masonry Structures, Lectures 2-3, slide 5
Applications in China

 The Great Wall of China

was constructed from 221 to
204 BC.
 The wall winds 2400 km
from Gansu to the Yellow
Sea, and is the longest
human-made structure in the
world.
 The wall is constructed of
Great Wall of China earth and stone with a brick
6 to 15m. tall facing in the eastern part.
4.6 to 9.1m wide at base
ave. 3.7 m wide at top

Masonry Structures, Lectures 2-3, slide 6

Byzantine Architecture

 Huge domed churches

were built on a scale far
larger than achieved with the
Romans.
 Innovative Byzantine
technology allowed architects
to design a basilica with an
immense dome over an
open, square space.
 Isalmic architects
Hagia Sophia, Istanbul developed a rich variety of
constructed 532-537 AD pointed, scalloped, horseshoe
dome fell after earthquake in 563 and S-curved arches for
mosques and palaces.

Masonry Structures, Lectures 2-3, slide 7

Masonry in the Americas

 Early pyramids built c.

1200 BC at the Olmec site of
LaVenta in Tabasco Mexico.
 Later monuments
constructed by the Maya,
Toltecs and Aztecs in central
Mexico, the Yucatan,
Guatemala, Honduras, El
Salvador and Peru were
based on the Olmec plan.
Pyramid of the Sun  Four-sided, flat-topped
Teotihuacan Mexico polyhedrons with stepped
66-m. high sides.
2nd century AD

Masonry Structures, Lectures 2-3, slide 8

Masonry in the Americas

 Aztec, Mayan and other

Indian cultures relied on
masonry for housing and
monuments.
 Stone veneers used by
Mayans at Uxmal in 9th
century. Slight outward lean of
these buildings made them
appear light and elegant.
Pueblo Bonito  Pueblo Bonito housed up to
Chaco Canyon, NM 1000 residents.
10th Century AD  Anasazi constructed
covers more than 3 acres multistory pueblos from stone,
mud and beams during period
of 1100-1300 AD.
Masonry Structures, Lectures 2-3, slide 9
Romanesque, Gothic and Renaissance

 With Romanesque
architecture (10th to 12th
century), large internal spaces
were spanned with barrel vaults
supported on thick, squat
columns and piers.
 Gothic architecture (12th to
16th century) used a pointed
arch which minimized outward
thrust and resulted in lighter
Santa Maria degli Angeli and thinner walls.
Firenza, Italy  Renaissance architecture was
constructed 1420-61 AD influenced by the round arch,
39 m. in diameter, 91 m. high the barrel vault, and the dome.
Filippo Brunelleschi
Masonry Structures, Lectures 2-3, slide 10
Masonry at the Turn of the Century

 URM brick bearing-wall

construction used for multistory
buildings. Design based on
empirical rules.
 URM construction popular for
low-rise buildings in inner core of
cities, many of which are still
standing today.
 In 1908, the Nat. Assoc. of
Cement Users developed the first
specification for concrete block.
Fifty million cmu’s produced in
Monadnock Building 1919 which grew to 467 million in
Chicago, 1891 1941.
D. Burnham and J. Root
Masonry Structures, Lectures 2-3, slide 11
Rational Structural Design

 Masonry compressive strength

standardized by 1910.
 Empirical design still prominent
through first half of twentieth
century.
 Research on structural masonry
done at the Structural Clay Products
Association and Portland Cement
Association.
 BIA in the 1966 and NCMA in 1970
developed standards for structural
code of Hammurabi design of brick and block.
Babylon, 1780 BC

Masonry Structures, Lectures 2-3, slide 12

Recent Code Developments

 TMS developed first standard for

brick/block masonry, and became
Chapter 24 of 1985 UBC. Further
revised in 1988, 1991 and 1994 (as
Chapter 21).
 ACI-ASCE 530 code published in
1988. Further revised in 1992 and
1995 as MSJC code.
 Strength design introduced into
1985 UBC.
 New chapter on strength design in
MSJC Building Code 2002 MSJC.
Requirements for Masonry

Masonry Structures, Lectures 2-3, slide 13

Masonry Seismic Provisions

 Chapters 8 and 8A of NEHRP

Recommended Seismic Provisions
for New Buildings (FEMA 222A,
1994)
 Appendix C of NEHRP Handbook
for Seismic Evaluation of Existing
Buildings (FEMA 178, 1992)
 FEMA 273/356 Guidelines for
Seismic Rehabilitation of Buildings

NEHRP Provisions for

New Buildings

Masonry Structures, Lectures 2-3, slide 14

Present Applications
 The use of masonry as a
structural material has been
developing rapidly in the
western US over the last
two decades.
 Tall buildings of structural
masonry are now being
constructed.
 A slow revolution in the
Excaliber Hotel, Las Vegas east.
tallest building of structural masonry
 URM still used for new
construction.
 Tall, slender walls
compete with tilt-up
construction.
Masonry Structures, Lectures 2-3, slide 15
Masonry Compressive Strength

