Masonry Design - TAMU

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ARCH 331Note Set 28.1Su2014abnMasonry DesignNotation: multiplier by effective depth ofmasonry section for moment arm, jdk multiplier by effective depth ofmasonry section for neutral axis, kdL name for length or span lengthM internal bending moment type of masonry mortarMm moment capacity of a reinforcedmasonry beam governed by steelstressMs moment capacity of a reinforcedmasonry beam governed by masonrystressMSJC Masonry Structural Joint Counciln modulus of elasticity transformationcoefficient for steel to masonryn.a. shorthand for neutral axis (N.A.)N type of masonry mortarNCMA National Concrete MasonryAssociationO type of masonry mortarP name for axial force vector allowable axial load in columnsPar radius of gyrationS section modulus type of masonry mortarSx section modulus with respect to anx-axist name for thicknessT name for a tension forceTs tension force in the steelreinforcement for masonry designTMS The Masonry Societyw name for distributed loadβ1 coefficient for determining stressblock height, c, in masonry LRFDdesignε m strain in the masonryεs strain in the steelρ reinforcement ratio in masonrydesign name for area net area, equal to the gross areasubtracting any reinforcementAnv net shear area of masonryAs area of steel reinforcement inmasonry designAst area of steel reinforcement inmasonry column designACI American Concrete InstituteASCE American Society of Civil Engineersb width, often cross-sectionalC name for a compression forceCm compression force in the masonryfor masonry designCMU shorthand for concrete masonry unitd effective depth from the top of areinforced masonry beam to thecentroid of the tensile steele eccentric distance of application of aforce (P) from the centroid of a crosssectionfa axial stressfb bending stressfm calculated compressive stress inmasonry′fm masonry design compressive stressfs stress in the steel reinforcement formasonry designfv shear stressFa allowable axial stressFb allowable bending stressFs allowable tensile stress inreinforcement for masonry designFt allowable tensile stressFv allowable shear stressFvm allowable shear stress of themasonryFvs allowable shear stress of the shearreinforcementh name for height effective height of a wall or columnIx moment of inertia with respect to anx-axisjAAn1

ARCH 331Note Set 28.1Su2014abnReinforced Masonry DesignStructural design standards for reinforced masonry are established by the Masonry StandardsJoint Committee consisting of ACI, ASCE and The Masonry Society (TMS), and presentsallowable stress design as well as limit state (strength) design.Materialsf’m masonry prism compressive strength from testingReinforcing steel grades are the same as those used for reinforced concrete beams.Units can be brick, concrete or stone.Mortar consists of masonry cement, lime, sand, and water. Grades are named from the wordMASONWORK, with average strengths of 2500psi, 1800 psi, 750 psi, 350 psi, and 75 psi,respectively.Grout is a flowable mortar, usually with a high amount of water to cement material. It is used tofill voids and bond reinforcement.Clay and concrete masonry units are porous, and their durability with respect to weathering is animportant consideration. The amount of water in the mortar is important as well as theabsorption capacity of the units for good bond; both for strength and for weatherproofing.Because of the moisture and tendency for shrinkage and swelling, it is critical to provide controljoints for expansion and contraction.SizesCommon sizes for claybrick and concretemasonry units (CMU) areshown in the figure,along with definitions.Standard Modular Clay Brick4 in. Normal Clay BrickTypical sectionproperties for CMU’s areprovided for reference atthe end of the document.Two Core Stretch UnitThree Core Stretch UnitAllowable Stress DesignFor unreinforced masonry, like masonry walls, tension stresses are allowed in flexure. Masonrywalls typically see compression stresses too.2

ARCH 331Note Set 28.1Su2014abnFor reinforced masonry, the steel is presumed to resist all tensile stresses and the tension in themasonry is ignored.Factors of Safety are applied to the limit stresses for allowable stress values:bending (unreinforced)bending (reinforced)bending (tension/unreinforced)beam shear (unreinforced for flexure)Fb 1/3 f m′Fb 0.45 f m′table 2.2.3.2Fv 1.5 f m′ 120 psibeam shear (reinforced) – M/(Vd) 0.25Fv 3.0beam shear (reinforced) – M/(Vd) 1.0Grades 40 or 50 reinforcementGrades 60 reinforcementWire joint reinforcementFv 2.0 f m′Fs 20 ksiFs 32 ksiFs 30 ksif m′where f’m specified compressive strength of masonryInternal Equilibrium for BendingCm compression in masonry stress x area f mb(kd )2Ts tension in steel stress x area AsfsSTRAINεmbCm Ts and STRESSfmCm fmb(kd)/2kdMm Ts(d-kd/3) Ts(jd)Ms Cm(jd)dn.a.jdtgroutAsεsfs/nMTs Asfsunitρ BIA Teknote 17 seriesAsbdΣF 0: A s f s fm bwherefm compressive stress in the masonry from flexurefs tensile stress in the steel reinforcementkd the height to the neutral axisb width of stress aread effective depth of section depth to n.a. of reinforcementjd moment arm from tension force to compression forceAs area of steeln Es/Em used to transform steel to equivalent area of masonry for elastic stressesρ reinforcement ratio3kd2

