1 Masonry Structures
2 SEISMIC DESIGN OF MASONRY STRUCTURES
3 NEHRP Recommended Provisions
Masonry Structures:
1 ? Context in the Provisions
? Reference standards
? Masonry basics
? Masonry behavior
? Organization of TMS 402 Code
? Types of shear walls
2 ? Shear wall in-plane design
? Masonry walls out-of-plane
? Overstrength concepts
? Details
? Simplified design for wall-type structures
? Shear wall design example
?
4 Objectives of Module
? Basics of masonry behavior
? The TMS 402 Building Code and TMS 602 Specification and the relationship of NEHRP Recommended Provisions documents to it
? Earthquake design of masonry structures and components using the 2008 TMS 402 Code and TMS 602 Specification
? Example of masonry shear wall design
5 NEHRP Recommended Provisions Masonry Design
? Context in the Provisions
? Design seismic loads
– Load combinations ASCE 7-10 Ch. 2 & 12
– Loads on structures ASCE 7-10 Ch. 12
– Loads on components
& attachments Chap. 6 ASCE 7-10 Ch. 13
? Design resistances ASCE 7-10 Ch. 14
– Strength design (mostly references TMS 402-08)
?
6 NEHRP Recommended Provisions Masonry Design
? Basic Documents
? NEHRP Recommended Provisions
? ASCE 7-10, Minimum Design Loads for Buildings and Other Structures
? TMS 402-8, Building Code Requirements for Masonry Structures
? TMS 602-8, Specification for Masonry Structures
? IBC 2012, International Building code
?
7 NEHRP Recommended Provisions Masonry Design
? Masonry Basics
8 Review Masonry Basics
? Basic terms
? Units
? Mortar
? Grout
? Accessory materials
– Reinforcement (may or may not be present), connectors, flashing, sealants
? Typical details
9 Basic Terms
? Bond patterns (looking at wall):
10 Masonry Units
? Concrete masonry units (CMU):
– Specified by ASTM C 90
– Minimum specified compressive strength (net area) of 1900 psi (average)
– Net area is about 55% of gross area
(varies with size)
– Nominal versus specified versus actual dimensions
– Type I and Type II designations no longer exist
11 Masonry Units
? Clay masonry units:
– Specified by ASTM C 62 or C 216
– Usually solid, with small core holes for manufacturing purposes
– If cores occupy ? 25% of net area, units can be considered 100% solid
– Hollow units are similar to CMU - can be reinforced
12 Masonry Mortar
? Mortar for unit masonry is specified by ASTM C 270
? Three cementitious systems
– Portland cement + lime + sand (“traditional”)
– Masonry cement mortar (lime is included in cement)
– Mortar cement mortar (lime is included in cement, higher air contents)
13 Masonry Mortar
? Plastic mortar properties
– Workability Important for good bond
– Water retentivity
– Rate of hardening
? Hardened mortar properties
– Bond Important, seldom specified
– Compressive strength
– Volume stability
– Durability
14 Masonry Mortar
? Within each cementitious system, mortar is specified by type (M a S o N w O r K):
– Going from Type K to Type M, mortar has an increasing volume proportion of portland cement. It sets up faster and has higher compressive and tensile bond strengths.
– As the volume proportion of portland cement increases, mortar is less able to deform when hardened.
– Types M and S are specified for modern structural masonry construction.
– Type N for non-loadbearing and for brick veneer
– Type O or K for historic masonry repairs
15 Masonry Mortar
? Under ASTM C270, mortar can be specified by proportion or by property.
? If mortar is specified by proportion, compliance is verified only by verifying proportions. For example:
– Type S PCL mortar has volume proportions of 1 part cement to about 0.5 parts hydrated mason’s lime to about 4.5 parts mason’s sand
– Type N masonry cement mortar (single-bag) has one part Type N masonry cement and
3 parts mason’s sand
16 Masonry Mortar
? Under ASTM C270, mortar can be specified by proportion or by property:
– Proportion specification is simpler -- verify in the field that volume proportions meet proportion limits.
– Property specification is more complex: (1) establish the proportions necessary to produce a mortar that, tested at laboratory flow, will meet the required compressive strength, air content, and retentivity (ability to retain water) requirements and (2) verify in the field that volume proportions meet proportion limits.
17 Masonry Mortar
? The proportion specification is the default. Unless the property specification is used, no mortar testing is necessary.
? The proportion of water is not specified. It is determined by the mason to achieve good productivity and workmanship.
? Masonry units absorb water from the mortar decreasing its water-cement ratio and increasing its compressive strength. Mortar need not have high compressive strength.
18 Grout
? Grout for unit masonry is specified by ASTM C 476
? Two kinds of grout:
– Fine grout (cement, sand, water)
– Coarse grout (cement, sand, pea gravel, water)
? ASTM C 476 permits a small amount of hydrated lime, but does not require any. Lime is usually not used in plant – batched grout.
19 Grout
? Under ASTM C476, grout can be specified by proportion or by compressive strength:
– Proportion specification is simpler. It requires only that volume proportions of ingredients be verified.
– Specification by compressive strength is more complex. It requires compression testing of grout in a permeable mold (ASTM C 1019).
20 Grout
? If grout is specified by proportion, compliance is verified only by verifying proportions. For
example:
– Fine grout has volume proportions of 1 part cement to about 3 parts mason’s sand.
– Coarse grout has volume proportions of 1 part cement to about 3 parts mason’s sand and about 2 parts pea gravel.
? Unless the compressive-strength specification is used, no grout testing is necessary.
21 Grout
? The proportion of water is not specified. The slump should be 8 to 11 in.
? Masonry units absorb water from the grout decreasing its water-cement ratio and increasing its compressive strength. High-slump grout will still be strong enough.
22 Role of fm?
? Concrete:
– Designer specifies value of fc?
– Compliance is verified by compression tests on cylinders cast in the field and cured
under ideal conditions
? Masonry
– Designer specifies value of fm?
– Compliance is verified by “unit strength method” or by “prism test method”
23 Verify Compliance with Specified fm?
? Unit strength method (Spec 1.4.B.2):
– Compressive strengths from unit manufacturer
– Grout strength equals or exceeds fm?,min = 2,000 psi
? Prism test method (Spec 1.4.B.3):
– Pro -- can permit optimization of materials
– Con -- require testing, qualified testing lab, and procedures in case of non-complying results
24 Example of Unit Strength Method (Specification Tables 1, 2)
? Clay masonry units (Table 1) Example:
– Unit compressive strength ? 4150 psi
– Type N mortar
– Prism strength can be taken as 1500 psi
? Concrete masonry units (Table 2) Example:
– Unit compressive strength ? 1900 psi
– Type S mortar
– Prism strength can be taken as 1500 psi
25 Application of Unit Strength Method (Specification Tables 1, 2)
? Designer determines required material specification:
– Designer states assumed value of fm?
– Specifier specifies units, mortar and grout that will satisfy “unit strength method”
– Compliance with fm? can be verified with no tests on mortar, grout, or prisms (but need verification of units’ compressive strength)
26 Comply with Specified Products and Execution
? Products -- Specification Part 2:
– Units, mortar, grout, accessory materials
? Execution -- Specification Part 3
– Inspection
– Preparation
– Installation of masonry units, mortar, reinforcement, grout, prestressing tendons
27 Procedure for Strength Design of Reinforced Masonry Shear Walls
? Select trial design.
? Compute factored design moments and shears for in- and out-of-plane loading. Include p- d for out-of-plane deflection and moment.
? Design flexural reinforcement as controlled by out-of-plane loading.
? Design flexural reinforcement as controlled by in-plane loading and revise design as necessary.
? Check to ensure ductility.
? Check shear capacity and revise if required.
? Check detailing.
28 Accessory Materials
Horizontally oriented expansion joint under shelf angle:
29 Component Design basics
Fully grouted wall:
Area assumed effective in longitudinal shear
30 Component Design basics
No grout in wall:
Face shells are the only area assumed effective in longitudinal shear.
31 Component Design basics
Partially grouted wall:
Area assumed effective in longitudinal shear includes grouted cells and adjacent webs. (Recent research suggest this assumption may be unconservative).
32 Component Design: Design of walls
33 Component Design basics
T - beam section assumed to resist out-of-plane flexure
(Masonry laid in running bond)
34 Component Design basics
Masonry can span horizontally
35 Component Design basics
36 NEHRP Recommended Provisions Masonry Design
Masonry Behavior
37 Masonry Behavior
? On a local level, masonry behavior is nonisotropic, nonhomogeneous, and nonlinear.
? On a global level, however, masonry behavior can be idealized as isotropic and homogeneous. Nonlinearity in compression is handled using an equivalent rectangular stress block as in reinforced concrete design.
? A starting point for masonry behavior is to visualize it as very similar to reinforced concrete. Masonry capacity is expressed in terms of a specified compressive strength, fm?, which is analogous to fc?.
