masonary design working stress

Amrhein, J. E. “Masonry Design” The Engineering Handbook. Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

© 1998 by CRC PRESS LLC

32Masonry Design

32.1 Basis of Design32.2 Masonry Materials32.3 Masonry Units

Clay Masonry • Solid Clay Units • Hollow Clay Units

32.4 Concrete MasonryHollow Load Bearing Concrete Masonry Units

32.5 MortarTypes of Mortar

32.6 Grout32.7 Unreinforced Masonry32.8 Strength of Masonry

Modulus of Elasticity • Specified Compressive Strength • Reinforcing Steel

32.9 Design of Reinforced Masonry MembersWorking Stress Design • Flexural Design • Moment Capacity of a Section • Shear • Columns

32.10 Design of Structural MembersStrength DesignGeneral • Strength Design Procedure • Strength Design for Sections with Tension Steel Only

James E. AmrheinMasonry Institute of America

Masonry structures have been constructed since the earliest days of mankind, not only for homesbut also for works of beauty and grandeur. Stone was the first masonry unit and was used forprimitive but breathtaking structures, such as the 4000-year-old Stonehenge ring on England'sSalisbury Plains. Stone was also used around 2500 B.C. to build the Egyptian pyramids in Giza. The1500-mile (2400-km) Great Wall of China was constructed of brick and stone between 202 B.C. and220 A.D.

Masonry has been used worldwide to construct impressive structures, such as St. Basil'sCathedral in Moscow, the Taj Mahal in Agra, India, as well as homes, churches, bridges, androads. In the U.S., masonry was used from Boston to Los Angeles and has been the primarymaterial for building construction from the 18th to the 20th centuries.

Currently, the tallest reinforced masonry structure is the 28-story Excalibur Hotel in Las Vegas,Nevada. This large high-rise complex consists of four buildings, each containing 1008 sleepingrooms. The load-bearing walls for the complex required masonry with a specified compressivestrength of 4000 psi (28 MPa).


Tallest concrete masonry building in the world, Excalibur Hotel, Las Vegas,Nevada

The Great Wall of China.

32.1 Basis of DesignThis chapter is based on the specification of materials, construction methods, and testing as givenin the ASTM standards. The design parameters are in accordance and reprinted with permissionfrom Building Code Requirements and Commentary for Masonry Structures (ACI 530, ASCE 5,TMS 402).

In addition, the Uniform Building Code, published by the International Conference of BuildingOfficials, provides requirements and recommendations for the design and construction of masonrysystems both unreinforced (plain) and reinforced. (See Table 32.1.)


D = Dead load or related internal moments and forces.e = Eccentricity of axial load, in.Em = Modulus of elasticity of masonry in compression, psi.Es = Modulus of elasticity of steel, psi.f = Calculated stress on section.fa = Calculated compressive stress in masonry due to axial load only, psi.fb = Calculated compressive stress in masonry due to flexure only; psi.f 0m = Specified compressive strength of masonry, psi.fs = Calculated tensile or compressive stress in reinforcement, psi.ft = Calculated tension stress on masonry, psi.fv = Calculated shear stress in masonry, psi.fy = Specified yield stress of steel for reinforcement and anchors, psi.Fa = Allowable compressive stress due to axial load only, psi.Fb = Allowable compressive stress due to flexure only, psi.Fs = Allowable tensile or compressive stress in reinforcement, psi.Fv = Allowable shear stress in masonry, psi.h = Effective height of column, wall, or pilaster, in.I = Moment of inertia of masonry, in:4

j = Ratio of distance between centroid of flexural compressive forces and centroid of tensile forces to depth,d.k = Ratio of depth of stress block to depth of section.l = Clear span between supports.L = Live load or related internal moments and forces.M = Maximum moment occurring simultaneously with design shear force V at the section underconsideration, in.-lb.n = Ratio of the modulus of elasticity of steel to the modulus of elasticity of masonry.p = Ratio of tensile steel area to total area of section, bd.P = Design axial load, lb.Pu = Factored load on section, strength design.r = Radius of gyration, in.s = Spacing of reinforcement, in.S = Section modulus.t = Nominal thickness of wall.T = Total tension force on section.v = Shear stress, psi.V = Design shear force.w = Load or weight per unit length or area.W = Wind load or related internal moments and forces or total uniform load.

