masonry out-of- plane walls: slender wall design and ...for... · slenderness limited to low axial...
TRANSCRIPT
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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)
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 2
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 3
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 4
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 5
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
• Load Case 2 • Pf = 63.8 kN/m• Mf = 15.7 kNꞏm/m• e = 246 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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 6
Self-Weight ONLY
• ww = 1.4 kPa• PDsw = 20.9 kN/m
• Load Case 1 • Pf = 26.1 kN/m• Mf = 15.7 kNꞏm/m• e = 588 mm
• Load Case 2 • Pf = 18.8 kN/m• Mf = 15.7 kNꞏm/m• e = 835 mm
kh/t > 30
PG FG
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 7
Alternative Solution Strategies
Fixed Ends• Assuring and Accounting for fixity• kh/t = 26.7• Improved Behaviour
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 8
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 9
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 10
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 11
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 12
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
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Engineered Masonry Design Course Friday April 27, 2018
© 2018 Canada Masonry Design Centre 13
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
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© 2018 Canada Masonry Design Centre 14
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