38 ... typical materials in reinforced masonry
39 Masonry Behavior
prism failure mechanism
40 Masonry Behavior Stress-Strain Curve for Prism Under Compression
41 Masonry Behavior
42 Masonry Behavior
Lack of ties between wythes
43 Masonry Behavior
Typical grout-block separation due to drying shrinkage
44 Masonry Behavior
45 Masonry Behavior
Crowded cells make grout flow difficult
46 Masonry Behavior
Spalled face shells on solid grouted wall
47 Masonry Behavior: Short Wall in plane
48 Masonry Behavior: Tall Wall in-plane
49 Reinforced Masonry/Behavior in Flexure hysteresis
50 Masonry Behavior: out-of-plane
51 Masonry Behavior
Out-of-plane wall failure
52 Summary of Masonry Behavior
4-Way Composite Action
? Units, mortar, reinforcement, grout
?
Compression
? High strength
? Brittle -- low ductility
? Confinement difficult to achieve
?
Tension
? Good strength when reinf. takes tension
? Very little strength without reinf.
? (continuous joints are a plane of weakness)
53 Design Implications from Masonry Behavior
Unreinforced
? Design as elastic / brittle material
? R factors very low
? Design force = EQ force
?
Reinforced
? Design similar to reinforced concrete
? Confinement, ductility difficult to achieve
? R factors lower than concrete
54 NEHRP Recommended Provisions Masonry Design
Organization of TMS 402 Code
55 Seismic Design for Masonry
Hierarchy of Standards
56 What is the TMS 402 Code
and TMS 602 Specification... ?
57 Organization of 2008 TMS 402 Code
58 Organization of 2008 TMS 602
Specification
59 Relation Between Code and Specification
? Code:
– Design provisions are given in Chapters 1-7 and Appendix A
– Sections 1.2.4 and 1.18 require a QA program in accordance with the specification
– Section 1.4 invokes the specification by reference.
? Specification:
– Section 3.7 verify compliance with specified fm?
– Comply with required level of quality assurance
– Comply with specified products and execution
60 Organization of TMS 402 Code
Chapter 1
1 1.1 – 1.6 Scope, contract documents and calculations, special systems, reference standards, notation, definitions
1.7 Loading
1.8 Material properties
1.9 Section properties
1.10 Connections to structural frames
2 1.11 Stack bond masonry
1.12 Corbels
1.13 Beams
1.14 Columns
1.15 Details of reinforcement
1.16 Anchor bolts
1.17 Seismic design requirements
1.18 Quality assurance program
1.19 Construction
61 Code 1.8, Material Properties
? Prescriptive modulus of elasticity: Em = 700 f’m for clay masonry
Em = 900 f’m for concrete masonry
or
Chord modulus of elasticity from tests
? Shear modulus, thermal expansion coefficients, and creep coefficients for clay, concrete, and AAC masonry
? Moisture expansion coefficient for clay masonry
? Shrinkage coefficients for concrete masonry
62 Code 1.9, Section Properties
? Use minimum (critical) area for computing member stresses or capacities
– Capacity is governed by the weakest section; for example, the bed joints of face-shell bedded hollow masonry
63 Code 1.9, Section Properties
? Radius of gyration and member slenderness are better represented by the average section
? For example, the net area of units rather than just the bed-joint area of face-shell bedded masonry
64 Code 1.15, Details of Reinforcement
? Reinforcing bars must be embedded in grout; joint reinforcement can be embedded in mortar
? Placement of reinforcement
? Protection for reinforcement
? Standard hooks
65 Code 1.17, Seismic Design
? Seismic requirements for masonry structures:
– Improves ductility of masonry members
– Improves connectivity in masonry structures
? Not applicable to:
– Glass unit masonry
– Veneers
66 Code 1.17, Seismic Design
? Define a structure’s Seismic Design Category (SDC) according to ASCE 7-10
– SDC depends on seismic risk (geographic location), underlying soil, importance
– SDCs are A, B, C, D, E, or F
? SDC determines
– Required types of shear walls (prescriptive reinforcement)
– Prescriptive reinforcement for other masonry elements
– Permitted design approaches for LFRS (lateral force-resisting system)
67 Code 1.17, Seismic Design
? Requirements for SDCs are cumulative; requirements in each “higher” category are added to requirements in the previous category:
SDC A = minimum requirements
SDC B = A + more
SDC C = A + B + more
SDC D = A + B + C + more etc…
68 Code 1.17, Seismic Design
? Shear walls must meet minimum prescriptive requirements for reinforcement and connections (ordinary reinforced, intermediate reinforced, or special reinforced)
?
?
69 Code 1.17, Seismic Design
? General analysis
– Element interaction
– Refer to ASCE7-10, Sec. 1.4, General Structural Integrity:
• Load path connections
• Notional lateral forces
• Connection to supports
• Anchorage of walls
70 Code 1.17, Seismic Design
? General analysis
– Drift limits: Use legally adopted building code or ASCE7
– Drift limits assumed satisfied for many wall types
– Special Reinforced Masonry walls are the exception to this rule
71 Code 1.17, Seismic Design
? Element classification
– Participating
• Part of the seismic force-resisting system
– Non-participating
• Non-participating walls must be isolated from the participating seismic force-resisting system (except as required for gravity support)
?
72 Code 1.17, Seismic Design
? Seismic Design Category A:
– All types of shear walls permitted:
• Empirical
• Plain
–Ordinary plain: Unreinforced
–Detailed Plain: Has minimum reinforcement
• Ordinary reinforced
• Intermediate reinforced
• Special reinforced
73 Code 1.17, Seismic Design
? Seismic Design Category B:
– Empirical design not permitted, all other types of shear walls permitted:
• Plain
–Ordinary plain
–Detailed plain
• Ordinary reinforced
• Intermediate reinforced
• Special reinforced
–
74 Code 1.17, Seismic Design
? Seismic Design Category C:
– Empirical and plain not permitted, all other types of shear walls permitted:
• Ordinary reinforced
• Intermediate reinforced
• Special reinforced
– Participating walls shall be reinforced
– Non-participating walls must meet minimum prescriptive requirements for horizontal or vertical reinforcement
– At least 80% of lateral resistance in a given line shall be by shear walls
75 Code 1.17, Seismic Design
? Seismic Design Category D:
– Only special reinforced type of shear wall permitted
– Shear walls must meet minimum prescriptive requirements for reinforcement and connections (special reinforced)
– Type N mortar and masonry cement mortars are prohibited in the lateral force-resisting system
–
– “Non-participating” walls must meet minimum prescriptive requirements for horizontal and vertical reinforcement
76 Code 1.17, Seismic Design
Seismic Design Category D:
? Extra caution against brittle shear failure for Special Reinforced Masonry Shear Walls
(1.17.3.2.6.1):
?
– Design shear strength shall exceed the shear corresponding to the development of 1.25 times the nominal flexural strength, but
– nominal shear strength need not exceed 2.5 times required shear strength
77 Minimum Reinforcement for Special Reinforced Shear Walls
78 Code 1.17, Seismic Design
? Seismic Design Categories E and F:
– Additional reinforcement requirements for non-participating stack-bond masonry
79 Minimum Reinforcement, SW Types
80 Code 1.18, Quality Assurance
? Requires a quality assurance program in accordance with the TMS 602 Specification:
– Three levels of quality assurance (A, B, C)
– Compliance with specified fm?
– Increasing levels of quality assurance require increasingly strict requirements for
inspection, and for compliance with specified products and execution
81 Code 1.18, Quality Assurance
? Minimum requirements for inspection, tests, and submittals:
– Empirically designed masonry, veneers, or glass unit masonry
• Table 1.18.1 for nonessential facilities
• Table 1.18.2 for essential facilities
– Engineered plain, reinforced, or prestressed masonry
• Table 1.18.2 for nonessential facilities
• Table 1.18.3 for essential facilities
82 1.19, Construction
? Minimum grout space (Table 1.19.1)
? Embedded conduits, pipes, and sleeves:
– Consider effect of openings in design
– Masonry alone resists loads
83 Organization of TMS 402 Code
Chapter 3, Strength Design
1 ? Fundamental basis
? Design strength
? f factors
? Deformation requirements
? Anchor bolts
2 ? Bearing strength
? Compressive strength
? Modulus of rupture
? Strength of reinforcement
? Unreinforced masonry
? Reinforced masonry
84 Fundamental Basis for Strength Design
? Factored design actions must not exceed nominal capacities, reduced by f factors
? Load factors come from ASCE7
? Quotient of load factor divided by f factor is analogous to safety factor of allowable-stress design, and should be comparable to that safety factor.
85 Code 3.1.3, Design Strength for Strength Design
? Design strength (f x nominal strength) must equal or exceed required strength
86 Code 3.1.4, Strength-reduction Factors (f) for Strength Design
87 Code 3.1.4, Strength-Reduction Factors (f) for Strength Design for Anchor Bolts
88 Code 3.1.5, Deformation Requirements
? Note drift limits from ASCE 7-10 Table 12.12.1
? Deflections of unreinforced masonry (URM) based on uncracked sections
? Deflections of reinforced masonry (RM) shall consider the effects of cracking
89 Code 3.1.6, Anchor Bolts
? Tensile capacity controlled by:
– Tensile breakout
– Yield of anchor in tension
– Tensile pullout (bent-bar anchor bolts only)
? Shear capacity controlled by:
– Shear breakout
– Masonry crushing
– Anchor pry-out
– Yield of anchor in shear
? For combined tension and shear, use linear interaction
90 Code 3.1.8.1.1, Compressive Strength of Masonry
? For concrete masonry, 1500 psi ? fm? ? 4000 psi
? For clay masonry, 1500 psi ? fm? ? 6000 psi
91 Code 3.1.8.2, Modulus of Rupture
? In-plane and out-of-plane bending
– Table 3.1.8.2
– Lower values for masonry cement and air-entrained portland cement-lime mortar
– Higher values for grouted masonry
– For grouted stack-bond masonry, fr = 250 psi parallel to bed joints for continuous horizontal grout section (i.e., fully grouted wall)
92 Code 3.1.8.3, Strength of Reinforcement
? fy ? 60 ksi
? Actual yield strength shall not exceed 1.3 times the specified value
? Columns: Compressive strength of reinforcement shall be ignored unless the reinforcement is tied in compliance with Code 1.14.1.3
?