ab = Depth of stress block for balanced strength design conditions.A = Area of compression area for walls or columns.An = Net cross-sectional area of masonry, in.2

As = Area of tension steel.Ase = Equivalent area of tension steel considering effect of vertical load.Av = Cross-sectional area of shear reinforcement, in:2

b = Width of section, in:2

bw = Width of wall beam.cb = Depth to neutral axis for balanced strength design conditions.C = Total compression force.d = Distance from extreme compression fiber to centroid of tension reinforcement, in.

Table 32.1 Notation


The masonry units considered are clay brick, concrete brick, hollow clay bricks, and hollowconcrete blocks. Masonry units are available in a variety of sizes, shapes, colors, and textures.

Clay MasonryClay masonry is manufactured to comply with the ASTM C 62, Specification for Building Brick(Solid Masonry Units Made From Clay or Shale); C 216, Specification for Facing Brick (SolidMasonry Units Made From Clay or Shale); and C 652, Specification for Hollow Brick (HollowMasonry Units Made From Clay or Shale). It is made by firing clay in a kiln for 40 to 150 hours,depending upon the type of kiln, size and volume of the units, and other variables. For buildingbrick and face brick the temperature is controlled between 1600±F (870±C ) and 2200±F (1200±C ),whereas the temperature ranges between 2400±F (1315±C ) and 2700±F (1500±C ) for fire brick.

Solid Clay UnitsA solid clay masonry unit, as specified in ASTM C 62 and C 216, is a unit whose netcross-sectional area, on every plane parallel to the bearing surface, is 75% or more of its grosscross-sectional area measured in the same plane. A solid brick may have a maximum coring of25%. See Fig. 32.1.

Figure 32.1 Solid clay brick.

Hollow Clay UnitsA hollow clay masonry unit, as specified in ASTM C 652, is a unit whose net cross-sectional areain every plane parallel to the bearing surface is less than 75% of its gross cross-sectional areameasured in the same plane. See Fig. 32.2.

32.3 Masonry Units

32.2 Masonry MaterialsThe principal materials used in plain masonry are the masonry units, mortar plus grout, andreinforcing steel for reinforced masonry. These materials are assembled into homogeneousstructural systems.


32.4 Concrete MasonryConcrete masonry units for load-bearing systems can be either concrete brick as specified byASTM C 55, Specification for Concrete Building Brick, or hollow load-bearing concrete masonryunits as specified by ASTM C 90, Specification for Hollow Load-Bearing Concrete MasonryUnits.

Concrete brick and hollow units are primarily made from portland cement, water, and suitableaggregates with or without the inclusion of other materials and may be made from lightweight ornormal weight aggregates or both.

Hollow Load Bearing Concrete Masonry UnitsASTM C 90-90, Specification for Load Bearing Concrete Masonry Units, requires all load-bearingconcrete masonry units to meet the requirements of Grade N designation. The types of hollowconcrete units are

Type I. For moisture-controlled concrete brick.Type II. Non−moisture-controlled units need not meet water absorption requirements.

32.5 MortarMortar is a plastic mixture of materials used to bind masonry units into a structural mass. It is usedfor the following purposes:

1. It serves as a bedding or seating material for the masonry units. 2. It allows the units to be leveled and properly placed. 3. It bonds the units together. 4. It provides compressive strength. 5. It provides shear strength, particularly parallel to the wall. 6. It allows some movement and elasticity between units.

Figure 32.2 Hollow clay brick.


7. It seals irregularities of the masonry units. 8. It can provide color to the wall by using color additives. 9. It can provide an architectural appearance by using various types of

joints.

Types of MortarThe requirements for mortar are provided in ASTM C 270, Mortar for Unit Masonry. There arefour types of mortar, which are designated M, S, N, and O. The types are identified by every otherletter of the word MaSoNwOrk.

