Dan Abrams + Magenes Course on Masonry

1. Classnotes for ROSE School Course in: Masonry Structures Notes Prepared by: Daniel P. Abrams Willett Professor of Civil Engineering University of Illinois at Urbana-Champaign October 7, 2004 Lesson 2 and 3: Properties of Masonry Materials Introduction, compressive strength, modulus of elasticity condition assessment, movements

2. Historical Use of Masonry as a Structural Material

16. Masonry Compressive Strength

17. Mechanics of Masonry in Compression t j t b P P masonry unit l stresses shown for  mortar >  unit mortar

18. Biaxial Strength of Masonry Units direct tensile strength of unit from test f’ udt f’ udt f’ udt f’ ut flat-wise compressive strength of unit from test f’ ut f’ ut brick splits when: compression tension

19. Biaxial Strength of Mortar multiaxial compressive strength mortar crushes when: 4.1 1.0 compression compression uniaxial compressive strength from test f’ jt f’ jt

20. Masonry Compressive Strength equilibrium relation: t j t b P P if mortar crushes: if brick splits:

21. Masonry Compressive Strength if mortar crushes and brick splits simultaneously: where U u = coefficient of non-uniformity (range 1.1 to 2.5) Hilsdorf equation

22. Nonlinear Mortar Behavior triaxial test 1000 psi v l 1000 psi 30 psi

23. Unit Splitting vs. Mortar Crushing Linear Mortar f’ udt unit failure envelope mortar failure envelope tension compression unit stress path mortar stress path mortar crushes failure f’ jt f’ ut

24. Unit Splitting vs. Mortar Crushing Nonlinear Mortar tension compression f’ udt mortar failure envelope unit failure envelope failure unit stress path mortar stress path unit splits f’ ut f’ jt

25. Incremental Lateral Tensile Stress on Masonry Unit 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. Assuming linear behavior for masonry unit, and nonlinear mortar behavior:

31. Compressive Strength of Masonry per UBC UBC Table 21-D Type M/S mortar Type N mortar 14,000 or more 12,000 10,000 8,000 6,000 4,000 5,300 4,700 4,000 3,350 2,700 2,000 4,400 3,800 3,300 2,750 2,200 1,600 Specified compressive strength of clay masonry, f’ m Specified Compressive Strength of Masonry, f’ m , (psi) Compressive Strength of Clay Masonry Units (psi)

32. Compressive Strength of Masonry per UBC UBC Table 21-D Type N mortar 3,000 2,500 2,000 1,500 1,000 2,800 2,350 1,850 1,350 950 Specified compressive strength of concrete masonry, f’ m Type M/S mortar 4,800 or more 3,750 2,800 1,900 1,250 Specified Compressive Strength of Masonry, f’ m , (psi) Compressive Strength of Concrete Masonry Units (psi)

34. Compressive Strength of Masonry per MSJC MSJC Specification Table 1 Net Area Compressive Strength of Clay Masonry Units (psi) Type M/S Mortar Type N Mortar Net Area Compressive Strength of Masonry ( psi) 1,700 3,350 4,950 6,600 8,250 9,900 13,200 2,100 4,150 6,200 8,250 10,300 - - 1,000 1,500 2,000 2,500 3,000 3,500 4,000 Compressive strength of clay masonry by unit strength method

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

36. Comparison of Default Prism Strengths UBC Table 21-D vs. MSJC Specifications Table 1 Default prism strengths are lower bounds to expected values.

37. Comparison of Default Prism Strengths UBC Table 21-D vs. Table 2 MSJC-Spec. Note: MSJC and UBC values are almost identical for concrete masonry. Default prism strengths are lower bounds to expected values.