93 Code 3.3, Reinforced Masonry
? Masonry in flexural tension is cracked
? Reinforcing steel is needed to resist tension
? Similar to strength design of reinforced concrete
94 Code 3.3, Reinforced Masonry
3.3.2 Design assumptions
3.3.3 Reinforcement requirements and details, including maximum steel area
3.3.4 Design of piers, beams and columns:
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97
98
99
100
101
– Nominal axial and flexural strength
– Nominal shear strength
3.3.5 Design of walls for out-of-plane loads
3.3.6 Design of walls for in-plane loads
Code 3.3.2, Design Assumptions
? Continuity between reinforcement and grout
? Equilibrium
? ?mu = 0.0035 for clay masonry, 0.0025 for concrete masonry
? Plane sections remain plane
? Elasto-plastic stress-strain curve for reinforcement
? Tensile strength of masonry is neglected
? Equivalent rectangular compressive stress block in masonry, with a height of 0.80 fm? and a depth of a = 0.80 c
Code 3.3.2
Flexural Assumptions
? Locate neutral axis based on extreme-fiber strains
? Calculate compressive force, C
? C = P + T
? M = ? Fi yi (sum moments about centroid of compressive stress block)
?
Code 3.3.3, Reinforcement Requirements and Details
? Bar diameter ? 1 / 8 nominal wall thickness
? Standard hooks and development length:
– Development length based on pullout and splitting
? In walls, shear reinforcement shall be bent around extreme longitudinal bars
? Splices:
– Lap splices based on required development length
– Welded and lap splices must develop 1.25 fy
Code 3.3.3.5,
Maximum Reinforcement
(Flexural Ductility Check)
? Does not apply if Mu/Vud <1.0
? Locate neutral axis based on extreme-fiber strains
? Calculate compressive force, C (may include compressive reinforcement)
? Tensile reinforcement + axial load = C
Code 3.3.4, Design of Beams, Piers, and Columns
? Slenderness is addressed by multiplying axial capacity by slenderness-dependent modification factors
Code 3.3.4, Nominal Shear Strength
Basis for requirements
– Objectives:
• Avoid crushing of diagonal strut
• Preclude critical (brittle) shear- related failures
Code 3.3.4, Nominal Shear Strength
? Vn = Vnm + Vns
102
103
104
105
106
107
n ns
? Vn shall not exceed:
– Mu / Vu dv ? 0.25 Vn ? 6 An ? fm?
– Mu / Vu dv ? 1.0 Vn ? 4 An ? fm?
– Linear interpolation between these extremes
– Objective is to avoid crushing of diagonal strut
– Objective is to preclude critical (brittle) shear-related failures
Code 3.3.4, Nominal Shear Strength
? Vm and Vs are given by:
Code 3.3.4.2, Requirements for Beams
? Pu ? 0.05 An fm?
? Mn ? 1.3 Mcr (To prevent brittle failures in lightly- reinforced beams)
? Lateral bracing spaced at most 32 times beam width (1.13.2)
? Nominal depth not less than 8 in.
Code 3.3.4.3, Requirements for Piers
? Isolated elements (wall segments are not piers)
? Pu ? 0.3 An fm?
? Nominal thickness 16 in. max. *
? Nominal plan length between 3 and 6 times the nominal thickness *
? Lateral support spacing requirements*
?
* Judgment-based dimensions - intended to distinguish piers from walls and to prevent local buckling
Code 3.3.4.4, Requirements for Columns
? Isolated elements (wall segments are not columns)
? ?g ? 0.0025 (1.14.1)
? ?g ? 0.04 (1.14.1, and also meet Code 3.3.3.5
? Lateral ties in accordance with Code 2.1.6.5
? Solid-grouted
? Least cross-section dimension ? 8 in.
? Nominal depth not greater than 3 times the nominal width
Code 3.3.5, Design of Walls for
Out-of-Plane Loads
? Capacity under combinations of flexure and axial load is based on the assumptions of Code
3.3.2
? Interaction diagram
? Note Pmax >> Pbalance
Code 3.3.5, Design of Walls for
Out-of-Plane Loads
? Maximum reinforcement by Code 3.3.3.5
? Procedures for computing out-of-plane moments and deflections considering secondary effects (P – D)
? Nominal shear strength by Code 3.3.4.1.2
? Note 3.3.5.2 – M and D equations are based on simple supports top & bottom. If other support conditions, use appropriate calculations. Don’t treat code as a cook-book!
108
109
110
111
112
113
114
115
116
117
118
119
120
121
Code 3.3.6, Design of Walls for
In-plane Loads
? Capacity under combinations of flexure and axial load is based on the assumptions of Code
3.3.2
? Interaction diagram:
Code 3.3.6, Design of Walls for
In-plane Loads
? Maximum reinforcement by Code 3.3.3.5
? Vertical reinforcement not less than one-third the horizontal reinforcement
? Nominal shear strength by Code 3.3.4.1.2
NEHRP Recommended Provisions Masonry Design
Simplified Design for Wall-type Structures
Simplified Design for Wall-type Structures
? Starting point for design
? Design the vertical strips in walls for lateral loads perpendicular to the wall and for vertical loads
? Simplified analysis for lateral loads
? Design the walls for loads parallel to the wall
? Design the lintels
? Design the diaphragms
? Detailing
Essential Function of Walls in Resisting Gravity Loads
1 Nonbearing walls resist (concentric) axial loads as vertical strips
2 Bearing walls resist axial loads (concentric and eccentric) as vertical strips
Essential Function of Walls in Resisting Lateral Forces
Effect of Openings for Lateral Load Perpendicular to the Wall
Effect of Openings
Openings increase most original design actions on each strip by a factor equal to the ratio of the effective width of the strip divided by the actual width
Design of Vertical Strips in Perpendicular Walls
Moments and axial forces due to combinations of gravity and lateral load
Design of Vertical Strips in
Out-of-Plane Walls
Moment-axial force interaction diagram (with the help of a spreadsheet)
Design of Shear Walls
Moments, axial forces, and shears due to combinations of gravity and lateral loads
Design of Shear Walls
Moment-axial force interaction diagram (with the help of a spreadsheet)
Design of Shear Walls
Shearing resistance
Per TMS 402:
Distribution of Shears to Shear Walls
122
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126
127
128
129
130
131
? Classical approach
– Determine whether the diaphragm is “rigid” or “flexible”
– Carry out an appropriate analysis for shears
Classical Analysis of Structures with Rigid Diaphragms
? Locate center of rigidity
? Treat the lateral load as the superposition of a load acting through the center of rigidity and a torsional moment about that center of rigidity
Simplified Analysis of Structures with Rigid Diaphragms
? Consider only the shearing stiffness, which is proportional to plan length
? Neglect plan torsion
Reasonable assumption for:
– Walls well-distributed and same thickness
– Low-rise buildings
– Short, long walls
Not valid for:
– Bldgs with large openings in walls
– Tall, narrow walls
Simplified Analysis of Structures with Rigid Diaphragms
Classical Analysis of Structures with Flexible Diaphragms
? Distribute shears according to tributary areas of the diaphragm independent of the relative stiffnesses of the shear walls
Classical Analysis of Structures with Flexible Diaphragms
Simplified Diaphragm Analysis
Diaphragm Design
? Diaphragm shears are resisted by total depth or by cover (for plank diaphragms). Diaphragm moments are resisted by diaphragm chords in bond beams.
Details
? Wall-diaphragm connections
? Design of lintels for out-of-plane loads between wall-diaphragm connections
? Connections between bond beam and walls
? Connections between walls and foundation
Compute Factored Design Moments and Shears
? Factored design moments and shears for in-plane loading depend on actions transferred to shear walls by horizontal diaphragms at each floor level.
? Factored design moments and shears for out-of-plane loading depend on wind or earthquake forces acting between floor levels
Design Flexural Reinforcement as Governed by Out-of-plane Loading
? Practical wall thickness is governed by available unit dimensions:
– 8- by 8- by 16-in. nominal dimensions is most common
– Specified thickness = 7-5/8 in.
– One curtain of bars, placed in center of grouted cells
? Practical wall thickness = 7-5/8 in.
? Can have nominal 6” through 12”
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137
138
139
140
? Proportion flexural reinforcement to resist out-of- plane wind or earthquake forces
Design Flexural Reinforcement as Governed by In-plane Loading
? Construct moment – axial force interaction diagram
– Initial estimate (more later)
– Computer programs
– Spreadsheets
– Tables
Strict Limits on Maximum Flexural Reinforcement
? Objective -- Keep compressive stress block from crushing (brittle failure):
– Walls must be below balance point.
