ARCH 631 Note Set 23.1 S2017abn. Masonry Design

Transcription

1 Masonry Design Notation: A = nae for area An = net area, equal to the gross area subtracting any reinforceent Anv = net shear area of asonry As = area of steel reinforceent in asonry design Ast = area of steel reinforceent in asonry colun design Av = area of concrete shear stirrup reinforceent ACI = Aerican Concrete Institute ASCE = Aerican Society of Civil Engineers b = width, often cross-sectional = total width of aterial at a horizontal section C = copression force in the asonry for asonry design CMU = shorthand for concrete asonry unit d = effective depth fro the top of a reinforced asonry bea to the centroid of the tensile steel D = shorthand for dead load e = eccentric distance of application of a force (P) fro the centroid of a cross section E = shorthand for earthquake load E = odulus of elasticity of asonry Es = odulus of elasticity of steel fa = axial stress fb = bending stress f = calculated copressive stress in asonry fv f f s Fa Fb Fs Ft Fv Fv = asonry design copressive stress = stress in the steel reinforceent for asonry design = shear stress = allowable axial stress = allowable bending stress = allowable tensile stress in reinforceent for asonry design = allowable tensile stress = allowable shear stress = allowable shear stress of the asonry Fvs = allowable shear stress of the shear reinforceent h = nae for height = effective height of a wall or colun In = oent of inertia of the net section j = ultiplier by effective depth of asonry section for oent ar, jd k = ultiplier by effective depth of asonry section for neutral axis, kd K = type of asonry ortar L = shorthand for live load M = internal bending oent = type of asonry ortar M = oent capacity of a reinforced asonry bea governed by steel stress Ms = oent capacity of a reinforced asonry bea governed by asonry stress MSJC = Masonry Structural Joint Council n = odulus of elasticity transforation coefficient for steel to asonry n.a. = shorthand for neutral axis (N.A.) N = type of asonry ortar NCMA = National Concrete Masonry Association O = type of asonry ortar P = nae for axial force vector Pa = allowable axial load in coluns Pe = critical (Euler) buckling load Q = first area oent about a neutral axis r = radius of gyration s = spacing of stirrups in reinforced asonry S = type of asonry ortar = section odulus t = nae for thickness Ts = tension force in the steel reinforceent for asonry design TMS = The Masonry Society V = internal shear force W = shorthand for wind load 485

2 1 s = coefficient for deterining stress block height, c, in asonry LRFD design = strain in the asonry = strain in the steel b = reinforceent ratio in asonry design = balanced reinforceent ratio in asonry design = suation sybol Masonry Design Structural design standards for reinforced asonry are established by the Masonry Standards Joint Coittee consisting of ACI, ASCE and The Masonry Society (TMS), and presents allowable stress design as well as liit state (strength) design. Materials Masonry ortars are ixtures of water, asonry ceent, lie, and sand. The strengths are categorized by letter designations (fro MaSoNwOrK). f = asonry pris test copressive strength Designation strength range M 500 psi S 1800 psi N 750 psi O 350 psi K 75 psi Grout is a flowable ortar, usually with a high aount of water to ceent aterial. It is used to fill voids and bond reinforceent. Defored reinforcing bars coe in grades 40, 50 & 60 (for 40 ksi, 50 ksi and 60 ksi yield strengths). Sizes are given noinally as # of 1/8. Clay and concrete asonry units are porous, and their durability with respect to weathering is an iportant consideration. The aount of water in the ortar is iportant as well as the absorption capacity of the units for good bond; both for strength and for weatherproofing. Because of the oisture and tendency for shrinkage and swelling, it is critical to provide control joints for expansion and contraction. Sizes Coon sizes for clay brick and concrete asonry units (CMU) are shown in the figure, along with definitions. Typical section properties for CMU s are provided for reference at the end of the docuent. 486 Standard Modular Clay Brick Two Core Stretch Unit 4 in. Noral Clay Brick Three Core Stretch Unit