Proportion specifications limit the amount of the constituent parts by volume. Water content,however, may be adjusted by the mason to provide proper workability under various fieldconditions. The most common cement-lime mortar proportions by volume are:

Type M mortar. 1 portland cement; 1/4 lime; 3 1/2 sandType S mortar. 1 portland cement; 1/2 lime; 4 1/2 sandType N mortar. 1 portland cement; 1 lime; 6 sandType O mortar. 1 portland cement; 2 lime; 9 sand

32.6 GroutGrout is a mixture of portland cement, sand pea gravel, and water mixed to fluid consistency sothat it will have a slump of 8 to 10 inches (200 to 250 mm). Requirements for grout are given inASTM C 476, Grout for Masonry.

Grout is placed in the cores of hollow masonry units or between wythes of solid units to bind thereinforcing steel and the masonry into a structural system. Additionally, grout provides:

1. More cross-sectional area, allowing a grouted wall to support greater vertical and lateralshear forces than a nongrouted wall

2. Added sound transmission resistance, thus reducing the sound passing through thewall

3. Increased fire resistance and an improved fire rating of the wall 4. Improved energy storage capabilities of a wall 5. Greater weight, thus improving the overturning resistance of retaining

walls

32.7 Unreinforced MasonryUnreinforced masonry considers the tensile resistance of masonry for the design of structures. Theeffects of stresses in reinforcement, if present, are neglected and all forces and moments areresisted by the weight of the masonry and the tension and compression capabilities of the system.

The stress due to flexural moment is ft = OAM=S , where M is the moment on the wall and S is


the section modulus. The condition is generally limited to the allowable flexural tension stressshown in Table 32.2.

Table 32.2 Allowable Flexural Tension for Clay and Concrete Masonry, psi* (kPa)

Mortar TypesPortland Cement/Lime Masonry Cement and Air-Entrained Portland

Cement LimeMasonry Type M or S kPa N kPa M or S kPa N kPa

Normal to bed jointsSolid units 40 276 30 207 24 166 15 103

Hollow units*

Ungrouted 25 172 19 131 15 103 9 62Fully grouted 68 470 58 400 41 283 26 180

Parallel to bed joints in running bondSolid units 80 550 60 415 48 330 30 207

Hollow unitsUngrouted and

partially grouted50 345 38 262 30 207 19 131

Fully grouted 80 550 60 415 48 330 30 207*For partially grouted masonry allowable stresses shall be determined on the basis of linear interpolation between

hollow units, which are fully grouted or ungrouted, and hollow units based on amount ofgrouting.

Example 32.1Thickness of Unreinforced Masonry Wall. An unreinforced building wall is10 ft (3 m) high and spans between footing and roof ledger. It could be subjected to a wind force of15 psf (103 kPa) should an 800 (200 mm) CMU wall or a 1200 (300 mm) CMU wall be used.Solution:

Moment on wallAssumed pinned top and bottom

M =wh2

8=

15 ¢ 1028

= 187:5 ft ¢ lb =ft (834 N ¢m=m)

Allowable tension stress type M or S mortar = 25 psi (172 kPa)Stress may be increased 1/3 due to temporary wind force

S =M

1:33ft=

187:5 £ 12

1:33 £ 25= 67:5 in: 3(1:1 ¢ 106 mm3)

For section modulus at 800 (200 mm) CMU (see Fig. 32.3):


I = 2

·bd3

12+ bdx2

¸= 2

·12£ 1:253

12+ 12 £ 1:25 £ 3:18752

¸

= 2 [1:95 + 152:40] = 308:7 in: 4(128:5 ¢ 106 mm4)

S =308:7 £ 2

7:625= 81 in: 3(1:3 ¢ 106 mm 3)

At 1200 (300 mm) CMU (see Fig. 32.4):

I = 2

·bd3

12+ bdx2

¸

= 2

·12 £ 1:53

12+ 12£ 1:5 £ 5:06252

¸

= 2 [3:375 + 461:3] = 929:4 in: 4 (386:8 ¢ 106 mm4)

S =I

t=2=

2£ 929:4

11:625= 159:9 in: 3(2:6 ¢ 106 mm3)

Thus, 800 CMU = 81:0 in: 3 (1:3 ¢ 106 mm3 ); 1200 CMU = 159:9 in: 3 (2:6 ¢ 106 mm3 ). Use 800

(200 mm) CMU.