– Maximum steel percentage decreases as axial load increases, so that design above balance point is impossible.
Revise Design as Necessary
? If flexural reinforcement required for out-of-plane moments is less than or equal to that required for in-plane moments, no adjustment is necessary. Use the larger amount.
? If flexural reinforcement required for out-of-plane moments exceeds that required for in- plane moments, consider making the wall thicker so that in-plane flexural capacity does not have to be increased. Excess in-plane reinforcement increases shear demand.
Check Shear Capacity (1)
? Elastic structures or those with considerable shear overstrength:
– Compute factored design shears based on factored design actions.
? Inelastic structures:
– Compute design shears based on flexural capacity
Check Shear Capacity (2)
? Vn = Vnm + Vns
? Vnm depends on (Mu / Vudv) ratio
? Vns = (0.5) Av fy (note efficiency factor when combining Vnm and Vns)
Shear Resistance from Masonry, Vnm (1)
? Vnm depends on (Mu / Vudv) ratio and axial force
? (Mu / Vudv) need not be taken greater than 1.0
Total Shear Resistance, Vn (1)
? Vn = resistance from masonry (Vnm) plus resistance from reinforcement (Vns)
? Upper limit on Vn depends on (Mu / Vu dv) ratio
Check Detailing
? Cover
? Placement of flexural and shear reinforcement
? Boundary elements not required:
– Ductility demand is low
– Maximum flexural reinforcement is closely controlled to delay the onset of toe crushing
Detailing (1)
? Cover:
– Automatically satisfied by putting reinforcement in grouted cells
? Placement of flexural and shear reinforcement:
141
142
143
144
145
146
147
148
149
150
151
152
153
– Minimum flexural reinforcement and spacing dictated by Seismic Design Category
– Flexural reinforcement placed in single curtain. Typical reinforcement would be at least
#4 bars @ 48 in.
– Place horizontal reinforcement in single curtain. Typical reinforcement would be at least
#4 bars @ 48 in.
– Add more flexural reinforcement if required, usually uniformly distributed.
In-Plane Flexural Strength of Lineal Walls (1)
Design Example (1) Refer to NEHRP Design Examples (FEMA P-751) Ch. 10, Masonry
Design Example (1)
Design Example (1)
Trial design: (6) cells w/ (2) #6
Design Example (1)
Ductility Check
Design Example (1)
Ductility Check (cont.)
Design Example (1)
Ductility Check (continued)
SC > ST + P
Cm + Cs1 + Cs2 > Ts1 + Ts2 + Ts3 + P
315.5 + 53.6 + 28.1 > 52.8 + 52.8 + 43.4 + 45.1
397 kips > 194 kips OK
OK because comp capacity > tension capacity
Design Example (1)
P = 0 Case
Design Example (1)
Balanced Case
Design Example (1)
Pn = SC - ST = 534 kips
fPn = (0.9)(534) = 481 kips
S Mcl = 0:
Mn = = 23,540 in.-kips
fMn = (0.9)(23,540) = 1,765 ft-kips
Design Example (1) fPn – fMn Diagram Design Example (1)
Web sites for more information
154
155
? BSSC = www.bssconline.org
? TMS = www.masonrysociety.org
? ACI = www.concrete.org
? ASCE / SEI = www.seinstitute.org
? MSJC = www.masonrystandards.org
? NCMA = www.ncma.org
? BIA = www.bia.org
Acknowledgements
? This presentation was adapted from material prepared by Prof. Richard E. Klingner, University of Texas at Austin and by Dr. James Harris, J.R. Harris & Co.
? Some of the material originally prepared by Prof. Klingner was for a US Army short course.
? Some of the material originally prepared by Prof. Klingner was for The Masonry Society and is used with their permission.
? The material originally prepared by Dr. Harris was for FEMA, The Building Seismic Safety
Council, and the American Society of Civil Engineers.
Questions?
Title Slide for Masonry Structures
Design of Masonry Structures -1
Topic 12 deals with the seismic design of masonry structures.
In this first slide, we see examples of different applications of masonry : on the left,
a low-rise bearing-wall building of reinforced masonry; in the center, a high-rise
bearing-wall building of reinforced masonry; and on the right, stone and clay unit
veneer over a frame structure.
Design of Masonry Structures -2
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -3
Because many in the intended audience may not have studied masonry recently,
the module begins with a review of the basic components of masonry and of the
basic behavior of wall-type structures. It then addresses the specification of
masonry units, mortar, grout, and accessory materials. It continues with the
rudiments of the mechanical behavior of masonry. It then reviews the Masonry
Standards Joint Committee (MSJC) Code and Specification, which is the
fundamental technical resource behind the NEHRP Recommended Provisions. It
concludes with the design and detailing of a reinforced masonry shear wall.
Design of Masonry Structures -4
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -5
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -6
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -7
Let’s start by reviewing masonry basics. Masonry is made up of units, mortar,
grout, and accessory materials. The mortar holds the units together as well as
apart, compensating for their dimensional tolerances. The grout is a fluid concrete
mixture used to fill voids in the masonry and to anchor deformed reinforcement.
Design of Masonry Structures -8
Masonry units can be laid in different bond patterns. The most common of these is
1/2 running bond, often called simply “running bond.”
Horizontal bed joints are
continuous; vertical head joints alternate courses, and the head joint of one course
aligns with the middle of the unit on the adjacent courses. In stack bond (referred to
in the MSJC Code and Specification as “other than running bond”), the head joints
are continuous between adjacent courses.
Design of Masonry Structures -9
Masonry units have three basic systems of dimensions: nominal, specified, and
actual.
Nominal dimensions are used to lay out a structure. A common size C90 unit has
nominal dimensions of 8 by 8 by 16 inches.
Specified dimensions are nominal dimensions minus one-half the thickness of a
joint on all sides of the unit. Since masonry joints are normally 3/8-in. thick, the
specified dimensions of a nominal 8 x 8 x 16-in. unit are 7-5/8 by 7-5/8 by 15-5/8
inches.
Actual dimensions are what the unit actually measures and should lie within the
specified dimensions, plus or minus the specified dimensional tolerance.
Design of Masonry Structures -10
Clay masonry units are specified by ASTM C62 (building brick) or C216 (facing
brick). They are usually solid and may have small core holes to facilitate drying and
firing. Because clay masonry units usually have more than enough compressive
strength, the core holes are ignored unless they occupy more than 25% of the area
of the units.
Design of Masonry Structures -11
Mortar for unit masonry is specified by ASTM C270. In specifying mortar, the
designer must make three decisions:
The first decision involves the cementitious system to be used. Three cementitious
systems are available: portland cement-lime mortar; masonry cement mortar; and
mortar cement mortar.
Design of Masonry Structures -12
Mortar for unit masonry is specified by ASTM C270. In specifying mortar, the
designer must make three decisions:
The first decision involves the cementitious system to be used. Three cementitious
systems are available: portland cement-lime mortar; masonry cement mortar; and
mortar cement mortar.
Design of Masonry Structures -13
Within each cementitious system, the designer must specify the mortar type.
Mortar type describes the amount of cement in the mortar compared to the amount
of other constituents.
The designations for mortar type were intentionally selected as alternating letters in
the phrase “mason work,”avoiding the connotations that might be associated with
designations such as “A,”“B,”“C,”and “D.”
Going from Type K to Type M, mortar has an increasing volume proportion of
portland cement or other cements. It sets up faster and has higher compressive
and tensile bond strengths. As the volume proportion of portland cement increases,
mortar is less able to deform when hardened.
Types N and S are specified for modern masonry construction.
Design of Masonry Structures -14
Under ASTM C270, mortar can be specified by proportion or by property. The
proportion specification is the default.
When mortar is specified by proportion, a Type S PCL mortar has volume
proportions of 1 part cement to about 0.5 parts hydrated mason’s lime to about 4.5
parts mason’s sand. A Type N masonry cement mortar (using the most common
single-bag case) has one part Type N masonry cement and about 3 parts mason’s
sand.
Note that the amount of water is not specified. This is because the water should be
adjusted by the mason in the field to achieve good workability.
Design of Masonry Structures -15
“Flow”
is a standard ASTM measurement of the workability of a mortar. Mortar in
the field typically has a flow of 130 to 135. ASTM specifications have no
requirements for the properties of mortar mixed to field flow. ASTM property
specifications are based on mortar with a so-called “laboratory flow”
of 110
representing the characteristics of mortar after some of the water has been
absorbed from it by the surrounding units.
To specify mortar by proportion according to ASTM C270 is relatively simple. The
required proportions are given in the specification, and compliance is verified by
verifying that the mortar is being batched using those proportions.
To specify mortar by property according to ASTM C270, one must evaluate, at
laboratory flow of 110, the compressive strength, air content, and retentivity of
different mortars and then decide on volume proportions that will meet the required
criteria. Finally, one must verify in the field that the mortar s being batched using
those proportions.
Design of Masonry Structures -16
The proportion specification is the default. Unless the property specification is
used, no mortar testing is necessary.
Some suggest that the words “by proportion”
be added to the end of specifications
to emphasize that compliance with proportion specifications involves no testing
whatsoever.