3 Masonry Walls Masonry walls can be reinforced or unreinforced, grouted or ungrouted, single wythe or cavity, prestressed or not. Cavity walls will require ties to force the two walls separated by the cavity to act as one. Fro centuries of practice, the height to thickness ratio is liited because of slenderness (h/t < 5 or 35 depending on code). Most walls will see bending fro wind or eccentricity along with bearing (cobined stresses). Allowable Stresses If tension stresses result, the allowable tensile strength for unreinforced walls ust not be exceeded. These are relatively low (40 70 psi) and are shown in Table..3.. If copression stresses result, the allowable strength (in bending) for unreinforced asonry Fb =1/3 f If copression stresses result, the allowable strength (in bending) for reinforced asonry Fb =0.45 f Shear stress in unreinforced asonry cannot exceed Fv = 1. 5 f 10 psi. Shear stress in reinforced asonry for M/(Vd) 0.5 cannot exceed Fv = 3.0 Shear stress in reinforced asonry for M/(Vd) 1.0 cannot exceed Fv =.0 f Allowable tensile stress, Fs, in grades 40 & 50 steel is 0 ksi, grade 60 is 3 ksi, and wire joint reinforceent is 30 ksi. where f = specified copressive strength of asonry f (F t) (PCL) 487

4 Loads on Lintels in Masonry Walls Arching action is present in asonry walls when there is an opening and sufficient wall width on either side of the opening to resist the arch thrust. A lintel is required to support the weight of the wall aterial above the opening. When arching action is present, the weight that ust be supported can be deterined fro a 45 degree angle. This area ay be a triangle, or trapezoid if the wall height above the lintel is less than half the opening width. The distributed load is calculated as height x wall thickness x specific weight of the asonry. When there are concentrated loads on the wall, the load can be distributed to a width at the lintel height based on a 60 degree angle. Reinforced Masonry Mebers For stress analysis in asonry flexural ebers the strain is linear the copressive stress in the asonry is linear the tensile stress in the steel is not at yield any asonry in tension is assued to have no strength the steel can be in tension, and is placed in the botto of a bea that has positive bending oent Load Cobinations D D+L D (Lr or S or R) D L (Lr or S or R) D + (0.6W or 0.7E) D L (0.6W) (Lr or S or R) D L (0.6W) (Lr or S or R) 0.6D + 0.6W 0.6D + 0.7E 488

5 Internal Equilibriu t d b grout unit n.a. As kd s STRAIN STRESS f C=fb(kd)/ jd M fs/n Ts=Asfs BIA Teknote 17 series C = copression in asonry = stress x area = Ts = tension in steel = stress x area = Asfs b(kd) f C = Ts and M = Ts(d-kd/3) = Ts(jd) and Ms =C(jd) where f = stress in ortar at extree fiber kd = height to neutral axis b = width of section fs = stress in steel at d A s = area of steel reinforceent d = depth to n.a. of reinforceent j = (1 k/3) For flexure design: M M or Ms so, M =T(jd) = 0.5fbd jk and Ms = C(jd) = bd jfs The design is adequate when fb Fb in the asonry and s Fs f in the steel. Shear Strength Shear stress is deterined by fv = V/Anv where Anv is net shear area. Shear strength is deterined fro the shear capacity of the asonry and the stirrups: Fv = Fv + Fvs. Stirrup spacings are liited to d/ but not to exceed 48 in. where: 1 M P Fv f 0.5 Vd An AvF sd Fvs 0.5 Anvs where M/(Vd) is positive and cannot exceed 1.0 (F v = 3.0 f when M/(Vd) 0.5 ) (F v =.0 f when M/(Vd) 1.0) Values can be linearly interpolated. 489

