12 - seismic design of ductile shear walls

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)



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



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



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



Seismic Force

Resisting Systems

2005

Seismic Force

Resisting Systems

2015



Moderately Ductile Squat Shear Walls

(Pages 499-506)Cl. 10.16 CSA S304

General Provisions

2004



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



2014 CSA S304





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



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



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



Moderately Ductile Shear Walls

(Pages 499-506)Cl. 10.16 CSA S304

General Provisions 2004



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



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



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



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



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



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



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



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



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



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




• 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


ϕ ϕ 1uh

θϕohw2

∆ϕ h3

ϕε

d c0.002ℓ

2

θ ϕ hpϕ ℓ

20.002

In the Plastic Hinge

θ ϕ hpℓ2



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



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



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

12 - seismic design of ductile shear walls

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