Figure 32.3 Plan cross section of 800 CMU wall, face shells only.


Figure 32.4 Plan cross section of 1200 CMU wall, face shells only.

Example 32.2 Vertical and Lateral Load on Unreinforced Masonry Wall. If a wall issubjected to a 20 psf (958 kPa) wind, and is 15 ft (4.6 m) high, and carries 2000 plf (96 kPa), whatthickness concrete masonry unit should be used?Solution:

M =wh2

8=

20 £ 152

8= 563 ft ¢ lb/ft (2500 N ¢ m/m)

Try 800 (200 mm) CMU.


S = 81 in: 3(1:3 ¢ 106 mm3)

P

A§ M

S=

2000

2 £ 12 £ 1:25§ 563 £ 12

81

= 66:7 § 83

= 150 psi compression (1:0 MPa )

= 16:3 psi tension (115 kPa )

Tension is less than 25 £ 43= 33:3 psi (230 kPa) allowable tension, so 800 (200 mm) CMU is

satisfactory.

32.8 Strength of MasonryThe ultimate compressive strength of the masonry assembly is given the symbol f 0

mu to distinguishit from the specified compressive strength f 0

m .

Modulus of ElasticityFor steel reinforcement, Es = 29 000 000 psi (199 955 MPa). For concrete masonry, see Table32.3.

Table 32.3 Modulus of Elasticity for Concrete Masonry*

Net Area CompressiveStrength ofUnits

Em for Type N Mortar Em for Type M or S Mortar

psi MPa psi £ 106¤ MPa £ 103 psi £ 106¤ MPa £ 103

6000 andgreater

41.4 3.5 24.5

5000 34.5 2.8 19.6 3.2 22.44000 27.6 2.6 18.2 2.9 20.33000 20.7 2.3 16.1 2.5 17.52000 13.8 1.8 12.6 2.2 15.41500 10.3 1.5 10.5 1.6 11.2

*Linear interpolation permitted.

Specified Compressive StrengthFor specified compressive strength of concrete masonry, see Table 32.4.


Type M or S mortar Type N mortarpsi* MPa psi* MPa psi* MPa

1250* (8.5)** 1300 9.0 1000 6.91900 (13.0) 2150 14.6 1500 10.32800 (19.3) 3050 20.6 2000 13.83750 (26.0) 4050 27.6 2500 17.24800 (33.1) 5250 36.5 3000 20.7

*For units of less than 4 in. (100 mm) height, 85% of the values listed.Note: Compressive strength based on the compressive strength of concrete masonry units and type of mortar used

in construction.

Reinforcing SteelReinforcing steel in masonry has been used extensively in the West since the 1930s, revitalizingthe masonry industry in earthquake-prone areas. Reinforcing steel extends the characteristics ofductility, toughness, and energy absorption that are so necessary in structures subjected to thedynamic forces of earthquakes.

Reinforcing steel may be either Grade 40, with a minimum yield strength of 40 000 psi (276MPa), or Grade 60, minimum yield strength of 60 000 psi (414 MPa).

Allowable stresses for reinforcing steel are as follows. Tension stress in reinforcement shall notexceed the following:

Grade 40 or Grade 50 reinforcement 20 000 psi (138 MPa)Grade 60 reinforcement 24 000 psi (165MPa)Wire joint reinforcement 30 000 psi (207MPa)

Compression stress has these restrictions:

1. The compressive resistance of steel reinforcement is neglected unless lateral reinforcement isprovided to tie the steel in position.

