Masonry Beams. Ultimate Limit States: Flexure and Shear

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Priscilla Philomena Golden
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1 Masonry Beams 4:30 PM 6:30 PM Bennett Banting Ultimate Limit States: Flexure and Shear Leture Outline 1. Overview (5) 2. Design for Flexure a) Tension Reinforement (40) b) Compression Reinforement (20) ) Intermediate Reinforement (20) 3. Design for Shear (25) 4. Content Review (5) 5. Supplemental elearning (5) 2018 Canada Masonry Design Centre 1

of reinforement After raking tensile strength of masonry ignored Masonry beams may only be solid (fullygrouted)

2 Overview Masonry Beam Masonry Lintel Movement Joint Conrete Blok Units for Beams Fundamental to Masonry Beams Similar to reinfored onrete Plane setions and ompatibility of strains Equilibrium of internal fores Perfet bond of reinforement After raking tensile strength of masonry ignored Masonry beams may only be solid (fullygrouted) and reinfored (yielding) Equivalent stress blok is used (different values from onrete) 2018 Canada Masonry Design Centre 2

3 Fundamental to Masonry Beams Different from reinfored onrete May not have ompression reinforement May not require skin reinforement (intermediate reinforement) May not have shear reinforement Spaing of reinforement is restrited by masonry unit No flanged beams Masonry beams are typially simply supported (frames are rare) Multi-span beams possible over several gaps Relatively short spans in walls suh as windows, doors, garages Flexure: Beam with Tension Reinforement (Pages ) Cl. 11 CSA S Canada Masonry Design Centre 3

4 m entre-to-entre of assumed pin-roller simple supports Beam Details 190 mm 3-Course beam 20 m units, Type

4 Masonry Beam Loads Uniformly Distributed Dead Load of 20.0 kn/m Uniformly Distributed Live Load of 15.0 kn/m Uniformly Distributed Self- Weight 2.4 m entre-to-entre of assumed pin-roller simple supports Beam Details 190 mm 3-Course beam 20 m units, Type S mortar, 20 MPa Blok strength Blok Strength is NOT design strength! U-Lintel on Bottom ourse 20M Tension Rebar 590 mm 520 mm 10 mm 15 mm 45 mm 2018 Canada Masonry Design Centre 4

5 Self- Weight Dead Load Design Moment Load Case #1 Load Case #2 1.4D L = 1.4 (20.0 kn/m kn/m) 1.25D L L L = 1.25 (20.0 kn/m kn/m) (15.0 kn/m) M f = 22.6 kn m M f = 36.4 kn m 2018 Canada Masonry Design Centre 5

C M r M f T Assumptions for Pure Bending ε mu = 0.

6 C M r M f T Assumptions for Pure Bending ε mu = Conditions at Ultimate Moment Capaity 1: Strain Compatibility (Plane setions remain plane) ε s =? 2018 Canada Masonry Design Centre 6

7 Conditions at Ultimate Moment Capaity χf m 2: Fore Equilibrium (Summation of Internal Fores is zero) T = f y χ0.85f m Conditions at Ultimate Moment Capaity β 1 2: Fore Equilibrium (Summation of Internal Fores is zero) T = f y 2018 Canada Masonry Design Centre 7

8 Conditions at Ultimate Moment Capaity 2: Fore Equilibrium (Summation of Internal Fores is zero) β 2 C = ϕ m χ (0.85f m )bβ 1 T = ϕ s A s f y Conditions at Ultimate Moment Capaity 2: Fore Equilibrium (Summation of Internal Fores is zero) Variable Value (CSA S Referene if Appliable) ϕ m 0.6 (Cl ) χ 0.5 (Cl sine strethers are used grout is NOT ontinuous horizontally) f m 10 MPa (Table 4 for a fully-grouted 20 MPa blok) b 190 mm (For a 20 m unit and its atual dimensions) β (Cl sine f m < 20 MPa) ϕ s 0.85 (Cl ) A s 300 mm 2 f y 400 MPa ϕ A f ϕ χ 0.85f bβ 2018 Canada Masonry Design Centre 8

9 ε mu = d Similar Triangles ε ε d Chek Assumption Tension reinforement yields at d - ε E 200,000MPa f 400MPa ε s =? Maximum Reinforement Masonry beams must be underreinfored Meaning that the extreme tension reinforement must yield at ultimate onditions Can be heked from similar triangles or using Cl d f 2018 Canada Masonry Design Centre 9

10 Speial Case The balaned ondition is defined as when the neutral axis depth, b, is exatly at the point where the reinforement will yield at ultimate onditions b 600 d 600 f The balane area of steel, A sb, is the required area to satisfy the balaned ondition suh that A sb ϕ χ 0.85f bβ b ϕ f Minimum Reinforement Minimum reinforement required for masonry beams Cl ρ min 0.8 f y 2018 Canada Masonry Design Centre 10