6 Reinforceent Ratio The aount of steel reinforceent is liited. Too uch reinforceent, or over-reinforced will not allow the steel to yield before the concrete crushes and there is a sudden failure. A bea with the proper aount of steel to allow it to yield at failure is said to be under reinforced. As The reinforceent ratio is a fraction: ρ and ust be less than b where the balanced bd reinforceent ratio is a function of steel strength and asonry strength. Flexure Design of Reinforceent One ethod is to choose a reinforceent ratio, find steel area, check stresses and oent: 1. find b and assue a value of b M. find k, j and calculate bd where Fs is allowed stress in steel. jfs Choose nice b & d values. M 3. find As Fs jd 3. check design for M < Ms = AsFs (jd) M 4. check asonry flexural stress against allowable: f F b 0. 5bd jk Load and Resistance Factor Design The design ethodology is siilar to reinforced concrete ultiate strength design. It is useful with high shear values and for seisic design. The liiting asonry strength is 0.80f. 490

7 Force-Moent Interaction Cobined stresses and the reduction of axial load with oent is siilar to that for reinforced concrete colun design as shown in the interaction diagra: Reinforceent is typically placed in the center of walls. Grouting is placed in hollows with reinforcing, while other hollows ay be epty. Stirrups are avoided. Biaxial bending can occur in coluns and stresses ust satisfy: fa fb 1 Fa Fb When axiu oent occurs soewhere other than at the end of the colun or wall, a virtual eccentricity can be deterined fro e = M/P. Masonry Coluns Coluns are classified as having b/t < 3 and h/t > 4. Slender coluns have a iniu side diension of 8 and ust have h/t 5. They ust be designed with an eccentricity of 10% of fa fb the side diension, and satisfy the interaction relationship of 1, the tensile stress F F cannot exceed the allowable: fb fa Ft and the copressive stress exceed allowable for reinforced asonry: fa fb Fb provided fa Fa. For purely axial loading, the capacity Pa depends on the slenderness ratio of h/r: Allowable Axial Load for Reinforced Masonry h Pa 0.5 f An 0.65AstFs 1 140r 491 for h/t 99 70r Pa 0.5 f An 0.65AstFs for h/t > 99 h Allowable Axial Stresses for Unreinforced Masonry (walls only) h Fa 0.5 f 1 for h/t r F a 70r 0.5 f h a for h/t > 99 b

8 where h = effective length r = radius of gyration An = effective (or net) area of asonry Ast = area of steel reinforceent = specified asonry copressive strength Fs = allowable copressive stress in colun reinforceent with lateral confineent. f The least radius of gyration can be found with as: r db 1 bd 3 b b 1 1 I A for a rectangle with side diensions of b & d where b is the saller of the two side diensions. Section Properties (NCMA TEK Manual for Concrete Masonry 14-1B 007) Table for Horizontal Cross Sections (net) Units Grouted Spacing Mortar Bedding A in /ft (10 3 /) I x in 4 /ft ( /) S x in 3 /ft ( /) r in () 4 Inch Single Wythe Walls, ¾ in. Face Shells (standard) Hollow No grout Faceshell 18.0 (38.1) 38.0 (51.9) 1.0 (1.13) 1.45 (36.9) Hollow No grout Full 1.6 (45.7) 39.4 (53.8) 1.7 (1.17) 1.35 (34.3) 100 % solid/grouted Full 43.5 (9.1) 47.4 (64.7) 6.3 (1.41) 1.04 (6.5) 49