2. Compressive stress in reinforcement may not exceed the lesser of 0:4fy or 24 000 psi (165MPa).

32.9 Design of Reinforced Masonry Members

Working Stress DesignReinforced masonry members are designed by elastic analysis using service loads and permissiblestresses, which considers that the reinforcing steel resists tension forces and the masonry and groutresists compression forces.

The design and analysis of reinforced masonry structural systems have been by the straight line,elastic working stress method. In working stress design (WSD), the limits of allowable stress for

Net Area Compressive Strength for Concrete Masonry Units Net Area Compressive Strength ofMasonry, f 0

m (specified)

Table 32.4 Compressive Strength of Concrete Masonry


the materials are established based on the properties of each material.The procedure presented is based on the working stress or straight line assumptions where all

stresses are in the elastic range and:

1. Plane sections before bending remain plane during and after bending. 2. Stress is proportional to strain, which is proportional to distance from the neutral

axis. 3. Modulus of elasticity is constant throughout the member. 4. Masonry carries no tensile stresses. 5. Span of the member is large compared to the depth. 6. Masonry elements combine to form a homogeneous and isotropic member. 7. External and internal moments and forces are in equilibrium. 8. Steel is stressed about the center of gravity of the bars equally. 9. The member is straight and of uniform cross section.

Flexural DesignThe basis of the flexural equations for working stress design, WSD, is the concept of the modularratio. The modular ratio, n, is the ratio of the modulus of elasticity of steel, Es , to the modulus ofelasticity of masonry, Em .

n =Es

Em

By use of the modular ratio, n, the steel area can be transformed into an equivalent masonry area.The strain is in proportion to the distance from the neutral axis and therefore the strain of the steelcan be converted to stress in the steel. In order to establish the ratio of stresses and strains betweenthe materials, it is necessary to locate the neutral axis.

The location of the neutral axis is defined by the dimensions, kd , which is dependent on themodular ratio, n, and the reinforcing steel ratio, p = As=bd . For a given modular ratio, n, theneutral axis can be raised by decreasing the amount of steel (reducing p) or lowered by increasingthe amount of steel (increasing p). See Figs. 32.5 and 32.6. Solving for k,

k =p

(np)2 + 2np ¡ np


Figure 32.5 Location of neutral axis for a beam.

Figure 32.6 Location of neutral axis for a wall, in plane of wall.


Moment Capacity of a SectionThe moment capacity of a reinforced structural masonry wall or beam can be limited by theallowable masonry stress (overreinforced), allowable steel stress (underreinforced), or both, inwhich case it would be a balanced design condition.

When a member is designed for the specified loads and the masonry and reinforcing steel arestressed to their maximum allowable stresses, the design is said to be a "balanced" design. Thisbalanced design is different from the balanced design for the strength design method. For workingstresses, balanced design occurs when the masonry is stressed to its maximum allowablecompressive stress and the steel is stressed to its maximum allowable tensile stress.

However, in many cases, the "balanced" design does not satisfy the conditions for the materialsavailable or for the predetermined member size or the economy of the project. It may beadvantageous to understress (underreinforce) the masonry or understress (overreinforce) the steelso that the size of the member can be maintained.

The moment capability of a section based on the steel stress is defined asMs = force £moment arm, where:

Force in the steel, T = Asfs = pbdfsMoment arm = jdMs = T £ jd = AsfsjdMs = pbdfsjd = fspjbd

2

The moment capability of a section based on the masonry stress is defined asMm = force £moment arm, where:

Force in the masonry, C = 12fb(kd)b =

12fbkbd

Moment arm = jdMm = C £ jd = (1

2fbkbd) £ (jd)

Mm = 12fbkjbd

2

Example 32.3Determination of Moment Capacity of a Wall. A partially grouted 800 (200mm) concrete masonry wall with type S mortar is reinforced with #5 bars at 3200 (813 mm) o.c. Thesteel is 5:300 (135 mm) from the compression face and is Grade 60. If f 0

m = 2500 psi (17.2 MPa),what is the moment capacity of the wall?Solution: For f 0

m = 2500 psi (17.2 MPa),

Fb = 0:33f 0m = 833 psi (5:6 MPa ) max. allowable compression

Em = 2400 000 psi (16 550 MPa ) (see Table 32.3)Also, for fy = 60 000 psi (414 MPa),