ARCH 331Note Set 28.1Su2014abnCriteria for Beam DesignFor flexure design:kdM m f mbjd 0.5 f m bd 2 jk or M s As f s jd ρbd 2 jf s2The design is adequate when f b Fb in the masonry and f s Fs .in the steel.Shear stress is determined by fv V/Anv where Anv is net shear area. Shear strength is determinedfrom the shear capacity of the masonry and the stirrups: Fv Fvm Fvs. Stirrup spacings arelimited to d/2 but not to exceed 48 in.where:1 P M ′ where M/(Vd) is positive and cannot exceed 1.0 f m 0.25 4.0 1.75 2 An Vd A Fd (Fv 3.0 f m′ when M/(Vd) 0.25 )Fvs 0.5 v s Anv s (Fv 2.0 f m′ when M(Vd) 1.0.) Values can be linearly interpolated.Fvm Load and Resistance Factor DesignThe design methodology is similar to reinforced concrete ultimate strengthdesign. It is useful with high shear values and for seismic design. The limitingmasonry strength is 0.80f’m.Criteria for Column Design(Masonry Joint Code Committee) Building Code Requirements and Commentary for MasonryStructures define a column as having b/t 3 and h/t 4.whereb width of the “wall”t thickness of the “wall”h height of the “wall”A slender column has a minimum dimension of 8” on one side and h/t 25.Columns must be reinforced, and have ties. A minimum eccentricity (causing bending) of 0.1times the side dimension is required.Allowable Axial Load for Reinforced Masonry h 2 ′Pa [0.25 f m An 0.65 Ast Fs ] 1 for h/t 99 140r 70r Pa [0.25 f m′ An 0.65 Ast Fs ] h 2for h/t 994

ARCH 331Note Set 28.1Su2014abnAllowable Axial Stresses for Unreinforced Masonry h 2 for h/t 99Fa 0.25 f m′ 1 140r 70r Fa 0.25 f m′ h 2for h/t 99whereh effective lengthr radius of gyrationAn effective (or net) area of masonryAst area of steel reinforcementf m′ specified masonry compressive strengthFs allowable compressive stress in column reinforcement with lateral confinement.Combined StressesWhen maximum moment occurs somewhere other than at the end of the column or wall, a“virtual” eccentricity can be determined from e M/P.Masonry Columns and WallsThere are no modification factors, but in addition to satisfyingfaf b 1.0 , the tensile stressFa Fbcannot exceed the allowable: f b f a Ft or the compressive stress exceed allowable forreinforced masonry: f a f b Fb provided f a Fa .5

ARCH 331Note Set 28.1Su2014abnExample 1Determine if the unreinforced CMU wall can sustain its loadswith the wind. Specify a mortar type and unit strength perMSJC.Mfaffb Fb 1 3 f m′ b 1.0SFa Fb2 h hFa 0.25 f m′ 1 for 99r 140r fa PA14-1B:2h 70r Fa 0.25 f m′ for 99r h 12 12in 2 h 12 ft ( 12in ) 44 .9 so Fa 0.25 f m′ 1 0.224 f m′r3.21in 140 3.21in fa 3.21”4k ( 1000 lb k ) 133 psi30in 2(1 ft kips/ft2) (ft)(in/ft)Mmax Pefb 1/3f’mf’m 154/(1/3) 462 psiMmax wL2/8M Pe/2psiMoment distribution Moment distribution fromfrom eccentricitydistributed wind load1;0.2241056 psi25 psi0.2241038 psi6f’m 1056 psi (governs)

ARCH 331Note Set 28.17Su2014abn

ARCH 331 Note Set 28.1 Su2014abn 4 Criteria for Beam Design For flexure design: jd . f bd jk kd Mm fmb m 0 5 2 2 or Ms As fs jd ρbd jf s 2 The design is adequate when fb Fb in the masonry and fs Fs.in the steel. Shear stress is determined by fv V/A nv where Anv is net shear area. Shear strength is determined