9 Table for Horizontal Cross Sections (net) continued Units Grouted Cores Mortar Bedding A in /ft I x in 4 /ft ( /) S x in 3 /ft ( /) r in () (10 3 /) 6 Inch Single Wythe Walls, 1 in. Face Shells (standard) Hollow No grout Faceshell 4.0 (50.8) (178) 46.3 (.49).33 (59.) Hollow None Full 3. (68.1) (190) 49.5 (.66).08 (5.9) 100% Solid/grouted Full 67.5 (143) (4) 63.3 (3.40) 1.6 (41.1) Hollow 16" o. c. Faceshell 46.6 (98.6) (16) 55.1 (.96) 1.79 (45.5) Hollow 4" o. c. Faceshell 39.1 (8.7) (07) 5. (.81) 1.87 (47.4) Hollow 3" o. c. Faceshell 35.3 (74.7) (03) 50.7 (.73) 1.91 (48.5) Hollow 40" o. c. Faceshell 33.0 (69.9) (00) 49.9 (.68) 1.94 (49.3) Hollow 48" o. c. Faceshell 31.5 (66.7) (199) 49.3 (.65) 1.96 (49.8) Hollow 7" o. c. Faceshell 9.0 (61.45) (196) 51.0 (.74).00 (50.8) Hollow 96" o. c. Faceshell 7.8 (58.8) 14.4 (194) 50.6 (.7).0 (51.3) Hollow 1" o. c. Faceshell 7.0 (57.1) (194) 50.4 (.71).03 (51.5) 8 Inch Single Wythe Walls, 1 ¼ in. Face Shells (standard) Hollow No grout Faceshell 30.0 (63.5) (4) 81.0 (4.35) 3.1 (81.5) Hollow No grout Full 41.5 (87.9) (456) 87.6 (4.71).84 (7.0) 100% solid/grouted Full 91.5 (194) 440. (601) (6.5).19 (55.7) Hollow 16" o. c. Faceshell 6.0 (131) (59) 99.3 (5.34).43 (61.6) Hollow 4" o. c. Faceshell 51.3 (109) (504) 93. (5.01).53 (64.3) Hollow 3" o. c. Faceshell 46.0 (97.3) (49) 90.1 (4.85).59 (65.8) Hollow 40" o. c. Faceshell 4.8 (90.6) 355. (485) 88.3 (4.75).63 (66.9) Hollow 48" o. c. Faceshell 40.7 (86.0) (480) 87.1 (4.68).66 (67.6) Hollow 7" o. c. Faceshell 37.1 (78.5) (47) 85.0 (4.57).71 (69.0) Hollow 9" o. c. Faceshell 35.3 (74.7) 34.8 (468) 89.9 (4.83).74 (69.6) Hollow 10" o. c. Faceshell 34.3 (7.6) (466) 89.5 (4.81).76 (70.1) 10 Inch Single Wythe Walls, 1 ¼ in. Face Shells (standard) Hollow No grout Faceshell 30.0 (63.5) (74) (5.9) 4.0 (107) Hollow No grout Full 48.0 (10) (88) 16.0 (6.77) 3.55 (90.) 100% solid/grouted Full (44) (118) (9.96).78 (70.6) Hollow 16" o. c. Faceshell 74.8 (158) (1017) (8.3) 3.04 (77.) Hollow 4" o. c. Faceshell 59.8 (17) (954) 145. (7.81) 3.16 (80.3) Hollow 3" o. c. Faceshell 5.4 (111) (93) (7.55) 3.4 (8.3) Hollow 40" o. c. Faceshell 47.9 (101) (904) (7.39) 3.9 (83.6) Hollow 48" o. c. Faceshell 44.9 (95.0) 65.4 (891) (7.9) 3.33 (84.6) Hollow 7" o. c. Faceshell 39.9 (84.5) (870) 13.4 (7.1) 3.39 (86.1) Hollow 96" o. c. Faceshell 37.5 (79.4) 69.3 (859) (7.03) 3.43 (87.1) Hollow 10" o. c. Faceshell 36.0 (76.) 64.7 (853) 19.8 (6.98) 3.45 (87.6) 1 Inch Single Wythe Walls. 1 ¼ in. Face Shells (standard) Hollow No grout Faceshell 30.0 (63.5) 811. (1108) (7.50) 5.0 (13) Hollow No grout Full 53.1 (11) (137) (8.98) 4.8 (109) 100% solid/grouted Full (95) (145) 70.3 (14.5) 3.36 (85.3) Hollow 16" o. c. Faceshell 87.3 (185) 16.3 (174) 17.(11.7) 3.64 (9.5) Hollow 4" o. c. Faceshell 68. (144) (1591) 00.5 (10.7) 3.79 (96.3) Hollow 3" o. c. Faceshell 58.7 (14) (155) 19. (10.3) 3.88 (98.6) Hollow 40" o. c. Faceshell 5.9 (11) (1486) 187. (10.1) 3.95 (100) Hollow 48" o. c. Faceshell 49.1 (104) (1459) (9.88) 3.99 (101) Hollow 7" o. c. Faceshell 4.7 (90.4) (1415) (9.59) 4.07 (103) Hollow 96" o. c. Faceshell 39.6 (83.8) (1393) (9.44) 4.1 (105) Hollow 10" o. c. Faceshell 37.6 (79.6) (1380) (9.34) 4.15 (105) 493