Masonry Structures, Lectures 2-3, slide 16

Mechanics of Masonry in Compression
 
P

y
l A
P  xb
zb

masonry
tj unit 

xb
zb stresses shown for
tb  y mortar > unit

 
 xm
y
zm

mortar
P  xm

 zm  y

Masonry Structures, Lectures 2-3, slide 17

Biaxial Strength of Masonry Units
flat-wise compressive strength
of unit from test
 y
f’ut
compressio
brick splits when: f’ut n
y
 xb  f 'udt (1  ) f’ut
f 'ut

direct tensile strength of unit

from test

 xb f’udt
tension f’udt
f’udt

Masonry Structures, Lectures 2-3, slide 18

Biaxial Strength of Mortar
f’jt
mortar crushes when:
  - f '  uniaxial compressive
y jt 
 xm   strength from test
 y
4 .1
compression

f’jt
4.1
1.0  y

f' jt multiaxial
compressive  
 xm strength
xm xm

compression

 y

Masonry Structures, Lectures 2-3, slide 19

Masonry Compressive Strength
equilibrium relation:
P
 xb ( tb l )   xm ( t j l )
tj
 xb   xm
tb
tj
if mortar crushes:
tb
(  y  f ' jt )
 xm  or
4.1
t j / tb t j / tb
 xb  (  y  f ' jt )   (  y  f ' jt ) where  
4 .1 4.1
if brick splits: P
y
 xb  f 'udt (1 - )
f 'ut
Masonry Structures, Lectures 2-3, slide 20
Masonry Compressive Strength

if mortar crushes and brick splits simultaneously:

y
 (  y  f ' jt )  f'udt (1  )
f ' ut
f'udt
 y   f' jt  f'udt   y f'ut

 f 'udt f ' jt 

y   f 'ut Hilsdorf equation
 f 'udt f 'ut 
y
f'm  prism strength 
Uu
where Uu = coefficient of non-uniformity (range 1.1 to 2.5)

Masonry Structures, Lectures 2-3, slide 21

Nonlinear Mortar Behavior
 y

1000 psi
triaxial test
 y

 
30 psi   xm   zm
xm xm
 zm  zm

y
 y
v
1000 psi
l

x 30 psi

z
Masonry Structures, Lectures 2-3, slide 22
Unit Splitting vs. Mortar Crushing
Linear Mortar

 y
mortar
unit
stress path stress path
f’ut
mortar
failure
envelope
unit
failure mortar crushes
envelope f’jt

failure
 xb
tension compression
 xm
f’udt

Masonry Structures, Lectures 2-3, slide 23

Unit Splitting vs. Mortar Crushing
Nonlinear Mortar
 y
unit
stress path f’ut
mortar
unit splits failure
envelope
unit
f’jt mortar
failure
stress path
envelope
failure

 xb
tension compression
 xm
f’udt

Masonry Structures, Lectures 2-3, slide 24

Incremental Lateral Tensile Stress on Masonry Unit
Assuming linear behavior for masonry unit, and nonlinear mortar behavior:
 Eb 
 y  b -  (  , ) 


E j (  xm ,  z m ) m xm zm 
 xb 
 
 Eb tb Eb tb
1  - b -  m (  xm ,  zm ) 
 E j (  xm , z m ) tj E j (  xm , z m ) t j 
where :
  Poisson’ s ratio for masonry unit
b

 m  Poisson’ s ratio for mortar

E  Young’ s modulus for masonry unit
b

E j  Young’ s modulus for mortar

t b  thickness of masonry unit
tj  thickness of mortar joint
 xm ,  zm  lateral mortar compressiv e stresses

From Atkinson and Noland “A Proposed Failure Theory for Brick Masonry in Compression,”
Proceedings, Third Canadian Masonry Symposium, Edmonton, 1983, pp. 5-1 to 5-17.

Masonry Structures, Lectures 2-3, slide 25

Effect of Mortar on Compression
Weaker Mortars

 y
M
S • weaker mortars result in weaker prism
strength because ratio of vmortar/vunit is larger
N
• weaker mortars result in greater extents of
nonlinear prism behavior
O

 y

Masonry Structures, Lectures 2-3, slide 26

Effect of Mortar on Compression
Stronger Mortars

 y
M
S
• may not adhere to units as well.
• a larger scatter of experimental data with the
stronger mortars.
N • create a stiffer prism which is more sensitive to
alignment problems during testing and more
brittle.
O
• more variable masonry compressive strength.

 y

Masonry Structures, Lectures 2-3, slide 27

Guidelines for Prism Testing
UBC Sec. 2105.3.2: Masonry Prism Testing

• A set of five prisms shall be built and tested prior to

construction in accordance with UBC Std. 21-17.
• At least three prisms per 5,000 sq. feet of wall area
shall be built and tested during construction.
• Test values for prism strength shall exceed design
values.