Fs = 24 000 psi (165 MPa ) max. allowable tensionEs = 29 000 000 psi (199 955 MPa )

For steel ratio,


p =As

bd

=0:31

32 £ 5:3= 0:0018

For modular ratio,

n =Es

Em

=29 000 000

2 400 000= 12:1

Furthermore,

np = 12:1 £ 0:0018 = 0:022

k =p

(np)2 + 2n ¡ np

=p

(0:022)2 + 2£ 0:0022 ¡ 0:022

= 0:189

kd = 0:189 £ 5:3 = 1:00 in: (25 mm)

The neutral axis falls on the shell of CMU.

j = 1 ¡ k

3= 1¡ 0:189

3= 0:937

Mm = 12fbkjbd

2 = 12(833)(0:189)(0:937)(12)(5:3)2

= 24 863 in.-lb /ft (9027 N ¢m=m )

= 2:07 ft k=ft (8940 N ¢m=m )

Ms = fspjbd2 = 24 000(0:0021)(0:937)(12)(5:3)2

= 15 918 in.-lb /ft (5800 N ¢m=m )

= 1:33 ft k=ft (5800 N ¢m=m ) Ã Controls


ShearStructural elements such as walls, piers, and beams are subjected to shear forces as well as flexuralstresses. The unit shear stress is computed based on the formula

fv =V

bjd

Beam ShearWhen masonry flexural members are designed to resist shear forces without the use of shearreinforcing steel, the calculated shear stress is limited to 1:0(f 0

m)1=2 , 50 psi max. If the unit shear

stress exceeds the allowable masonry shear stress, all the shear stress must be resisted byreinforcing steel.

For flexural members with reinforcing steel resisting all the shear forces, the maximumallowable shear stress is 3:0(f 0

m )1=2 psi with 150 psi as a maximum. The steel resists the shear bytension and it must be anchored in the compression zone of the beam or the wall.

The unit shear, fv , is used to determine the shear steel spacing based on the formula:

Spacing, s =AvFs

fvb

Unit shear stress, fv =AvFs

bs

For continuous or fixed beams, the shear value used to determine the shear steel spacing may betaken at a distance d=2 from the face of the support. The shear value at the face of the supportshould be used to calculate the shear steel spacing in simple beams.

The maximum spacing of shear steel should not exceed d=2 . The first shear-reinforcing barshould be located at half the calculated spacing but no more than d=4 from the face of support.

ColumnsColumns are vertical members that basically support vertical loads. They may be plain masonry orreinforced masonry. Reduction in the load-carrying capacity is based on the h=r ratio, where h isthe unbraced height and r is the minimum radius of gyration for the unbraced height.

The reduction factor for members having an h=r ratio not exceeding 99 is [1 ¡ (h=140r)2] . Formembers with an h=r greater than 99 the factor is (70r=h)2 . The maximum allowable axial stressfor walls or plain columns is Fa = 1

4f 0m times the reduction factor.

The maximum allowable axial load on a reinforced masonry column is:

Pa = (0:25f 0mAe + 0:65AsFsc ) (reduction factor)

and is limited to Pa · 1=4Pe , where


Pe =¼2EmI

h2

³1 ¡ 0:577

e

r

´ 3

The maximum allowable unit axial stress is Fa = Pa=Ae .The reduction factor based on the h=r ratio is the same for reinforced columns and for walls.

The same consideration is made for the determination of the effective height, h.The effective thickness, t, is the specified thickness in the direction considered. For

nonrectangular columns the effective thickness is the thickness of a square column.

32.10 Design of Structural MembersStrength Design

GeneralThe structural design of reinforced masonry is changing from the elastic working stress method tostrength design procedures.

The concept of strength design states that, when a reinforced masonry section is subjected tohigh flexural moments, the masonry stress from the neutral axis to the extreme compression fibersconforms to the stress-strain curve of the materials as if it were being tested in compression. SeeFig. 32.7.