38. Masonry Elastic Modulus

39. Elastic Modulus of Masonry in Compression Basic Mechanics  t j t b P =  y A net [1] [2] [3] [4] [5] [6] [7]

40. Elastic Modulus of Masonry in Compression Basic Mechanics Reference: Structural Masonry by S. Sahlin, Section D.2 [8]  t j t b P =  y A net [12] [9] [10] [11]

41. Elastic Modulus of Masonry in Compression 1.2 concrete block masonry clay-unit masonry 0.76 0.0 0.2 0.4 0.6 0.8 1.0 0 0.5 1 1.5 2  t = 0.0498 (typical for concrete block masonry)  t = 0.152 (typical for brick masonry)

42. 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 f m  m MSJC Sec. 1.8.2.1.1 for clay-unit masonry E m = 700 f’ m for concrete-unit masonry E m = 900 f’ m UBC 2106.2.13 MSJC Sec. 1.8.2.2.2 G = 0.4 E m estimate without prism test data UBC Sec. 2106.2.12.1 for clay-unit or concrete masonry E m = 750 f’ m < 3000 ksi f’ mt E m 0.33 f’ mt 0.05 f’ mt

43. Strength of URM Bearing Walls

45. Unreinforced Bearing and Shear Walls Historically walls were sized in terms of h/t ratio which was limited to 25. Empirical design of masonry UBC 2105.2 h < 35 ’ Associated BIA Technical Note: 24 series The Contemporary Bearing Wall Building wind = 15 psf h

46. Concentric Axial Compression Buckling Load Euler buckling load: P =  y A net t h’ = kl for rectangular section:

47. Concentric Axial Compression Note: for MSJC and UBC plot, r=0.289t is assumed h’/t 25 50 75 100  y 0.25 f’ m MSJC/UBC f’ m 24.8 Euler curve

48. Code Allowable Compressive Stress 0 0.1 0.2 0.3 0 50 100 150 200 for h’/r > 99 : F a = 0.25 f’ m [(70r/h’) 2 ] MSJC Eq. 2-13 and UBC Eq. 7-40 MSJC Section 2.2.3 and UBC Section 2107.3.2: for h’/r < = 99: F a = 0.25 f’ m [1 - (h’/140r) 2 ] MSJC Eq. 2-12 and UBC Eq. 7-39

49. Concentric Axial Compression UBC 2106.2.4: Effective Wall Height translation restrained no sidesway restraint MSJC 2.2.3: Buckling Loads e = eccentricity of axial load rotation restrained 2.0 rotation unrestrained 2.0 h’=kh rotation restrained 0.70 h rotation unrestrained 1.0 k = h’/h

50. Concentric Axial Compression UBC 2106.2.3: Effective Wall Thickness A. Single Wythe t = specified thickness t mortar or grout filled collar joint B. Multiwythe C. Cavity Walls each wythe considered separate both wythes loaded P 1 P 2 t 1 t 2 air space wire joint reinforcement P t 1 t 2 one wythe loaded

51. Concentric Axial Compression Neglect web area if face-shell bedding is used. UBC 2106.2.5: Effective Wall Area Effective area is minimum area of mortar bed joints plus any grouted area. face shell effective thickness raked joint effective thickness

52. 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. Per NCMA TEK 14-1A for face shell bedding: A net = 30.0 in 2 I net = 308.7 in 4 r = 2.84 in. (r based only on loaded wythe) P a concrete footing 20’-0” Case “A”: Prisms have been tested. f’ m = 2500 psi for block wall f’ m = 5000 psi for brick wall Case “B”: No prisms have been tested. (Type I CMU’s and Type S mortar will be specified.) f’ m = 1500 psi for block wall metal ties face-shell bedding 7.63” 8”CMU 3.63” 4” brick

53. Example: Case “A” MSJC Section 2.2.3 & UBC 2107.3.2 * no buckling check per UBC. P a = 11.9 kip / ft for both codes MSJC Section 2.2.3: check buckling *

54. Example: Case “B” MSJC Section 2.2.3 & UBC 2107.3.2 MSJC Section 2.2.3: check buckling Governs for MSJC, take 1/2 for UBC since no special inspection is provided.