Note that testing is not required if half of allowable stresses are used for design.

NCMA TEK 18-1 Concrete Masonry Prism Testing

Masonry Structures, Lectures 2-3, slide 28

Guidelines for Prism Testing
UBC Standard 21-17: Test Method for
Compressive Strength of Masonry Prisms

• Methods for prism construction,

transportation and curing. h
• Preparation for testing, test procedures, etc.
• Calculation for compressive stress. Net area,
correction factors. tp

Table 21-17A
prism h/tp 1.3 1.5 2.0 2.5 3.0 4.0 5.0
correction
0.75 0.86 1.00 1.04 1.07 1.15 1.22
factor
Use lesser of average strength or 1.25 times least strength.

Masonry Structures, Lectures 2-3, slide 29

Code Values for Prism Strength
UBC Sec. 2105.3.4: Unit Strength Method

• Use test values per UBC 21-17.

• Take f’m equal to 75% of average prism record value. (2105.3.3)
• Take f’m from Table 21-D if no prisms are tested.

Associated BIA Technical Note: 35 Early Strength of Brick Masonry

Masonry Structures, Lectures 2-3, slide 30

Compressive Strength of Masonry per UBC
UBC Table 21-D

Specified compressive strength of clay masonry, f’m

Compressive Strength Specified Compressive Strength

of Clay Masonry Units of Masonry, f’m, (psi)
(psi)
Type M/S mortar Type N mortar
14,000 or more 5,300 4,400
12,000 4,700 3,800
10,000 4,000 3,300
8,000 3,350 2,750
6,000 2,700 2,200
4,000 2,000 1,600

Masonry Structures, Lectures 2-3, slide 31

Compressive Strength of Masonry per UBC
UBC Table 21-D

Specified compressive strength of concrete masonry, f’m

Compressive Strength Specified Compressive Strength

of Concrete Masonry of Masonry, f’m, (psi)
Units (psi)
Type M/S mortar Type N mortar

4,800 or more 3,000 2,800

3,750 2,500 2,350
2,800 2,000 1,850
1,900 1,500 1,350
1,250 1,000 950

Masonry Structures, Lectures 2-3, slide 32

MSJC Specifications for Prism Strength

• Sec. 1.4.B Compressive Strength Determination

• Sec. 1.4B.2 Unit Strength method
– Table 1 Compressive Strength for Clay Masonry
– Table 2 Compressive Strength for Concrete Masonry
• Sec. 1.4B.3 Prism Test Method
– ASTM C 1314

Masonry Structures, Lectures 2-3, slide 33

Compressive Strength of Masonry per MSJC
MSJC Specification Table 1

Compressive strength of clay masonry by unit strength method

Net Area Compressive Strength Net Area

of Clay Masonry Units (psi) Compressive
Strength of Masonry
Type M/S Mortar Type N Mortar
(psi)
1,700 2,100 1,000
3,350 4,150 1,500
4,950 6,200 2,000
6,600 8,250 2,500
8,250 10,300 3,000
9,900 - 3,500
13,200 - 4,000

Masonry Structures, Lectures 2-3, slide 34

Compressive Strength of Masonry per MSJC
MSJC Specification Table 2
Compressive strength of concrete masonry by unit strength method
Compressive Strength Net Area
of Concrete Masonry Units (psi) Compressive
Strength of Masonry
Type M/S Mortar Type N Mortar
(psi)
1,250 1,300 1,000
1,900 2,150 1,500
2,800 3,050 2,000
3,750 4,050 2,500
4,800 5,250 3,000

MSJC values of compressive strength from Table 1 and Table 2 are intended to be
used in lieu of prism tests to estimate needed mortar types and unit strengths for a
required compressive strength.

Masonry Structures, Lectures 2-3, slide 35

Comparison of Default Prism Strengths
UBC Table 21-D vs. MSJC Specifications Table 1
C l ay -U n it M a s o n r y

M / S, UBC
5
Pr is m St re ngth, f'm ksi

N, UBC
4
M /S , M SJ C

3 N , M SJ C

0
0 5 10 15 20
Un it Stre ngth, ks i

Default prism strengths are lower bounds to expected values.

Masonry Structures, Lectures 2-3, slide 36

Comparison of Default Prism Strengths
UBC Table 21-D vs. Table 2 MSJC-Spec.