10 Table for Horizontal Cross Sections (net) continued Units Grouted Cores Mortar Bedding A in /ft I x in 4 /ft ( /) S x in 3 /ft ( /) r in () (10 3 /) 14 Inch Single Wythe Walls. 1 ¼ in. Face Shells (standard) Hollow No grout Faceshell 30.0 (63.5) (1574) 169. (9.09) 6.0 (157) Hollow No grout Full 58. (13) (1970) 11.8 (11.4) 4.98 (16) 100% solid/grouted Full (346) 59.4 (3454) (0.0) 3.93 (99.8) Hollow 16" o. c. Faceshell 99.9 (11) (690) 89.(15.5) 4.5 (108) Hollow 4" o. c. Faceshell 76.6 (16) (450) 63.4 (14.) 4.41 (11) Hollow 3" o. c. Faceshell 64.9 (137) (330) 50.5 (13.5) 4.51 (115) Hollow 40" o. c. Faceshell 58.0 (13) (58) 4.8 (13.0) 4.59 (117) Hollow 48" o. c. Faceshell 53.3 (113) (10) 37.6 (1.8) 4.64 (118) Hollow 7" o. c. Faceshell 45.5 (96.3) (130) 9.0 (1.3) 4.74 (10) Hollow 96" o. c. Faceshell 41.6 (88.1) (090) 4.7 (1.1) 4.79 (1) 14 Inch Single Wythe Walls. 1 ¼ in. Face Shells (standard) continued Hollow 10" o. c. Faceshell 39.3 (83.) (067) 1.1 (11.9) 4.83 (13) 16 Inch Single Wythe Walls. 1 ¼ in. Face Shells (standard) Hollow No grout Faceshell 30.0 (63.5) (1) (10.) 7.0 (183) Hollow No grout Full 63. (134) (773) 59.9 (13.9) 5.67 (144) 100% solid/grouted Full (397) (509) (6.3) 4.51 (115) Hollow 16" o. c. Faceshell 11.4 (38) 896. (3955) 370.7(19.9) 4.84 (13) Hollow 4" o. c. Faceshell 85.0 (180) (3561) (17.9) 5.0 (17) Hollow 3" o. c. Faceshell 71. (151) (3364) (17.0) 5.14 (131) Hollow 40" o. c. Faceshell 63.0 (133) (346) 304. (16.4) 5. (133) Hollow 48" o. c. Faceshell 57.5 (1) (3167) 96.9 (16.0) 5.8 (134) Hollow 7" o. c. Faceshell 48.3 (10) 3.0 (3036) 84.5 (15.3) 5.39 (137) Hollow 96" o. c. Faceshell 43.7 (9.5) (3970) 78.4 (15.0) 5.45 (138) Hollow 10" o. c. Faceshell 41.0 (86.8) (931) 74.7 (14.8) 5.49 (139) 494