Upload
others
View
20
Download
0
Embed Size (px)
Citation preview
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 1
Seismic Design of Ductile Shear Walls
12:30 PM – 2:30 PM
Bennett Banting
Lecture Outline1. 2004 and 2014 Standards Overview (15)
2. Moderately Ductile Squat Shear Walls a) 2004 Design (15)
b) 2014 Design (30)
3. Moderately Ductile Shear Walls a) 2004 Design (30)
b) 2014 Design (30)
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 2
2005 NBCC• Post-disaster
• “…a building that is essential to the provision of services in the event of a disaster…”
2005 Seismic Exemption
• Large portions of Canada exempt from seismic design
• Seismic Hazard Index < 0.12
• 2015 Change• No exemption
• Simplified analysis when seismic hazard index less than 0.16
• Post-Disaster structures under this threshold need not have Rd = 2.0
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 3
Equivalent Static Procedure• Applicable still for most masonry
buildings• Low rise• Low risk areas• Regular structures
• Elastic Force
Equal Displacement Assumption• Elastic Force
• 5% Damping• Reduced by ductility and
over strength factors• Rd, Ro
• Unreinforced masonry • Designed to be elastic• Rd, Ro = 1.0• No ductility (conservatively
assumed)
F
Δ
Fdesign
ΔuΔy
Felastic
Rd
Ro
Expected Strength
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 4
CSA S304
Change Change: Variety of Provisions that cover all wall types
Add Add: Seismic Chapter 16
Add Add: Ductile Shear Walls Category
Eliminate Eliminate: Limited Ductility Shear Walls Category
Challenges with the 2004 Standard• Limited Prescriptive Requirements
• Capacity design principles• Stiffness degradation• Reinforcement detailing• Inelastic curvature capacity calculations• Squat Wall Reinforcement
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 5
Seismic Force
Resisting Systems
2005
Seismic Force
Resisting Systems
2015
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 6
Moderately Ductile Squat Shear Walls
(Pages 499-506)Cl. 10.16 CSA S304
General Provisions
2004
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 7
Unsupported Height-to-Thickness Ratio• Ductility
• Reversed cycles of displacement• Yielding in tension → compression
• Propensity for buckling• Single layer of reinforcement
• h/(t+10) < 20
Reinforcement Ratios
ϕsρh ϕsρvPf
bwℓwfyϕsρv
Vf Pfbwℓwfy
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 8
2014 CSA S304
Reinforcement Ratios
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 9
Reinforcement Ratios
ρhVf
ϕsbwhwfyρv ρh
Psϕsbwℓwfy
Flexure-Governed
and Shear-Governed
Walls
• Minimum level of ductility assured • No feasible means to evaluate precise
shear ductility• 2 Pathways
• Flexural Failure• Must increase shear resistance to
ensure flexural failure
• Shear Failure• No additional shear resistance if shear
governed
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 10
Shear Governed Wall• hw = 3,000 mm
• ℓw = 3,200 mm
• DL = 150kN +S.W., EL = 50kN, LL = 50kN, SL = 75kN
• Mf = 150 kNꞏm
• Vf = 50 kN
• Partially-Grouted Construction• 20cm Concrete Block Units
• 25MPa Specified Block Strength
• Vertical Reinforcement = 15M @ 1,200mm
• Horizontal Reinforcement = 10M @ 1,200mm
Flexural Governed Wall• hw = 3,000 mm
• ℓw = 3,200 mm
• DL = 150kN +S.W., EL = 50kN, LL = 50kN, SL = 75kN
• Mf = 150 kNꞏm
• Vf = 50 kN
• Fully-Grouted Construction• 20cm Concrete Block Units• 25MPa Specified Block Strength
• Vertical Reinforcement = 15M @ 1,200mm
• Horizontal Reinforcement = 10M @ 1,200mm
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 11
Reinforcement Detailing• Where reinforcing bars are used
• 90° Standard Hook
• No lapping of horizontal reinforcement within 600 mm or ℓw/5 of wall ends
Review
• Moderately Ductile Squat Shear Walls• A standard wall type for low-rise structures• 2004 design requirements made it difficult to detail• Unintentional consequence
• 2014 CSA S304• Better clarification on reinforcement ratios• Capacity design• Specific end anchorage conditions for horizontal
reinforcement
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 12
Moderately Ductile Shear Walls
(Pages 499-506)Cl. 10.16 CSA S304
General Provisions 2004
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 13
Plastic Hinge
Visualized by
Curvature
Mcr
My
Mr
ϕy ϕu
EmIo
EmIcr
ϕy
ϕu
hp
Plastic Hinging
• Concentration of inelastic rotations • Facilitates ductility
• Extent(s) of Plastic Hinge1. Academic 2. Analysis for Capacity3. Prescriptive Detailing
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 14
Plastic Hinge Region• Extent greater of ℓw or hw/6
• Supported h/(t + 10) < 14 • 20 cm = 2.8 m• 25 cm = 3.5 m• 30 cm = 4.2 m
• εmu = 0.025
• hw / ℓw < 4• c < 0.2ℓw
• 4 ≤ hw / ℓw < 8• c < 0.15ℓw
Plastic Hinge Region
• Clause 10.16.4 Applies as well• Generally Cl. 10.16.5 is more
restrictive• One key requirement is missing in
CL. 10.16.5
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 15