Co ncrete -Un it Ma son ry

3 .5

M/S , UB C
3
M/S , M SJC
N, UB C
P rism Streng th, f'm ksi

2 .5
N , M SJC

1 .5

0 .5

0
0 2 4 6 8 10

U nit Strength , ksi

Note: MSJC and UBC values are almost identical for concrete masonry.
Default prism strengths are lower bounds to expected values.

Masonry Structures, Lectures 2-3, slide 37

Masonry Elastic Modulus

Masonry Structures, Lectures 2-3, slide 38

Elastic Modulus of Masonry in Compression
Basic Mechanics

 j  deformation of mortar   j t j  E t j y
[1]
P = y Anet 
j

 b  deformation of unit   b t b  E t by

b
[2]

  deformation of masonry  E ( t j  t b )
y

m
[3]
 
   j   b  E t j  Ey t b
y

tj j b [4]

tb tj
  t  thickness ratio  t [5]
b
E
 m  modulus ratio  E j [6]
b

t j  tb  ( 1   t )tb [7]

Masonry Structures, Lectures 2-3, slide 39

Elastic Modulus of Masonry in Compression
Basic Mechanics
y y
from 3 and 7 :  
 m ( t j  t b )   m ( 1   t )t b
[8]
P = y Anet
y y
from 1,5 and 6 :  j  tj   t tb [9]
Ej  m Eb

y y y
tj from 4, 8 and 9 : ( 1   t )t b   t tb  tb [10]
Em  m Eb Eb
tb
 (1 t ) 1 t
 ( 1) [11]
Em Eb  m

(1 t )
m  b
t [12]
(1 )
m

Reference: Structural Masonry by S. Sahlin, Section D.2

Masonry Structures, Lectures 2-3, slide 40

Elastic Modulus of Masonry in Compression

Em (1   t )
Em Emasonry
 

Eb (1  t )
Eb Eunit m
1.2

1.0

t= 0.152
0.8

concrete block masonry

0.76 (typical for brick masonry)

0.6
t= 0.0498
clay-unit masonry

(typical for concrete block masonry)

0.4

0.2

E mortar
0.0 m 
E unit
0 0.5 1 1.5 2

Masonry Structures, Lectures 2-3, slide 41

Code Assumptions for Elastic Modulus
UBC Sec. 2106.2.12 and 2106.2.13 & MSJC Sec. 1.8.2.2.1 and 1.8.2.2.2

secant method estimate without prism test data

UBC Sec. 2106.2.12.1

for clay-unit or concrete masonry
fm
Em Em = 750 f’m < 3000 ksi
f’mt MSJC Sec. 1.8.2.1.1
for clay-unit masonry
Em = 700 f’m
for concrete-unit masonry
0.33 f’mt Em = 900 f’m
UBC 2106.2.13
0.05 f’mt MSJC Sec. 1.8.2.2.2
m
G = 0.4 Em

Masonry Structures, Lectures 2-3, slide 42

Strength of URM Bearing Walls

Masonry Structures, Lectures 2-3, slide 43

Unreinforced Bearing and Shear Walls
Structural Walls have 3 functions:
floor or roof loads
• resist vertical compression (bearing wall)

• resist bending from eccentric

vertical loads and/or
transverse wind, earthquake,
or blast loads
a ds
• resist in-plane shear and lo l)
e wal
in-plane rs
e e
bending from lateral loads shear and n sv plan
applied to building system in tra t-of-
moment (ou
direction parallel with plane (shear wall)
of wall

Ref: BIA Tech. Note 24 The Contemporary Bearing Wall

Masonry Structures, Lectures 2-3, slide 44

Unreinforced Bearing and Shear Walls
Historically walls were sized in terms of h/t ratio which
was limited to 25.
2

M = wh  F S  F  t 
2

8 b
6 
b

h  8 F  8 (50 psi) ( 144 )

2
b
t 6 w 6 (15 psf)
2

wind
= 15 psf
h h
 25.3
t

Empirical design of masonry

UBC 2105.2 h < 35’

Associated BIA Technical Note: 24 series The Contemporary Bearing Wall Building

Masonry Structures, Lectures 2-3, slide 45

Concentric Axial Compression
Buckling Load
Euler buckling load:
P = y Anet
Pcr   Em2I  cr   Em2 I
2 2
( kl ) ( kl ) A

for rectangular section:

h’ = kl

bt 3
I A  bt
12
I bt 3 t2
r    0.289t
A 12bt 12
t

Masonry Structures, Lectures 2-3, slide 46

 Concentric Axial Compression

2 bt 3
π Εm( ) 0 .82 Ε
σcr  12  m
2 kl 2
y (kl) bt ( )
t
if Em  750 f 'm and h'  kl, then  cr  615 f'2m
f’m ( h' )
t
24.8