Figure 32.7 Stress due to flexural moment for balanced condition.

It also states that when the tension reinforcing reaches its yield stress, it will continue to elongatewithout an increase in moment or forces. This condition occurs at the yield plateau of the steel asshown on the stress-strain curve in Fig. 32.8.

The compressive stress block of the masonry, as shown in Fig. 32.9, is simplified from thecurved or parabolic shape to a rectangular configuration. This rectangular stress block, which iscalled Whitney's stress block, is approximated as having a length of a and a height of 0.85 f 0

m .


Figure 32.8 Idealized stress-strain diagram for reinforcing steel.

Figure 32.9 Assumed stress block at yield condition.

Masonry systems have compression stress-strain curves similar to those of concrete, in that thecurves are curved or parabola-shaped and that they reach a strain of at least 0.003. Accordingly,the parameters of reinforced concrete strength design are being adopted with minor changes formasonry design.

Strength Design ProcedureThere are two conditions included in strength design: load parameters and design parameters.

Load ParametersService or actual loads are generally used for working stress design procedures. For strengthdesign procedures, the actual or specified loads are increased by appropriate load factors. Theseload factors consider live and dead load, wind, earthquake, temperature, settlement, and earthpressure.

In addition to load factors, a capacity reduction factor, Á, is used to adjust for the lack of perfectmaterials, strength, and size. The phi factor also varies for the stress considered, whether flexuralor shear.


3. The masonry strain is limited to 0.003 in./in. 4. The steel ratio, p, is limited to 50% of the balanced reinforcing ratio, pb , to ensure that a

ductile mechanism forms prior to brittle, crushing behavior.

Strength Design for Sections with Tension Steel OnlyAs stated above, the limits for flexural design using strength methods are that the stress in the steelis at yield strength and that the strain in the masonry is at 0.003. When these conditions occur atthe same moment, the section is considered to be a balanced design. See Figure 32.10.

Figure 32.10 Strain and stress distribution on a flexural member, balanced design.

The depth to the neutral axis, cb , for a balanced design is

cb =0:003

0:003 + fy=Es

d =87 000

87 000 + fyd

Defining Terms

Allowable work stress design or elastic design: A technique based on and limiting the stress inthe structural element to a value that is always in the elastic range.

Brick: Solid unit · 25% void; hollow unit > 25% < 75% void.Grout: Material to tie reinforcing steel and masonry units together to form a structural systemModular ratio: Ratio between the modulus of elasticity of steel to the modulus of elasticity of

masonry.Mortar: Plastic material between units in bed and head joints.Steel ratio: Area of steel to area of masonry.Strength design: A technique based on capacity of structural section considering the maximum

strain in masonry, yield strength of steel, load factors for various loads considered, and phi

Design ParametersThe parameters for strength design are as follows:

1. The steel is at yield stress. 2. The masonry stress block is rectangular.


factors for materials and workmanship.

References

Amrhein, J. E. 1994. Reinforced Masonry Engineering Handbook, 5th ed. Masonry Institute ofAmerica, Los Angeles, CA.

Beall, C. 1984. Masonry Design and Detailing. Prentice Hall, Englewood Cliffs, NJ.Drysdale, R. G., Hamid, A. A, Baker, L. R. 1993. Masonry Structures, Behavior and

Design. Prentice Hall, Englewood Cliffs, NJ.Schneider, R. A., Dickey, W. L. 1987. Reinforced Masonry Design, 2nd ed. Prentice Hall,

Englewood Cliffs, NJ.

Further Information

ACI. 1992. Building Code Requirements and Commentary for Masonry Structures; Specificationsfor Masonry Structures; Commentaries. American Concrete Institute, American Society ofCivil Engineers, and The Masonry Society, Detroit, MI.

Matthys, J. H. (Ed.) 1993. Masonry Designers Guide 1993. ACI, ASCE, and TMS.Uniform Building Code. 1994. International Conference of Building Officials, Whittier, CA.


masonary design working stress

Documents

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