Ductility Verification
• Ductility• Ratio of inelastic
deformations to elastic deformations
• Types• Curvature • Rotation • Displacement
μϕϕu
ϕyμθ
θuθy
μ∆∆u∆y
Elastic Beam
Theory
ϕ ϕ 1uh
θϕohw2
∆ϕ h3
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 16
Elastic Limit
• Elastic definition• Reinforcement up to yield• Masonry linear elastic region
• Define Yield Curvature• ϕy
• εs = εy
∆ϕ h
3
Plastic Hinge Theory
• Elastic Deformation until yielding
• Yielding extends up from base• Development of bars• Tension shift from shear cracks• Penetration of yield strains into
footing
• Plastic hinge• Top of wall rotates about centre
of hinge
V ΔyΔy + Δp = Δu
∆ ∆y ϕu ϕy hp hwhp2
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 17
Plastic Limit
• Ultimate Limit States• Masonry crushing failure• Reinforcement past yield
• Ultimate Curvature• ϕu
• εmu = 0.0025 now
• Rotation Concentrated in Plastic Hinge• Elastic curvatures elsewhere above
From Previous Lecture • Mf = 1,600 kNꞏm
• Pf = 550 kN
• 6.0 m Long• hp = 6.0m
• 8.0 m Tall
• 25 cm Units
• 30 MPa Block, Type S Mortar, Fully-Grouted
• 20M Vertical Reinforcement @1.2 m
Determine ϕy, ϕu, μΔ
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 18
Determine Yield Curvature 1. Strain Compatibility
a) Extreme tension reinforcement yielding
b) Elastic stress-strain in masonry
c) Compression reinforcement considered
d) No material reduction factors
ϕε
d c
Determine Yield Displacement
2. Force Equilibriuma) Elastic stresses in reinforcementb) Elastic stress is masonry
c = 1,189.2 mm
Fs εsEsAs
C εmEmbc2
ϕy
εyd1 c
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 19
Determine Ultimate
Curvature
• Strain Compatibility• Possible iterative solution with multiple
bars yielding or not yielding• Set εmu = 0.025
• No material reduction factors• Consider compression stress in
reinforcement
• Force Equilibrium• c = 468.4 mm
ϕu
0.0025c
Shear Resistance
• Reduce shear capacity within plastic hinge
• Masonry + Axial Load reduce by 50%
• Reduced sliding shear capacity at base of wall
• Reversed cycles of loading
• Reduce “C” by compressive force in reinforcement
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 20
Reinforcement Requirements
2014 CSA S304
• Major Changes • Unsupported Height Limits of Plastic Hinge• Partial Grouting of Plastic Hinge• Horizontal Reinforcement Requirements• Lap Splices • Extent of Plastic Hinge• Ductility Verification• Shear Capacity in Plastic Hinge
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 21
Unsupported Wall Height• Plastic Hinge Region
• h/(t + 10) < 20• Unless• h/(t +10) < 30
• Flange
• Boundary Element• Limited compression zone
c < 4bw or 0.3ℓw
Partially-Grouted Plastic
Hinge
• Low Aspect Ratio
• Low seismic hazard index
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 22
Reinforcement Details • 90° Hooks when reinforcing bars
are used in horizontal reinforcement
• No restriction on amount of vertical reinforcement lapped at any one cross-section
• Lap splices increased to 1.5ℓd
Inelastic Rotational Demand
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 23
Inelastic Rotational Demand
• Explicit validation of rotational ductility
• Top displacements estimated from crack section properties
• Consider whole building effects on rotations
• Plastic hinge • Centre of rotation
(denominator)• hp = ℓw
∆ ∆ℓ2
0.003
Inelastic Rotational Demand
ϕ ϕ 1uh
θϕohw2
∆ϕ h3
ϕε
d c0.002ℓ
2
θ ϕ hpϕ ℓ
20.002
In the Plastic Hinge
θ ϕ hpℓ2
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 24
Inelastic Rotational Capacity
• Plastic Hinge capacity is based on conservatively small plastic hinge
• ℓ / 2
• Plastic Hinge demand is based on a conservatively large plastic hinge
• ℓw
θℓ2
0.002
From Previous Lecture • Mf = 1,600 kNꞏm
• Pf = 550 kN
• 6.0 m Long
• 8.0 m Tall
• Δf1 = 2.19 mm∆f1Vh3
3EI1.20Vh0.4EA
Ag tℓw
Igtℓ12
θ∆ R R ∆ γ
hℓ2
0.003
θε ℓw2c
0.002
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 25
Shear Strength • Shear Design Strength
• Flexural ductility reduces shear strength
• Masonry and Axial Load Component multiplied by 75%
• Shear Design Force• Capacity design principles to assure
flexural failure
• Shear to meet that equal to lesser of nominal moment capacity
• RdRo = 1.3
Building Effects
• Plastic hinge and displacement based on longest wall
• Acknowledges rigid diaphragm effects
• Top displacement equal • Not rotations or ductility
demand
Engineered Masonry Design Course Saturday April 28, 2018
© 2018 Canada Masonry Design Centre 26
Building Effects
• Multiple Walls• Multiple ductilities• Earthquake force reduced by
single RdRo
• Attempt to reconcile this with longest wall
Review
• Moderately Ductile Shear Walls (2004)• Cumbersome to design• Lack of prescriptive details• Very restrictive reflecting state of research
• Moderately Ductile Shear Walls (2014)• Updated and more advanced• Reflective of CSA A23.3 and masonry research • Should help with post-disaster structures