Euler curve
cutoff at f 'm   cr  615f'2m , or h' /t  24 .8
 cr 
615f'm ( h' )
t
( h' )
2

t
0.25 f’m MSJC/UBC

h’/t
25 50 75 100

Note: for MSJC and UBC plot, r=0.289t is assumed

Masonry Structures, Lectures 2-3, slide 47

Code Allowable Compressive Stress

Fa
f 'm MSJC Section 2.2.3 and UBC Section 2107.3.2:

0.3
for h’/r < = 99: Fa = 0.25 f’m [1 - (h’/140r)2]
MSJC Eq. 2-12 and UBC Eq. 7-39
for h’/r > 99 : Fa = 0.25 f’m [(70r/h’)2]
0.2
MSJC Eq. 2-13 and UBC Eq. 7-40

0.1

h'
0
0 50 100 150 200 r

Masonry Structures, Lectures 2-3, slide 48

Concentric Axial Compression
UBC 2106.2.4: Effective Wall Height

translation restrained no sidesway restraint

h h’=kh

k = h’/h rotation rotation rotation rotation

unrestrained restrained unrestrained restrained
1.0 0.70 2.0 2.0

MSJC 2.2.3: Buckling Loads

π 2 Em I
1
P  Pe Pe  ( 1  0.577 e )3 (2  11 / 2 - 15)
4 h' 2 r
e = eccentricity of axial load

Masonry Structures, Lectures 2-3, slide 49

Concentric Axial Compression
UBC 2106.2.3: Effective Wall Thickness

A. Single Wythe C. Cavity Walls

t = specified thickness
both wythes loaded one wythe loaded
B. Multiwythe
P
P1 P2
t
mortar or air space
grout filled
collar joint
wire joint
reinforcement

t1 t2 t1 t2

each wythe t  t12  t22

considered separate

Masonry Structures, Lectures 2-3, slide 50

Concentric Axial Compression
UBC 2106.2.5: Effective Wall Area

Effective area is minimum area of mortar bed joints plus any grouted area.

face shell
raked joint

effective thickness effective thickness

Neglect web area if face-shell bedding is used.

Masonry Structures, Lectures 2-3, slide 51

 Example: Concentric Axial Compression
Determine the allowable vertical load capacity of the unreinforced cavity wall
shown below per both the UBC and the MSJC requirements.

Pa
Case “A”: Prisms have been tested.
8”CMU 4” brick f’m = 2500 psi for block wall
f’m = 5000 psi for brick wall
face-shell
bedding metal ties
Case “B”: No prisms have been tested.
20’-0”

f’m = 1500 psi for block wall

(Type I CMU’s and
7.63” Type S mortar will be specified.)
3.63”

Per NCMA TEK 14-1A for face shell bedding:

concrete footing Anet = 30.0 in2 Inet = 308.7 in4 r = 2.84 in.
(r based only on loaded wythe)

Masonry Structures, Lectures 2-3, slide 52

Example: Case “A”
MSJC Section 2.2.3 & UBC 2107.3.2
h' 12( 20')
  84 .5
r 2 .84 in.
for h'/r  99 : Fa  0 .25 f'm [ 1  (h'/ 140 r)2 ]
Fa  0 .159 f'm  0 .159 ( 2500 psi)  397 psi
Pa  ( 0 .397 ksi)( 2 x 1 .25 in. x 12 in.)  11 .9 kip/ft

MSJC Section 2.2.3: check buckling *

1 π 2 Εm I e 3
P  Pe  0 .25 2
( 1  0 .577 )
4 h r
E m  900 f'm MSJC Sect ion 1 .8 .2 .2 .1
E m  900  2500  2 ,250 ,000 psi  2250 ksi
π 2( 2 .25 x 10 3 )( 308 .7 )
P  0 .25 2
 29 .8 kip/ft buckling d oesn't gov ern
( 240 )

Pa = 11.9 kip / ft for both codes

* no buckling check per UBC.
Masonry Structures, Lectures 2-3, slide 53
Example: Case “B”
MSJC Section 2.2.3 & UBC 2107.3.2
h' 12( 20' )
  84.5
r 2.84 in .
for h' / r  99 : Fa  0.25 f 'm [ 1  ( h' / 140 r )2 ]
Fa  0 .159 f 'm  0.159( 1500 psi )  283 psi Governs for MSJC, take
1/2 for UBC since no
Pa  ( 0.283 ksi )( 2 x 1.25 in . x 12 in .)  7.2 kip / ft special inspection is
provided.
MSJC Section 2.2.3: check buckling
1  2 m I e 3
P  Pe  0.25 2
( 1  0. 577 )
4 h r
 m  900 f 'm MSJC Section 1.8.2.2.1
 m  900  1500  1350 ,000 psi  1350 ksi
 2 ( 1.35 x 10 3 )( 308.7 )
P  0.25 2
 17.85 kip / ft buckling doesn' t govern
( 240 )