The proportion of water is not specified. It is determined by the mason to achieve
good productivity and workmanship.
Masonry units absorb water from the mortar decreasing its water-cement ratio and
increasing its compressive strength. Mortar need not have high compressive
strength.
Design of Masonry Structures -17
Grout for unit masonry is specified by ASTM C 476, which addresses two kinds of
grout: fine grout which is composed of cement, sand and water and coarse grout,
which is composed of cement, sand, pea gravel and water. The fairly common
practice of specifying grout as concrete is acceptable but only if the resulting
mixture proportion conforms to C476.
ASTM C 476 permits a small amount of hydrated lime but does not require any.
Lime is usually not used in plant-batched grout because lime is not available in such
plants.
Design of Masonry Structures -18
Under ASTM C476, grout can be specified by proportion or by compressive
strength.
The proportion specification is simpler. It requires only that volume proportions of
ingredients be verified.
Specification by compressive strength is more complex. It requires compression
testing of grout in a permeable mold (ASTM C 1019).
Design of Masonry Structures -19
If grout is specified by proportion, compliance is verified only by verifying
proportions.
For example, fine grout has volume proportions of 1 part cement to about 3 parts
mason’s sand. Coarse grout has volume proportions of 1 part cement to about 3
parts mason’s sand and about 2 parts pea gravel.
Unless the compressive-strength specification is used, no grout testing is
necessary.
Design of Masonry Structures -20
The proportion of water in grout is not specified. The slump should be 8 to 11
inches.
Masonry units absorb water from the grout, decreasing its water-cement ratio and
increasing its compressive strength. High-slump grout will still be strong enough.
Design of Masonry Structures -21
In designing and specifying masonry according to the MSJC Code, the role of f’
m is
analogous to that of f’
c for concrete.
For concrete, the designer states an assumed value of fc.
and compliance is verified
by compression tests on cylinders cast in the field and cured under ideal conditions.
For masonry, the designer states an assumed value of fm.
and compliance is verified
either by the “unit strength method,”
or by the “prism test method.”
Design of Masonry Structures -22
The MSJC Code offers two ways of demonstrating compliance with the specified f’
m.
The simplest is the “unit strength method.”
Using compressive strengths for
standard ASTM units obtained by the unit manufacturer as part of production quality
control, mortar meeting ASTM C270 and grout meeting ASTM C476 or having a
compressive strength of at least 2000 psi, conservative values for f’
m can be taken
from Tables 1 and 2 of the Specification.
Alternatively, prisms can be constructed and tested by ASTM C1314.
Design of Masonry Structures -23
For example, in clay masonry, if units have a compressive strength of at least 4150
psi and ASTM C270 Type N mortar is used, the prism strength can be taken as
1500 psi.
In concrete masonry, if units have a compressive strength of at least 1900 psi
(which happens to be the minimum for C90 units) and ASTM C270 Type S mortar is
used, the prism strength can be taken as 1500 psi.
A specified prism strength of 1500 psi is very common for masonry.
Design of Masonry Structures -24
If compliance with the specified f’
m is verified by the unit strength method and
compliance with ASTM C270 (mortar) and ASTM C476 (grout) is verified by
proportion), no job-specific testing whatsoever is required.
Design of Masonry Structures -25
Finally, the MSJC Specification requires compliance with the specified products
(Article 2), which means units, mortar, grout and accessory materials, and with the
specified execution (Article 3), which means inspection, preparation and installation
of masonry, reinforcement, grout and prestressing tendons.
Design of Masonry Structures -26
Design of Masonry Structures -27
One of the most important details in a masonry building is the expansion joint under
shelf angles in clay masonry veneer. Clay masonry expands over time; concrete
and concrete masonry shrink. If the veneer is laid without the expansion joint, it will
end up supporting the building even though it is not made to resist the resulting
compression.
Design of Masonry Structures -28
Slide shows diagram of fully grouted wall with mortar in all cells.
Design of Masonry Structures -29
Slide shows non-grouted wall. The webs are ordinarily not mortared.
Design of Masonry Structures -30
Note that the webs that are not adjacent to a grouted cell usually do not
have any mortar.
Design of Masonry Structures -31
This loading applies to all masonry walls, whether “participating”
or not. If
not participating, the connections at the top must allow relative motion in the
plane of the wall.
Design of Masonry Structures -32
Tee-beam design is much the same as in reinforced concrete.
Design of Masonry Structures -33
This style of construction was popular in the mid twentieth century.
Design of Masonry Structures -34
Basic concept of analysis for distribution of seismic forces; the unit force will
be higher in the stiffer elements.
Design of Masonry Structures -35
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -36
In the context of the MSJC Code and Specification as referenced by the
NEHRP Recommended Provisions, masonry is composed of units held
together by mortar. The masonry is usually reinforced (either by prescription
or by design methodology), and the reinforcement is surrounded by grout.
The result is an integral material very similar to reinforced concrete.
Design of Masonry Structures -37
Modern reinforced masonry is commonly composed of hollow concrete or
clay masonry units, jointed together by cementitious mortar. Deformed
reinforcement is placed vertically and horizontally within voids in the
masonry, which are then filled with grout, a fluid concrete-like mixture.
Design of Masonry Structures -38
Emphasize that the failure of a masonry prism in compression usually occurs upon
a tensile splitting failure, and the restraint of the lateral expansion of the mortar is
what creates the tension in the masonry unit.
Design of Masonry Structures -39
Compressive stress-strain behavior is evaluated using a masonry “prism”
composed of units bonded by mortar and filled with grout (if it is intended to
represent grouted construction). The individual behavior of units, mortar,
and grout is not nearly as important as the behavior of the composite.
Design of Masonry Structures -40
Head joints are weak because the mortar shrinks. In contrast to bed joints,
there is no gravity action to maintain the contact.
Design of Masonry Structures -41
A multi-wythe wall may act as a composite wall, or it may act as a series of
parallel thin walls.
Design of Masonry Structures -42
Slide shows photograph of grout-block separation.
Design of Masonry Structures -43
Slide shoes various defects in grouted wall.
Design of Masonry Structures -44
Slide shows cell with congested reinforcement making it difficult to flow grout into
place.
Design of Masonry Structures -45
Slide shows photo of masonry wall with spalled face shells.
Design of Masonry Structures -46
The truss analogy is that vertical and diagonal struts of masonry resist
compression in conjunction with horizontal and vertical tension ties of rebar.
Design of Masonry Structures -47
If unreinforced masonry does not fail in shear or slide, it will rock (overturn).
If the masonry is reinforced, the vertical steel forms a couple with masonry in
compression to resist the overturning moment.
Design of Masonry Structures -48
Reinforced masonry is relatively ductile in bending. The confinement figure
is not particularly pertinent, as it is difficult to confine masonry.
Design of Masonry Structures -49
Slide shows possible out-of-plane failures (flexural strength and anchorage
failures) in masonry walls.
Design of Masonry Structures -50
Slide shows photo of house with out-of-plane masonry wall failures.
Design of Masonry Structures -51
Summary of Masonry Behavior
Design of Masonry Structures -52
Design implications for masonry structures
Design of Masonry Structures -53
This is a list of topics covered in this review module on masonry design
according to the NEHRP Recommended Provisions, which is developed for
the Federal Emergency Management Agency (FEMA) by the Building
Seismic Safety Council (BSSC) of the National Institute of Building Sciences
(NIBS).
Design of Masonry Structures -54
Slide is a diagram of design standards uied for Masonry structures.
Design of Masonry Structures -55
The NEHRP Recommended Provisions reference the MSJC Code and
Specification. That document is developed under ANSI-consensus rules by the
Masonry Standards Joint Committee, which is sponsored jointly by The Masonry
Society, The American Concrete Institute, and The American Society of Civil
Engineers.
Design of Masonry Structures -56
This slide shows the organization of the MSJC Code. It is linked to the MSJC
Specification.
Design of Masonry Structures -57
The MSJC Specification is referenced by and linked to the MSJC Code. The
Specification has three articles governing general provisions, products, and
execution, respectively.
Design of Masonry Structures -58
The MSJC Code references and is intended to be used with the MSJC
Specification.
In the Code, design provisions are given in Chapters 1 through 7 and Appendix A.
Sections 1.2.4 and 1.14 require a QA program in accordance with the Specification.
Section 1.4 invokes the Specification by reference.
The Specifications requires verification of compliance with specified fm.; compliance
with the required level of quality assurance; and compliance with the specified
products and execution.
Design of Masonry Structures -59
Chapter 1 of the MSJC Code is an “umbrella”
chapter. It gives basic requirements
that govern over the other provisions. As with other slides, the sections marked in
orange are emphasized in the slides that immediately follow.
Design of Masonry Structures -60
Code Section 1.8 deals with material properties to be used for design. It specifies
the values of chord modulus of elasticity, shear modulus, thermal expansion
coefficients, and creep coefficients for clay, concrete, and AAC masonry. It also
gives moisture expansion coefficients to be used for clay masonry and shrinkage
coefficients to be used for concrete masonry.
Design of Masonry Structures -61
The MSJC Code uses two different ways of computing section properties. To
compute member stresses or capacities, use the weakest section. For hollow unit
masonry bedded on the outside only (face-shell bedding), this is the area of the face
shells only.
