masonry out-of- plane walls: slender wall design and ...for... · slenderness limited to low axial...

Engineered Masonry Design Course Friday April 27, 2018

© 2018 Canada Masonry Design Centre 1

Masonry Out-of-Plane Walls: Slender Wall Design and Serviceability4:30 PM – 5:30 PMBennett Banting

Lecture Outline

1. Slenderness Limited to Low Axial Loads (25)2. Serviceability Deflections (25)3. Supplemental eLearning (5)4. Design Checklist (5)



Slenderness Limited to Low Axial Loads:

-kh/t > 30

(Pages 386-388)Cl. 10 CSA S304

kh/t > 30• When the slenderness ratio exceeds 30

• Unreinforced masonry not permitted• Cl. 10.7.4.6 Applies

• More Restrictive design• Under-reinforced cross-section• Low axial loads

• Alternative Solution• Ensure fixity in wall

• k = 0.8



Slender Reinforced

Walls

kt/h > 30

Wall Details • Compare Fully-Grouted and

Partially-Grouted Walls• Details from previous lecture• hw = 8,000 mm• k = 1.0

kh/t = 33.3



Fully-Grouted

vs. Partially-Grouted

Property Fully-Grouted Wall Partially-Grouted Wall

½ Self-Weight 20.9 kN/m 12.2 kN/m

Pfmax 194.4 kN/m 100.1 kN/m

(EI)o 1,322 E9 N-mm2/m 1,159 E9 N-mm2/m

(EI)cr 510.2 E9 N-mm2/m 510.2 E9 N-mm2/m

ek 40 mm 68.1 mm

Cl. 10.7.4.6

10.7.4.6.2: Units > 140 mm

10.7.4.6.3: Eccentric Pin Connections

Assumed w/ Single Curvature

10.7.4.6.4:Pf ≤ 0.1ϕmf′mAe

10.7.4.6.5:c ≤ 0.6d

10.7.4.6.6:Total Magnified Moment



Solution Strategy: Fully-Grouted Wall

• ww = 1.4 kPa• PD = 50 kN• PDsw = 20.9 kN/m

• Load Case 1 • Pf = 76.1 kN/m• Mf = 15.7 kNꞏm/m• e = 206 mm


Ignore Grout (this range of P)

Pcritical

• These very slender walls tend to have low buckling capacity

• Walls in this range have high eccentricity

• (EI)eff = (EI)cr• Recall Pcr is proportionate to:• (EI)eff• 1/h2

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Mag

nific

atio

n Fa

ctor

P/Pcr



Self-Weight ONLY

• ww = 1.4 kPa• PDsw = 20.9 kN/m



kh/t > 30

PG FG



Alternative Solution Strategies

Fixed Ends• Assuring and Accounting for fixity• kh/t = 26.7• Improved Behaviour



Unit Strength, Size, Reinforcement• Switch to a larger block with

double layer of reinforcement • Increases d• Increases EI

• Irregular configuration• Tables in textbook do not apply

Section Properties

Io neff 1 As1, eff y d1 2 neff 1 As2, eff y d2 2beff, grtunit312

beff, ug12 tunit3 tunit 2tf 2

y 120mm neffEs

850f m, eff

0 nugAs1 d1 kd nugAs2 d2 kd beffkd 22

nugEs

850f m, ugifkd tf

Icr nug As1 d1 kd 2 nug As2 d2 kd 2 beff3

3

beff, gr beff, ug 1,000mm/m

beff, ug min s, 4ts

1,000mm/m



Service Load Deflections

- Span > 25d

(Pages 386-388)Cl. 10 CSA S304

Serviceability Limits

• Importance Factor • h/180 for most cases• Generally more critical than

serviceability of beams• Wind Load deflections



Deflections

Wall Cross-Section

• Partially-Grouted Wall Cross-section• hw = 6,000 mm• Pin-roller

• k = 1.0• P = 120 kN/m

• Include ½ the self-weight of the wall

• ω = 2.4 kPa• I = 0.75• Ms = 8.1 kNꞏm/m



Cracking Moment

• Equivalent Cross-Sectional Properties

• Last lecture

• Service Moment > Cracking Moment• Consider Secondary Effects as well

Mcr ft fcsyt Io fcs

PAe

When Ms < Mcr

∆s 5Msh248EmIo

Ms wh28 P ∆s

Convergence at

Ms = 8.4 kN ꞏ m/mΔ = h / 2,205



When Ms > Mcr

∆s 5Mcrh248EmIo

5 Ms Mcr h248EmIcr

Ms wh28 P ∆s

Let Mcr = 7.63 kN ꞏ m/m

Convergence at Ms = 12.9 kN ꞏ m/mΔ = h / 154

Supplemental eLearning Modules

Unreinforced Masonry Walls – Special Considerations

Intersecting Walls and Stack Pattern Masonry



Out-of-Plane Wall Design Checklist

Wall height, length, block size, block strength, type of mortar

As per wall design There is usually a starting point for basic wall information before a design is conducted

Estimate self-weight Appendix B Pg. 751 Typical weights for masonry

Determine applied loads, moment and shear diagrams

Cl. 4.2.2.2 Load Factors

Select tension reinforcement Cl. 10.15.1.1Cl. 10.15.1.2Cl. 10.15.2.2Cl. 10.15.2.5Cl. 10.15.3CSA A371Block Supplier

Minimum ReinforcementMinimum SpacingMinimum Seismic AreaMinimum Seismic SpacingMaximum ReinforcementMinimum ClearancesActual Unit Dimensions

Determine moment capacity Cl. 4.3.2Cl. 10.2.6Cl. 10.3Cl. 10.6.1Cl. 7.2Cl. 5.1.3.5.2Table 4Pages 494-497

Material Strength Modification FactorsEquivalent Rectangular Stress BlockEffective Area for Partial Grouting Effective Compression Zone WidthMoment Capacity of Unreinforced SectionsWhen to Ignore GroutEffective Partially-Grouted StrengthMoment Calculation

Check maximum axial load and minimum moment

Cl. 10.4Cl. 10.7.2

Maximum Axial LoadMinimum Eccentricity for Applied Axial Load



Slenderness effects for total moment

Cl. 10.5Cl. 10.7.3.3Cl. 10.7.4.2Cl. 10.7.4.3Cl. 10.7.4.6Table B.1

Effective HeightSlenderness LimitsP-Δ MethodMoment Magnifier MethodSlender Walls with Low Axial LoadEffective Length Factors

Check for shear Cl. 10.10.2Cl. 10.10.1.4

Out-of-Plane Shear Strength Out-of-Plane Sliding Shear Strength

Serviceability check Cl. 4.8.1Cl. 10.14.2Cl. 10.14.3

Rigidity RequirementsMid-Height Serviceability CheckMaximum Wind Load Deflection

masonry out-of- plane walls: slender wall design and ...for... · slenderness limited to low axial...

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