Masonry Structures, Lectures 2-3, slide 54

Eccentric Axial Compression
e axial stress bending stress
P P M = Pe
Pe

P Mc M
fa  fb  
A I S
h

combined axial stress plus bending

-fa + fb
fa + fb
t

Ref: NCMA TEK 14-4 Eccentric Loading of Nonreinforced Concrete Masonry

Masonry Structures, Lectures 2-3, slide 55

Eccentric Axial Compression
UBC Section 2107.2.7 and MSJC 2.2.3: Unity Formula

limiting compressive stress fa f

 b  1.0 (controls for small e’s)
Fa Fb

where Fa= allowable axial compressive stress (UBC 2107.3.2 or MSJC Sec. 2.2.3)
Fb= allowable flexural compressive stress = 0.33 f´m (UBC 2107.3.3 or MSJC Sec 2.2.3)

UBC 2107.3.5 or MSJC 2.2.3: Allowable Tensile Stress

limiting tensile stress -fa + fb < Ft (controls for large e’s)

where Ft = allowable tensile stress

References
Associated NCMA TEK Note
31 Eccentric Loading of Nonreinforced Concrete Masonry (1971)
Associated BIA Technical Note
24B Design Examples of Contemporary Bearing Walls
24E Design Tables for Columns and Walls

Masonry Structures, Lectures 2-3, slide 56

Allowable Tensile Stresses, Ft
MSJC Table 2.2.3.2 and UBC Table 21-I
Mortar
Direction of Tension Type
and Portland Cement/Lime
or Mortar Cement Masonry Cement/Lime
Type of Masonry M or
all units are (psi)
M or N N
S S
tension normal
to bed joints
solid units 40 30 24 15
hollow units 25 19 15 9
fully grouted units 68* 58* 41* 26*

tension parallel
to bed joints
solid units 80 60 48 30
hollow units 50 38 30 19
fully grouted units 80* 60* 48* 29*

* grouted masonry is addressed only by MSJC

Masonry Structures, Lectures 2-3, slide 57

 Allowable Flexural Tensile Stresses, Ft
flexural tension normal to bed joints

Note: direct tensile stresses across wall

thickness is not allowed per UBC or MSJC.

flexural tension parallel to bed joints

strong units weak units

No direct tensile strength assumed normal to head

joints, just shear strength along bed joint.

Masonry Structures, Lectures 2-3, slide 58

Example: Eccentric Axial Compression
Determine the allowable vertical load capacity per UBC and MSJC.

e = 3.0”
f’m = 2000 psi (from tests)
Pa Type S mortar

Ft = 25 psi per UBC 2107.3.5 and MSJC Table 2.2.3.2

1.25”

face-shell
20’-0”

bedding

8”CMU
ungrouted Per NCMA Tek 141A:
(per running foot)
Anet = 30.0 in2
7.63” Ix= 309 in4
Sx = 81.0 in3
concrete footing r= 2.84”

Masonry Structures, Lectures 2-3, slide 59

Example

Tension controlling:

- fa  fb  Ft  25 psi

Pa Pae
-   Ft h
Anet Snet

Pa Pa( 3 .0")
-   25 psi Pa  6750 lbs.
30.0 81.0

Masonry Structures, Lectures 2-3, slide 60

Example
Compression controlling: UBC 2107.3.4 and MSJC 2.2.3
Fb  0.333 f 'm  0.333( 2000 psi )  667 psi
h 12.0 ( 20' )
  74.8
r 2.84 in.
  h  2 
Fa = 0.25f m 1 -   
  140r  
Fa = 0.159 f m = 0.159(2000 psi) = 318 psi
Pa Pa e Pa Pa e
Anet Snet 30.0  81.0  1.0
  1.0
Fa Fb 318 psi 667 psi
Pa  6233 lbs .  6750 lbs . compressio n controls

Masonry Structures, Lectures 2-3, slide 61

Example
MSJC Section 2.2.3: Check Buckling
(no buckling check per UBC)

Em  900 f 'm per MSJC Sec. 1.8.2.1.1

3
 2 Em I  e
P < 0.25Pe = 0.25  1  0 .577 
h2  r
3
  ( 1800 ksi)(308.7 in 4 )  3.00 
0.25 Pe = 0.25 2  1  0 . 577 
(240 in)  2.84 
P < .25Pe = 1417 lbs < 6233 lbs. buckling controls

Pa (lbs)
Code
Tension Compression Buckling
UBC 6750 6233 -----
MSJC 6750 6233 1417

Masonry Structures, Lectures 2-3, slide 62

 Kern Distance for URM Wall
Assuming Ft = 0 for solid
section.
e
- fa + fb = 0
P
P Mc
-  0
A I
A = bt I = bt 3 /12
P Pe(t/2)
t -  3 0
bt bt /12 b/3
fa
+ e = t/6
t/3 kern t
fb
=
b
-fa + fb = 0
fa + fb If load is within kern,
then no net tensile stress.