Design of Masonry Structures -62
For computing slenderness-related properties, use the average section (the net
area of units of face-shell bedded masonry).
Design of Masonry Structures -63
Reinforcing bars must be embedded in grout; joint reinforcement can be embedded
in mortar. Minimum distances between reinforcement and the insides of cells or
void spaces are specified as are minimum cover distances for protection of
reinforcement from corrosion. Standard hooks are defined.
Design of Masonry Structures -64
Section 1.17 applies to all masonry except glass unit masonry and veneers.
It seeks to improve performance of masonry structures in earthquakes by
improving the ductility of masonry members and the connectivity of masonry
members.
Seismic requirements for autoclaved aerated concrete (AAC) masonry are
somewhat different and are not addressed here.
Design of Masonry Structures -65
In Code Section 1.17, the structure’s Seismic Design Category (SDC) is defined
according to ASCE 7. The SDC depends on seismic risk (geographic location),
importance, and underlying soil.
The SDC determines the required types of shear walls (prescriptive reinforcement);
the prescriptive reinforcement required for other masonry elements; and the
permitted design approaches for LFRS (lateral force-resisting system).
Design of Masonry Structures -66
Seismic design requirements are keyed to ASCE 7 Seismic Design
Categories (from A up to F). Requirements are cumulative; requirements in
each “higher”
category are added to requirements in the previous category.
Design of Masonry Structures -67
Seismic design requirements are keyed to ASCE 7 Seismic Design
Categories (from A up to F). Requirements are cumulative; requirements in
each “higher”
category are added to requirements in the previous category.
Design of Masonry Structures -68
Basics of seismic design
Design of Masonry Structures -69
Basics of seismic design.
Design of Masonry Structures -70
Basics of seismic design.
Design of Masonry Structures -71
In Seismic Design Category A, a drift limit of 0.007 and a minimum design
connection force are imposed for wall-to-roof and wall-to-floor connections.
In Seismic Design Category B, the lateral force resisting system cannot be
designed empirically.
Design of Masonry Structures -72
In Seismic Design Category A, a drift limit of 0.007 and a minimum design
connection force are imposed for wall-to-roof and wall-to-floor connections.
In Seismic Design Category B, the lateral force resisting system cannot be
designed empirically.
Design of Masonry Structures -73
In Seismic Design Category C, all walls must be considered shear walls
unless isolated. Shear walls must meet minimum prescriptive requirements
for reinforcement and connections (ordinary reinforced, intermediate
reinforced, or special reinforced) and other walls must meet minimum
prescriptive requirements for horizontal or vertical reinforcement.
Design of Masonry Structures -74
In Seismic Design Category D, masonry that is part of the lateral force
resisting system must be reinforced so that .v + .h .
0.002, and .v and .h .
0.0007. Type N mortar and masonry cement mortars are prohibited in the
lateral force resisting system. Shear walls must meet minimum prescriptive
requirements for reinforcement and connections (special reinforced) and
other walls must meet minimum prescriptive requirements for horizontal and
vertical reinforcement.
Design of Masonry Structures -75
Basics of seismic design.
Design of Masonry Structures -76
This slide illustrates the minimum reinforcement requirements for special reinforced
masonry shear walls.
Design of Masonry Structures -77
In Seismic Design Categories E and F, additional requirements are imposed
for stack-bond masonry because it is inherently weaker in flexure across
continuous head joints.
Design of Masonry Structures -78
This slide summarizes the requirements for different shear wall types and the
Seismic Design Categories in which each type is permitted to be used.
Design of Masonry Structures -79
Section 1.158of the MSJC Code requires a quality assurance program in
accordance with the Specification. The section contemplates three levels of quality
assurance (A, B, C): compliance with specified fm., increasing levels of quality
assurance with increasingly strict requirements for inspection, and for compliance
with specified products and execution.
Design of Masonry Structures -80
Section 1.18 of the MSJC Code gives minimum requirements for inspection,
tests, and submittals.
Design of Masonry Structures -81
That section specifies a minimum grout spacing (Table 1.19.1).
With respect to embedded conduits, pipes and sleeves, it requires that the
effects of openings be considered in design and that masonry alone be
considered effective in resisting loads.
With respect to anchorage of masonry to structural members, frames and
other construction, it requires that the type, size, and location of connectors
be shown on drawings.
Design of Masonry Structures -82
Now let’s move to Chapter 3 of the MSJC Code dealing with strength design. It is
this chapter that first addresses the fundamental basis for strength design.
Design of Masonry Structures -83
Factored design actions must not exceed nominal capacities, reduced by .
factors.
The quotient of load factor divided by ...factor is analogous to safety factor of
allowable stress design and should be comparable to that safety factor.
Design of Masonry Structures -84
The design strength must exceed required strength.
To give additional protection against brittle shear failure, the design shear strength
must exceed the shear corresponding to the development of 1.25 times the nominal
flexural strength (capacity design). The nominal shear strength need not, however,
exceed 2.5 times the required shear strength.
Design of Masonry Structures -85
The table of this slide summarizes the capacity reduction factors used by the MSJC
Code. For reinforced masonry, they are quite similar to those of ACI 318.
Design of Masonry Structures -86
This slide summarizes capacity reduction factors for the design of anchor bolts.
Design of Masonry Structures -87
The MSJC Code imposes the drift limits of ASCE 7-02. It requires that deflections
of unreinforced masonry be based on uncracked sections and that deflections of
reinforced masonry be based on cracked sections.
Design of Masonry Structures -88
Tensile capacity is governed by tensile breakout, by yield of the anchor in tension,
and by tensile pullout (for bent-bar anchor bolts only).
Shear capacity is governed by shear breakout and by yield of the anchor in shear.
Combined tension and shear are conservatively handled using a linear interaction
relationship.
Design of Masonry Structures -89
Compressive strength of masonry.
Design of Masonry Structures -90
In contrast to earlier versions of the MSJC Code, the 2005 and 2008 editions
specify identical values of the modulus of rupture for in-plane and out--ofplane
bending (Table 3.1.8.2). Modulus of rupture values are lower for
masonry cement and air-entrained portland cement-lime mortar and are
higher for grouted masonry. For grouted stack-bond masonry, fr = 250 psi
parallel to bed joints.
Design of Masonry Structures -91
The specified yield strength of reinforcement is not to be taken in excess of
60 ksi.
The actual yield strength is not to exceed 1.3 times the specified value (to
avoid excesses of actual flexural capacity, which can lead to excessive shear
demand).
The compressive strength of reinforcement is to be ignored unless the
reinforcement is tied in compliance with Code 2.1.6.5.
Design of Masonry Structures -92
Masonry in flexural tension is considered to be cracked. Flexural tension is
to be resisted entirely by reinforcing steel. Design is similar to strength
design of reinforced concrete.
Design of Masonry Structures -93
Section 3.3 of the MSJC Code deals in detail with the assumptions
underlying strength design of reinforced masonry:
Section 3.3.3 addresses reinforcement requirements and details, including
maximum steel percentage.
Section 3.3.4 addresses design of piers, beams and columns, including
nominal axial and flexural strength and nominal shear strength
Section 3.3.5 addresses design of walls for out-of-plane loads.
Section 3.3.6 addresses design of walls for in-plane loads.
Let’s look at each of these in more detail.
Design of Masonry Structures -94
The basic assumptions of flexural design in reinforced masonry are quite
similar to those of reinforced concrete.
Continuity between reinforcement and grout is assumed. Equilibrium must
be satisfied. The maximum usable strain is to be taken as .mu = 0.0035 for
clay masonry and 0.0025 for concrete masonry.
Plane sections are assumed to remain plane. An elastoplastic stress-strain
curve is used for for reinforcement; and the tensile strength of masonry is to
be neglected.
The compressive stress block is idealized as an equivalent rectangle with a
height of 0.80 fm.
and a depth of 0.80 c.
Design of Masonry Structures -95
This slide summarizes how those flexural assumptions are applied. As will
be discussed subsequently, sections are required to be tension-controlled so
the strain gradient varies across the depth of the cross-section from the
maximum useful strain in the masonry to a steel strain at least equal to yield.
Reinforcement is considered to be elastoplastic. The equivalent rectangular
stress block is taken as shown.
The axial force in the cross-section is computed as the difference between
the compressive and the tensile forces, and the moment is computed as the
summation of each of those forces times its respective distance from the
plastic centroid (usually the centerline) of the cross-section.
For concrete and masonry design, the plastic centroid is defined as the line
of action of the resultant force in the cross-section corresponding to a
uniform compressive strain equal to the maximum useful strain in the
concrete or masonry.
Design of Masonry Structures -96
Section 3.3.3 of the MSJC Code addresses reinforcement requirements and details.
The diameter of reinforcement in eighths of an inch must not exceed 1/8 the
nominal wall thickness. For example, in a nominal 8-in. wall, reinforcement must
not be larger in diameter than #8 (nominal diameter 8/8 inch). This is intended to
prevent failure by the masonry by splitting along the bar.
Standard hooks are defined. Development length is based on pullout and on
splitting (bar-to-cover and bar-to-bar). In walls, shear reinforcement must be bent
around extreme longitudinal bars (intended to increase the effectiveness of the
hooks).
Required splice length is based on required development length; welded and lap
splices must develop 1.25 fy .
