Masonry Out-of- Plane Walls: Slender Wall Design and Serviceability

Transcription

1 Masonry Out-of- Plane Walls: Slender Wall Design and Serviceability 4:30 PM 5:30 PM Bennett Banting Lecture Outline 1. Slenderness Limited to Low Axial Loads (25) 2. Serviceability Deflections (25) 3. Supplemental elearning (5) 4. Design Checklist (5) 2018 Canada Masonry Design Centre 1

2 Slenderness Limited to Low Axial Loads: -kh/t > 30 (Pages ) Cl. 10 CSA S304 kh/t > 30 When the slenderness ratio exceeds 30 Unreinforced masonry not permitted Cl Applies More Restrictive design Under-reinforced cross-section Low axial loads Alternative Solution Ensure fixity in wall k = Canada Masonry Design Centre 2

3 Slender Reinforced Walls kt/h > 30 Wall Details Compare Fully-Grouted and Partially-Grouted Walls Details from previous lecture h w = 8,000 mm k = 1.0 kh/t = Canada Masonry Design Centre 3

4 Property Fully-Grouted Wall Partially-Grouted Wall Fully- Grouted vs. Partially- Grouted ½ Self-Weight 20.9 kn/m 12.2 kn/m P fmax kn/m kn/m (EI) o 1,322 E9 N-mm 2 /m 1,159 E9 N-mm 2 /m (EI) cr E9 N-mm 2 /m E9 N-mm 2 /m e k 40 mm 68.1 mm : Units > 140 mm : Eccentric Pin Connections Assumed w/ Single Curvature Cl : P f 0.1ϕ m f m A e : c 0.6d : Total Magnified Moment 2018 Canada Masonry Design Centre 4

5 w w = 1.4 kpa P D = 50 kn P Dsw = 20.9 kn/m Solution Strategy: Fully- Grouted Wall Load Case 1 P f = 76.1 kn/m M f = 15.7 knm/m e = 206 mm Load Case 2 P f = 63.8 kn/m M f = 15.7 knm/m e = 246 mm Ignore Grout (this range of P) P critical 60 These very slender walls tend to have low buckling capacity Walls in this range have high eccentricity (EI)eff = (EI)cr Recall P cr is proportionate to: (EI) eff Magnification Factor P/Pcr 1/h Canada Masonry Design Centre 5

6 w w = 1.4 kpa P Dsw = 20.9 kn/m Self-Weight ONLY Load Case 1 P f = 26.1 kn/m M f = 15.7 knm/m e = 588 mm Load Case 2 P f = 18.8 kn/m M f = 15.7 knm/m e = 835 mm PG FG kh/t > Canada Masonry Design Centre 6

7 Alternative Solution Strategies Fixed Ends Assuring and Accounting for fixity kh/t = 26.7 Improved Behaviour 2018 Canada Masonry Design Centre 7

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 y 120 mm E s n eff 850f m, eff b eff, gr beff, ug 1,000mm/m I o n eff 1 A s1, eff y d 1 2 n eff 1 A s2, eff y d 2 2 b eff, grtunit 3 b eff, ug t unit3 t unit 2tf 2 E s n ug 850f if kd tf m, ug s b eff, ug min s, 4t 1,000mm/m 0 nugas 1 d 1 kd n ug A s2 d 2 kd b eff kd 2 2 I cr n ug A s1 d 1 kd 2 n ug A s2 d 2 kd 2 beff Canada Masonry Design Centre 8

9 Service Load Deflections - Span > 25d (Pages ) Cl. 10 CSA S304 Serviceability Limits Importance Factor h/180 for most cases Generally more critical than serviceability of beams Wind Load deflections 2018 Canada Masonry Design Centre 9

10 Deflections Wall Cross- Section Partially-Grouted Wall Cross-section h w = 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 M s = 8.1 knm/m 2018 Canada Masonry Design Centre 10

11 Cracking Moment Equivalent Cross-Sectional Properties Last lecture Service Moment > Cracking Moment Consider Secondary Effects as well M cr f t fcs y t I o f cs P A e s 5Msh 2 48EmIo When M s < M cr M s wh2 8 P s Convergence at M s = 8.4 kn m/m Δ = h / 2, Canada Masonry Design Centre 11

12 s 5Mcrh2 48EmIo 5 M s Mcr h 2 48EmIcr When M s > M cr M s wh2 8 P s Let M cr = 7.63 kn m/m Convergence at M s = 12.9 kn m/m Δ = h / 154 Supplemental elearning Modules Unreinforced Masonry Walls Special Considerations Intersecting Walls and Stack Pattern Masonry 2018 Canada Masonry Design Centre 12

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 Cl Load Factors and shear diagrams Select tension reinforcement Cl Cl Cl Cl Cl CSA A371 Block Supplier Determine moment capacity Cl Cl Cl Cl Cl. 7.2 Cl Table 4 Pages Check maximum axial load and minimum moment Cl Cl Minimum Reinforcement Minimum Spacing Minimum Seismic Area Minimum Seismic Spacing Maximum Reinforcement Minimum Clearances Actual Unit Dimensions Material Strength Modification Factors Equivalent Rectangular Stress Block Effective Area for Partial Grouting Effective Compression Zone Width Moment Capacity of Unreinforced Sections When to Ignore Grout Effective Partially-Grouted Strength Moment Calculation Maximum Axial Load Minimum Eccentricity for Applied Axial Load 2018 Canada Masonry Design Centre 13

14 Slenderness effects for total moment Cl Cl Cl Cl Cl Table B.1 Check for shear Cl Cl Serviceability check Cl Cl Cl Effective Height Slenderness Limits P-Δ Method Moment Magnifier Method Slender Walls with Low Axial Load Effective Length Factors Out-of-Plane Shear Strength Out-of-Plane Sliding Shear Strength Rigidity Requirements Mid-Height Serviceability Check Maximum Wind Load Deflection 2018 Canada Masonry Design Centre 14