Masonry Structures, Lectures 2-3, slide 63

 Kern Distance for URM Wall
Specific Tensile Strength, Ft, for solid section.

e - f a + f b = Ft
P
P Mc
-   Ft
A I
P Pe(t/2)
-  3  Ft b Ft b 2 t
bt bt /12 
t 3 3P

fa t Ft t 2 b
e  t Ft t 2 b
+ 6 6P  kern t
3 3P
fb
= b
-fa + fb = Ft
fa + fb If load is within kern,
then tensile stress < Ft.

Masonry Structures, Lectures 2-3, slide 64

Strength of Walls with no Tensile Strength
Resultant load inside of kern.

P
P M [1]
fm  
A S
t P 6 Pe
fm   2 [2]
bt bt
e
P 6e
fm  (1 ) [3]
bt t
fm
f m  Fa orFb
Fb  0.33 f 'm
P

Masonry Structures, Lectures 2-3, slide 65

Strength of Walls with no Tensile Strength
Resultant load outside of kern.
Neglect all masonry in tension.
P Note: This approach is outside of UBC and
MSJC since Ft may be exceeded.

2P
fm   compressive edge stress  Fa or Fb [1]
b
 t t
 e   3( e) [2]
t 3 2 2
t/ 2P 2P 1
fm  
 2 b 3 b( t  e ) t 2 [3]
3 e 2 t2
4P
fm fm =
e
 Fa or Fb
 3bt(1 - 2 ) [4]
t

Partially cracked wall is not prismatic along its height. Stability of the
P wall must be checked based on Euler criteria modified to account for
zones of cracked masonry. Analytical derivation for this case is provided
in Chapter E of Structural Masonry by S. Sahlin.

Masonry Structures, Lectures 2-3, slide 66

Example
Determine the maximum compressive edge
stress.
P = 10 kip/ft. Part (a) e = 1.0 in. < t/6 = 1.27 in. within kern!
e
P 6e 
fm = 1 
bt  t 
10,000 lbs.  6 ( 1.0 in.) 
fm =  1    195 psi
( 12 in.)(7.63 in.)  ( 7.63 in.) 

Part (b) e = 2.5 in. > t/6 = 1.27 in. outside of kern!

t = 7.63” 4P
fm =
 e
two-wythe brick wall 3bt  1 - 2 
 t
4 (10,000 lbs)
fm = = 422 psi
 2.5 in. 
3( 12 in.)(7.63 in.) 1 - 2 
 7.63 in. 

Masonry Structures, Lectures 2-3, slide 67

Condition Assessment

Masonry Structures, Lectures 2-3, slide 68

Insitu Material Properties
 Compressive strength
 Elastic modulus

 Flexural tensile strength

Masonry Structures, Lectures 2-3, slide 69

 Insitu Material Properties

 Shear strength

 Shear modulus
 Reinforcement

 PCE 
0.75  0.75 v te  
 An 
v me 
1 .5
Masonry Structures, Lectures 2-3, slide 70
Condition Assessment

Knowledge factor
  = 0.75 when visual exam is done

Visual examination
 measure dimensions
 identify construction type
 identify materials
 identify connection types

Masonry Structures, Lectures 2-3, slide 71

 Condition Assessment

Knowledge factor
  = 1.00 with comprehensive knowledge level

Nondestructive tests
 ultrasonic
 mechanical pulse velocity
 impact echo or radiography

Masonry Structures, Lectures 2-3, slide 72

Movements

Masonry Structures, Lectures 2-3, slide 73

Differential Movements
• One common cause of cracking is differential movement between
wythes.
• Different materials expand or contract different amounts due to:
– temperature
– humidity
– freezing
– elastic strain
• Cementitious materials shrink and creep
• Clay masonry expands
• Consider differential movements relative to steel or concrete frames

shrink expand
Ref: BIA Tech. Note 18 Movement - Volume Changes and Effect of Movement, Part I

Masonry Structures, Lectures 2-3, slide 74

Coefficients of Thermal Expansion
Ave. Coefficient of Thermal Expansion
Material Linear Thermal Expansion (inches per 100’ for
(x 10-6 strain/oF) 100oF
temperature increase)
Clay Masonry
clay or shale brick 3.6 0.43
fire clay brick or tile 2.5 0.30
clay or shale tile 3.3 0.40
Concrete Masonry
dense aggregate 5.2 0.62
cinder aggregate 3.1 0.37
expanded shale aggregate 4.3 0.52
expanded slag aggregate 4.6 0.55
pumice or cinder aggregate 4.1 0.49
Stone
granite 4.7 0.56
limestone 4.4 0.53
marble 7.3 0.88
Thermal coefficients for other structural materials can be found in BIA Technical Note 18.