Design of Masonry Structures -97
This slide illustrates the principle behind the maximum reinforcement
limitations of Section 3.3.3.5 of the MSJC Code. Assumed is a critical strain
gradient, whose maximum value on the compression side of the element is
the maximum useful strain in masonry and whose maximum value on the
tension side of the element is a multiple of the specified yield strain in that
reinforcement. That multiple depends on the expected flexural ductility
demand on the element. In contrast to the calculation of flexural capacity,
the contribution of compressive reinforcement can be considered.
That critical gradient defines the location of the neutral axis and the
dimensions of the compressive stress block. That, in turn, gives the
maximum compressive capacity of that block. The combination of tensile
steel area (acting at a stress limited by fy) and axial compression must not
exceed that compressive capacity. The intent of this provision is to prevent
compressive crushing of that block and, therefore, ensure tension-controlled
behavior.
Design of Masonry Structures -98
The 2005 MSJC Code does not use moment magnifiers. Slenderness is
addressed by multiplying axial capacity by slenderness-dependent
modification factors. Since axial loads are usually quite low compared to
axial capacity in concentric compression, slenderness effects are usually not
significant.
Design of Masonry Structures -99
Slide shows truss analogy for developing shear strength in wall.
Design of Masonry Structures -100
Section 3.3.4 of the MSJC Code addresses nominal shear strength of
reinforced masonry in a way that is quite similar to design of reinforced
concrete. Nominal shear resistance is taken as the summation of resistance
from masonry, plus resistance from shear reinforcement. To prevent
diagonal crushing of masonry, upper limits are imposed on Vn (and thereby
on Vs).
Design of Masonry Structures -101
Nominal shear resistance due to masonry depends on the aspect ratio of the
element, and varies from 2.25 to 4 times the product of the square root of f’
m,
and the cross-sectional area of the element.
Nominal shear resistance due to shear reinforcement is computed similarly
to reinforced concrete as the product of the number of layers of shear
reinforcement crossing a 45-degree crack, the cross-sectional area of each
layer of reinforcement, and the specified tensile yield strength of the
reinforcement. The MSJC Code uses an efficiency factor to account for the
fact that shear reinforcement does not yield uniformly over the height of a
wall element.
Design of Masonry Structures -102
Section 3.3.4 2 of the MSJC Code addresses requirements for beams,
defined as elements whose design axial load is low. To prevent brittle
fracture of tensile reinforcement following flexural cracking, nominal capacity
is required to be at least equal to 1.3 times the computed cracking capacity.
To prevent lateral-torsional buckling, lateral bracing is required to be spaced
at most 32 times the beam width. To ensure reasonable flexural capacity,
the total depth (nominal dimension) cannot be less than 8 in.
Design of Masonry Structures -103
In the context of the MSJC Code and Specification, a “pier”
is an isolated
structural element resisting axial compression and meeting certain geometric
criteria. Wall segments are normally not piers.
For piers, design axial load cannot exceed 0.3 An fm.. The nominal thickness
must be between 6 and 16 in. The nominal plan length must be between 3
and 6 times the nominal thickness. The clear height must not be more than
5 times the nominal plan length.
Design of Masonry Structures -104
In the context of the MSJC Code and Specification, a “column”
is an
isolated structural element resisting axial compression, and meeting certain
geometric criteria. Wall segments are normally not columns.
Columns must have a ratio of total longitudinal reinforcement to gross cross-
sectional area between 0.0025 and 0.04. They must meet maximum flexural
reinforcement requirements of Section 3.3.3.5 of the MSJC Code.
Longitudinal reinforcement must be supported laterally (tied) in accordance
with Section 2.1.6.5 of the MSJC Code. Their least cross-sectional
dimension must be at least 8 in., and their nominal depth must not exceed 3
times their nominal width.
Design of Masonry Structures -105
Walls are designed under out-of-plane loads using a strength interaction
diagram.
Design of Masonry Structures -106
Maximum reinforcement requirements are given by Section 3.3.3.5 of the
MSJC Code. Slenderness effects are addressed (for walls loaded out of
plane only) by computing a magnified moment based on computed out-ofplane
deflections.
Nominal shear strength is given by Section 3.3.4.1.2.
Design of Masonry Structures -107
Flexural design of walls for in-plane loads is again handled using a strength
interaction diagram. Because such walls have multiple layers of
reinforcement over their depth, hand computations are tedious, and hand
approximations (see design example at the end of this module) or computer
spreadsheet calculations are preferable.
Design of Masonry Structures -108
Code Section 3.3.6 addresses design of walls for in-plane loads. Maximum
longitudinal (flexural) reinforcement is specified by Section 3.3.3.5. Nominal
shear strength is calculated by Section 3.3.4.1.2. Vertical reinforcement
must be at least one-half the horizontal reinforcement. Usually this will not
govern since a certain amount of vertical reinforcement is needed to resist
out-of-plane loads (see the example at the end of this module).
Design of Masonry Structures -109
Most practicing engineers are very familiar with the behavior of frame-type
structures. Many, however, may never have formally studied the behavior of
wall-type structures. For that reason, it is appropriate to review that
behavior. The following series of slides presents the basic starting point for
design of wall-type structures and their components.
Design of Masonry Structures -110
Most practicing engineers are very familiar with the behavior of frame-type
structures. Many, however, may never have formally studied the behavior of
wall-type structures. For that reason, it is appropriate to review that
behavior. The following series of slides presents the basic starting point for
design of wall-type structures and their components.
Design of Masonry Structures -111
This slide shows how a wall-type building resists gravity loads. Nonbearing
walls resist concentric axial loads from their own weight only. Bearing walls
resist concentric axial loads from their own weight, and possibly eccentric
axial loads from the reactions of roof elements. Both types of wall can be
idealized as vertically spanning strips simply supported at the level of floor
slab and horizontal diaphragms.
Design of Masonry Structures -112
This slide shows how wall-type structures resist lateral loads.
Vertically spanning strips in the walls oriented perpendicular to the direction
of lateral load resist combinations of axial load (from self-weight and roof
bearing) and moments from out-of-plane wind.
Reactions from those strips are transferred to horizontal diaphragms that
must resist in-plane shears and moments. The load transfer to diaphragms
and the in-plane resistance are accomplished with the help of the bond
beams that act as diaphragm chords.
The diaphragms, in turn, transfer their reactions to walls oriented parallel to
the direction of lateral load, which then act as shear walls.
Design of Masonry Structures -113
When walls oriented perpendicular to the direction of lateral load have door
or window openings, these interrupt the path of vertical force transmission
and change the design concept to a combination of horizontally spanning
and vertically spanning strips.
The openings’
vertical strips resist the loads that act directly on them and
also reactions from the horizontal strips that they support. Strip B, for
example, resists loads acting on its own width and also loads from the right
half of the horizontal strips at the door and from the left half of the horizontal
strips at the window. Strip B therefore resists loads tributary to an effective
width extending from the center of the opening to the left, to the center of the
opening to the right.
Design of Masonry Structures -114
Openings in effect increase the original design actions on each strip by a
factor equal to the ratio of the effective width of the strip divided by the actual
width. This is precise for wind loads. It is usually conservative for seismic
loads because the masses associated with doors and windows are often
less than those associated with walls.
Basically, because the openings don’t change the loads on the wall, the
wall’s required vertical reinforcement remains the same, and the designer
must simply move that steel horizontally so that it does not coincide with the
openings.
Design of Masonry Structures -115
Vertically spanning strips in walls perpendicular to the direction of lateral load
are subjected to axial load and possibly to eccentric gravity load from the
roof.
If the strips are assumed to be simply supported at the level of the slab, the
moment diagram due to eccentric gravity load varies linearly from its
maximum value at the roof, to zero at the slab. These moments must be
combined with moments from out-of-plane wind and earthquake forces.
This example shows the effect on the moment diagram due to a parapet and
also shows that wind can act in either direction.
Design of Masonry Structures -116
Design of the vertical strips consists simply of comparing the combination of
factored design moment and axial load, with the design capacity expressed
in terms of a moment-axial force interaction diagram, including the effects of
phi-factors.
In such walls, axial loads are usually quite low, and the out-of-plane flexural
capacity of the strips is essentially proportional to their flexural
reinforcement.
Moment-axial force interaction diagrams can be computed by hand or by
spreadsheet. Such walls usually have only a single layer of reinforcement at
their midplane.
Because such a single layer usually cannot be supported laterally, it is not
considered effective in resisting compressive stress. It is permitted to be
included in computing maximum tensile reinforcement.
Design of Masonry Structures -117
Parallel walls must be designed to resist shears from the diaphragms plus
moments and axial forces.
Design of Masonry Structures -118
Flexural design of shear walls is expressed in terms of the relationship
between combinations of factored moment and axial force and a moment-
axial force interaction diagram.
The easiest way to generate such a diagram is by use of a spreadsheet in
which the position of the neutral axis is moved from one side of the cross-
section to the other; forces in masonry and reinforcement are computed; and
the resulting axial force and moment are calculated.