55. Eccentric Axial Compression Ref: NCMA TEK 14-4 Eccentric Loading of Nonreinforced Concrete Masonry h P e Pe t combined axial stress plus bending f a + f b -f a + f b axial stress P bending stress M = Pe

56. Eccentric Axial Compression 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 where F a = allowable axial compressive stress (UBC 2107.3.2 or MSJC Sec. 2.2.3) F b = allowable flexural compressive stress = 0.33 f´ m (UBC 2107.3.3 or MSJC Sec 2.2.3) limiting compressive stress (controls for small e’s) UBC Section 2107.2.7 and MSJC 2.2.3: Unity Formula limiting tensile stress -f a + f b < F t where F t = allowable tensile stress (controls for large e’s) UBC 2107.3.5 or MSJC 2.2.3: Allowable Tensile Stress

57. Allowable Tensile Stresses, F t MSJC Table 2.2.3.2 and UBC Table 21-I 40 25 68* 80 50 80* 30 19 58* 60 38 60* 24 15 41* 48 30 48* 15 9 26* 30 19 29* * grouted masonry is addressed only by MSJC all units are (psi) Direction of Tension and Type of Masonry Mortar Type Portland Cement/Lime or Mortar Cement Masonry Cement/Lime M or S M or S N N tension normal to bed joints solid units hollow units fully grouted units tension parallel to bed joints solid units hollow units fully grouted units

58. Allowable Flexural Tensile Stresses, F t weak units flexural tension parallel to bed joints strong units No direct tensile strength assumed normal to head joints, just shear strength along bed joint. flexural tension normal to bed joints Note: direct tensile stresses across wall thickness is not allowed per UBC or MSJC.

59. Example: Eccentric Axial Compression f’ m = 2000 psi (from tests) Type S mortar Determine the allowable vertical load capacity per UBC and MSJC. Per NCMA Tek 141A: (per running foot) A net = 30.0 in 2 I x = 309 in 4 S x = 81.0 in 3 r= 2.84” F t = 25 psi per UBC 2107.3.5 and MSJC Table 2.2.3.2 e = 3.0” concrete footing 20’-0” P a 7.63” 8”CMU ungrouted face-shell bedding 1.25”

60. Example Tension controlling:

61. Example Compression controlling: UBC 2107.3.4 and MSJC 2.2.3

62. Example MSJC Section 2.2.3: Check Buckling (no buckling check per UBC) Code UBC MSJC P a (lbs) Tension Compression Buckling 6750 6233 6750 6233 ----- 1417

63. Kern Distance for URM Wall e = t/6 f a + f b e Assuming F t = 0 for solid section. -f a + f b = 0 t P = + f a f b b t/3 t b/3 kern If load is within kern, then no net tensile stress.

64. Kern Distance for URM Wall Specific Tensile Strength, F t , for solid section. f a + f b e -f a + f b = F t t P = + f a f b b t kern If load is within kern, then tensile stress < F t .

65. Strength of Walls with no Tensile Strength Resultant load inside of kern. f m P e P t

66. Strength of Walls with no Tensile Strength Neglect all masonry in tension. Note: This approach is outside of UBC and MSJC since F t may be exceeded. Partially cracked wall is not prismatic along its height. Stability of the 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. Resultant load outside of kern. P e t t/2 f m P [1] [2] [3] [4]

67. Example Part (a) e = 1.0 in. < t/6 = 1.27 in. within kern! Part (b) e = 2.5 in. > t/6 = 1.27 in. outside of kern! Determine the maximum compressive edge stress. e two-wythe brick wall P = 10 kip/ft. t = 7.63”

68. Condition Assessment

73. Movements

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

80. Control Joint Details for Concrete Masonry Ref. NCMA TEK 10-2A Control Joints in Concrete Masonry Walls control joint unit grout fill paper raked head joint and caulk

81. Expansion Joints in Clay Masonry Pressure-relieving or expansion joints accommodate expansion of clay masonry. Ref: Masonry Design and Detailing , Christine Beall, McGraw-Hill BIA Tech. Note 18A Movement - Design and Detailing of Movement Joints, Part II expansion joint

82. Spacing of Expansion Joints For brick masonry: 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 T max = maximum mean wall temperature, °F T min = minimum mean wall temperature, °F L )] T T ( 0000045 . 0 0002 . 0 [ W min max    min max T T ) p ( 000 , 24 S   S = maximum spacing of joints in inches p = ratio of opaque wall area to gross wall area

83. Expansion Joint Details for Brick Veneer Walls 20 oz. copper silicone or butyl sealant neoprene extruded plastic

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

85. 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

89. End of Lessons 2 and 3