Masonry Structures, Lectures 2-3, slide 75

Moisture Movements
• Many masonry materials expand when their moisture content is
increased, and then shrink when drying.
• Moisture movement is almost always fully reversible, but in some
cases, a permanent volume change may result.

Moisture Expansion of Clay Masonry = 0.020%

Freezing Expansion of Clay Masonry = 0.015%

Masonry Structures, Lectures 2-3, slide 76

Moisture Movements in Concrete Masonry
• Because concrete masonry units are susceptible to shrinkage, ASTM
limits the moisture content of concrete masonry depending on the
unit’s linear shrinkage potential and the annual average relative
humidity. For Type I units the following table is given.
Moisture Content, % of Total Absorption
(average of three units)

Linear Shrinkage, % Humidity Conditions at Job Site

humid intermediate arid

0.03 or less 45 40 35
0.03 to 0.045 40 35 30
0.045 to 0.065 35 30 25

Masonry Structures, Lectures 2-3, slide 77

Control Joints in Concrete Masonry
• Control joints designed to control shrinkage cracking in masonry.

Spacing recommendations per ACI for Type I moisture controlled units.

Vertical S pacing of Joint Reinforcement

Recommended control None 24” 16” 8”

joint spacing

Ratio of panel length 2 2.5 3 4

to height, L/h

Panel length in feet 40 45 50 60

(not to exceed L regardless of H)

Cut spacing in half for Type II and reduce by one-third for solidly grouted walls.

Masonry Structures, Lectures 2-3, slide 78

Control Joints in Concrete Masonry

Control joints should be placed at:

– all abrupt changes in wall height
– all changes in wall thickness
– coincidentally with movement joints in floors, roofs and
foundations
– at one or both sides of all window and door openings

Masonry Structures, Lectures 2-3, slide 79

Control Joint Details for Concrete Masonry

paper grout fill

control joint unit

raked head joint
and caulk

Ref. NCMA TEK 10-2A Control Joints in Concrete Masonry Walls

Masonry Structures, Lectures 2-3, slide 80

Expansion Joints in Clay Masonry

Pressure-relieving or expansion joints

accommodate expansion of clay masonry.

expansion joint

Ref: Masonry Design and Detailing, Christine Beall, McGraw-Hill

BIA Tech. Note 18A Movement - Design and Detailing of Movement Joints, Part II

Masonry Structures, Lectures 2-3, slide 81

Spacing of Expansion Joints
For brick masonry:

W  [ 0.0002  0. 0000045( Tmax Tmin )] L

where W = total wall expansion in inches
0.0002 = coefficient of moisture expansion
0.0000043 = coefficient of thermal expansion
L = length of wall in inches
Tmax= maximum mean wall temperature, °F
Tmin = minimum mean wall temperature, °F
24 ,000( p )
S
Tmax  Tmin
S = maximum spacing of joints in inches
p = ratio of opaque wall area to gross wall area

Masonry Structures, Lectures 2-3, slide 82

Expansion Joint Details for Brick Veneer Walls

20 oz. copper silicone or butyl sealant

neoprene extruded plastic

Masonry Structures, Lectures 2-3, slide 83

Vertical Expansion of Veneer

flashing with
weep holes
rc
steel shelf beam
angle
1/4” to 3/8”
min. clearance
concrete block
compressible
filler
joint reinforcement
clay-brick or wire tie
veneer

Masonry Structures, Lectures 2-3, slide 84

Expansion Problems

In cavity walls, cracks can form at an external corner because the

outside wythe experiences a larger temperature expansion than the
inside wythe.

sun

Masonry Structures, Lectures 2-3, slide 85

Expansion Problems
• Diagonal cracks often occur between window and door openings if
differential movement is not accommodated.

Masonry Structures, Lectures 2-3, slide 86

Expansion Problems
• Clay-unit masonry walls or veneers can slip beyond the edge of a
concrete foundation wall because the concrete shrinks while the clay
masonry expands. As a result, cracks often form in the masonry at
the corner of a building.

Brick
Veneer

Concrete
Foundation

Masonry Structures, Lectures 2-3, slide 87

Expansion Problems
• Brick parapets are sensitive to temperature movements since they are
exposed to changing temperatures on both sides.

Elongation will be longer

than for wall below.
parapet sun

roof

Masonry Structures, Lectures 2-3, slide 88

End of Lessons 2 and 3

Masonry Structures, Lectures 2-3, slide 89