Design of Masonry Structures -119
The shear design of shear walls is quite similar to that of reinforced concrete
shear walls. Nominal resistance is taken as the summation of resistance
from masonry plus the resistance from shear reinforcement. Nominal
resistance due to masonry is considered to vary with the aspect ratio of the
element. Capacity design is required for shear walls --they must either be
designed for a design strength at least equal to 1.25 times the shear
associated with development of the nominal flexural strength or for a nominal
strength at least equal to 2.5 times the required shear strength.
Because the nondimensional aspect ratio need not be taken greater than
1.0, nominal resistance due to masonry varies from 2.25 to 4.0 times the
product of the area and the square root of the specified compressive
strength of the masonry.
Design of Masonry Structures -120
In designing low-rise masonry buildings for lateral load, it is also necessary
to compute the distribution of lateral loads to shear walls.
The classic approach is to first determine whether the diaphragm is “rigid”
or
“flexible”
compared to the lateral force resisting system and then to carry out
the appropriate analysis for wall shears. In the next few slides, the
appropriate analysis for each case is briefly explained.
At the end, however, the designer is encouraged to reduce design effort by
simplifying the analysis for each case and finally by bounding the shears
from each case.
Design of Masonry Structures -121
In a structure with a rigid diaphragm, the classic approach is first to locate
the “center of rigidity,”
or shear center of the plan. The shear center is the
point through which lateral forces must be applied so that the building will not
twist in plan.
The lateral load is then decomposed into a load acting through the center of
rigidity and a torsional moment about the center of rigidity.
The lateral load produces direct shears on shear walls oriented parallel to
the direction of the lateral load; the torsional moment produces torsional
shears on all shear walls. For each wall, direct shears and torsional shears
are added to get the design shear. This process is tedious.
Design of Masonry Structures -122
This process can be simplified considerably by neglecting plan torsion. This
assumption is generally valid if the building has several walls oriented in
each plan direction and well-distributed about the plan perimeter. It is not
valid for garage-type buildings with one side almost completely open.
For low-rise buildings, it also is possible to neglect flexural deformations
because they are quite small. Considering shearing deformations only and
assuming uniform wall thickness and story height, the shearing stiffness of
different walls is simply proportional to their plan lengths.
Design of Masonry Structures -123
Consider the building plan shown above in which the wall on the left has a
plan length of 40 ft and the wall on the right is composed of three segments
with a plan length of 8 ft each.
The left and right walls together have a total stiffness proportional to their
total plan length of 64 ft. The wall on the left represents 40/64 (or 5/8) of that
stiffness and, therefore, resists 5/8 the applied shear. The wall on the right
resists the remaining 3/8 of the applied shear.
Design of Masonry Structures -124
For buildings with flexible diaphragms, the diaphragm is idealized as a
simply supported beam acting in the horizontal plane and resting on the
shear walls. Because the shear walls are very stiff compared to the
diaphragm, the shears on the shear walls depend on the tributary areas of
the diaphragm that each shear wall supports.
Design of Masonry Structures -125
For the same building studied above but with a flexible diaphragm, the left
and right shear walls each resist 1/2 the total lateral load.
Design of Masonry Structures -126
Further, it is possible to avoid the need to classify the diaphragm as “rigid”
or “flexible.”
Simply design each wall for the more critical of the simplified
rigid-diaphragm case and the flexible-diaphragm case.
For this example, the left-hand wall had a shear of 5/8 V for the rigid-
diaphragm case and a shear of 1/2 V for the flexible-diaphragm case. It
could therefore be designed for the more severe of the two design shears or
5/8 V.
The right-hand wall would be similarly designed for the worse of 3/8 V (rigid)
and 1/2 V (flexible) or 1/2 V.
Even though these two design shears sum to more than V, the design is
conservative and valid. It might be too conservative for a few cases in which
event the diaphragm stiffness would have to be evaluated.
Design of Masonry Structures -127
If the diaphragm is continuous, diaphragm shears are resisted by the total
depth of the diaphragm. If the diaphragm is discontinuous, diaphragms are
resisted by cover only. Flexural resistance comes from forces in diaphragm
chords separated by the internal lever arm (distance between chords)
Design of Masonry Structures -128
After designing the out-of-plane strips, the in-plane shear walls and the
lintels, additional details would have to be addressed: wall-diaphragm
connections, design of lintels for out-of-plane loads between wall-diaphragm
connections, connections between bond beam and walls, and connections
between walls and foundations.
Design of Masonry Structures -129
The first step is computation of factored design shears and moments.
Factored design moments and shears for in-plane loading depend on actions
transferred to shear walls by horizontal diaphragms at each floor level.
Factored design moments and shears for out-of-plane loading depend on
wind or earthquake forces acting between floor levels.
Design of Masonry Structures -130
The next step is to design the flexural reinforcement as governed by out-ofplane
loading, which usually will govern over the reinforcement necessary to
resist in-plane loading.
The practical wall thickness is governed by available unit dimensions. Using
concrete masonry units, nominal dimensions of 8 by 8 by 16 in. are most
common. This implies a specified thickness of 7-5/8 in., and a single curtain
of reinforcement, placed in the center of grouted cells.
The specified wall thickness is 7-5/8 in.
Proportion flexural reinforcement to resist out-of-plane wind or earthquake
forces. Because axial loads are small, the necessary reinforcement can be
estimated by dividing the maximum factored design moment from out-ofplane
loads by the product of the specified steel yield strength and the
internal lever arm.
Design of Masonry Structures -131
The next step is to design flexural reinforcement as governed by in-plane
loading. A moment-axial force interaction diagram can be computed by hand
or by spreadsheet. As an initial estimate for hand calculations, the approach
of Cardenas and Magura can also be used, and is discussed in a few more
slides.
Design of Masonry Structures -132
As noted previously, the 2005 MSJC Code places strict limits on maximum
flexural reinforcement. To keep the compressive stress block from crushing,
the maximum steel percentage decreases as axial load increases so that
design above the balance point is impossible.
Design of Masonry Structures -133
After determining the reinforcement required to resist out-of-plane loads, and
the reinforcement required to resist in-plane loads, the greater of the two
requirements governs. If out-of-plane requirements considerably exceed in-
plane requirements, consider making the wall thicker. In-plane over-
capacities in flexure can lead to an unacceptable increase in shear demand if
capacity design is used (see subsequent example).
Design of Masonry Structures -134
In checking shear capacity, the first step is to estimate the design shear.
If the structure is essentially elastic, factored design shears should be
computed based on factored design actions.
If the structure is expected to have significant inelastic flexural deformation,
then capacity design should be used. Design shears should be computed
based on flexural capacity.
In the above figure, the gray diagrams represent shears and moments from
factored design loads. The black diagrams represent shears and moments
corresponding to nominal flexural capacity. They are the gray
diagrams,divided by the capacity reduction factor for flexure. The red
diagrams represent the shears and moments corresponding to the probable
flexural capacity. They are the black diagrams, multiplied by the ratio of the
probable yield strength of the flexural reinforcement divided by the specified
yield strength and also multiplied by the ratio of the probable area of
reinforcement divided by the required reinforcement.
Design of Masonry Structures -135
As discussed previously, shear resistance is calculated similarly to that of
reinforced concrete.
Design of Masonry Structures -136
As discussed previously, Vm depends on aspect ratio.
Design of Masonry Structures -137
As discussed previously, total shear resistance is limited to prevent diagonal
crushing of masonry.
Design of Masonry Structures -138
Finally, the designer must check detailing, including cover and placement of
flexural and shear reinforcement. Boundary elements are not required
because ductility demand is usually low and maximum flexural reinforcement
is closely controlled.
Design of Masonry Structures -139
Detailing requirements usually are not difficult to satisfy.
Cover requirements are satisfied automatically by putting reinforcement in
grouted cells.
Flexural and shear reinforcement must comply with the minimum flexural
reinforcement and spacing dictated by the Seismic Design Category.
Flexural reinforcement is normally placed in single curtain.
Typical reinforcement would be at least #4 bars @ 48 in.
Horizontal reinforcement is also placed in the same single curtain.
Typical reinforcement would be at least #4 bars @ 48 in.
Additional reinforcement (usually uniformly distributed) can be added if
required to resist in-plane flexure.
Design of Masonry Structures -140
Now let’s look briefly at Cardenas and Magura’s approximation for flexural
strength.
Design of Masonry Structures -141
Slide shows elevation of wall for example problem in P-751.
Design of Masonry Structures -142
Slide shows a pier of the wall and forces acting on pier.
Design of Masonry Structures -143
Slide shows section of wall with grouted cells and reinforcement.
Design of Masonry Structures -144
Slide shows strain profile on wall section.
Design of Masonry Structures -145
Slide shows stress profile on wall section.
Design of Masonry Structures -146
Slide shows ductility check calculations.
Design of Masonry Structures -147
Slide shows analysis of section with zero axial load.
Design of Masonry Structures -148
Slide shows strain profile under balanced conditions.
Design of Masonry Structures -149
Slide provides calculations for wall axial strength and corresponding flexural
strength.
Design of Masonry Structures -150
Axial Force –Bending Moment interaction diagram for wall section.
Design of Masonry Structures -151
Diagram determining if wall has adequate strength.
Design of Masonry Structures -152
Further information on the topics presented here is given in these web sites.
Design of Masonry Structures -153
Acknowledgements
Design of Masonry Structures -154
Slide prompts participants for questions
Design of Masonry Structures -155