11 β 2 C = ϕ m χ (0.85f m )bβ 1 Moment Resistane d Moment Internal moment ouple reated by the tension and ompression fores ats to resist applied moment Take moment about any internal point Centroid of ompression blok or reinforement saves omputation M r T d β 1 2 ϕsa s f y d β 1 2 T = ϕ s A s f y Review Remember to use masonry-speifi values for ε mu, β 1, χ, ϕ m Do not flip between reinfored onrete design Reall the differene between blok strength and masonry strength (always fully-grouted, type S typial) Masonry strengths of: 5 MPa, 7.5 MPa, 10 MPa, 13.5 MPa, 17 MPa For engineering alulations we use atual dimensions Beam heights of: 190 mm, 390 mm, 590 mm, 790 mm, 990 mm et. Beam widths of: 140 mm, 190 mm, 240 mm, 290 mm Always hek assumptions and limits Reinforement yields 2018 Canada Masonry Design Centre 11

12 Review: CSA S304 Clauses 2018 Canada Masonry Design Centre 12

13 2018 Canada Masonry Design Centre 13

Flexure: Beam with Compression Reinforement (Page 258)

other design options exhausted Inrease blok strength or

may be an option in some ases Sometimes shear stirrups an at

14 Flexure: Beam with Compression Reinforement (Page 258) Compression Reinforement Useful to meet moment demands when other design options exhausted Inrease blok strength or amount of tension reinforement A wider blok or deeper beam may be an option in some ases Sometimes shear stirrups an at as ompression reinforement stirrups as well 2018 Canada Masonry Design Centre 14

Compression Reinforement Cl. 11.2.6.4 6.0 mm Diameter Stirrups as a Minimum (D4.5 Wire) Spaing of Lesser of 16 Bar Diameters or 48 Tie Diameters as a Maximum Cl. 12.

25M (use 25 mm) 190 mm Beam Details 43 mm 11 mm 62 mm 3-Course beam 20 m units, Type S mortar, 20 MPa Blok strength Knok-out depth = 70 mm Minimum over = 40 mm Minimum

15 Compression Reinforement Cl mm Diameter Stirrups as a Minimum (D4.5 Wire) Spaing of Lesser of 16 Bar Diameters or 48 Tie Diameters as a Maximum Cl Least dimension of member 10M Stirrups Maximum spaing for the following ompression steel sizes 160 mm 10M (use 10 mm) 240 mm 15M (use 15 mm) 320 mm 20M (use 20 mm) 400 mm 25M (use 25 mm) 190 mm Beam Details 43 mm 11 mm 62 mm 3-Course beam 20 m units, Type S mortar, 20 MPa Blok strength Knok-out depth = 70 mm Minimum over = 40 mm Minimum learane = 13 mm U-Lintel on Bottom ourse 25M Tension Rebar (A s ) 15M Compression Rebar (A s ) 10M Compression Stirrups mm 11 mm 13 mm 45 mm 2018 Canada Masonry Design Centre 15

16 CSA A371 ε mu = Conditions at Ultimate Moment Capaity d ε s d 1: Strain Compatibility (Plane setions remain plane) ε s 2018 Canada Masonry Design Centre 16

17 Strain Compatibility using Similar Triangles d - d ε mu ε s ε mu d - - d ε s ε s d - ε ε d ε d ε s Conditions at Ultimate Moment Capaity 2 C s = ϕ s A s f y C = ϕ m χ (0.85f m )bβ 1 2: Fore Equilibrium (Summation of Internal Fores is zero) T = ϕ s A s f y 2018 Canada Masonry Design Centre 17

18 Conditions at Ultimate Moment Capaity 2: Fore Equilibrium (Summation of Internal Fores is zero) Variable Value (CSA S Referene if Appliable) ϕ m 0.6 (Cl ) χ 0.5 (Cl sine strethers are used grout is NOT ontinuous horizontally) f m 10 MPa (Table 4 for a fully-grouted 20 MPa blok) b 190 mm (For a 20 m unit and its atual dimensions) β (Cl sine f m < 20 MPa) Unknown ϕ s 0.85 (Cl ) 500 mm 2 (25M bar) A s f y A s 400 MPa 200 mm 2 (15M bar) ϕ A f ϕ A f ϕ χ 0.85f bβ Strain Compatibility using Similar Triangles ε mu ε s d - - d ε s ε ε d ε d 2018 Canada Masonry Design Centre 18

19 d β 2 C s = ϕ s A s f y C = ϕ m χ (0.85f m )bβ 1 Moment Resistane d Moment Take moment about any internal point Moment about tension steel M r C d β 1 2 C s d d M r ϕ χ 0.85f bβ d β 1 2 ϕ A f d d T = ϕ s A s f y Review Compression reinforement does not need to yield It must be manually heked to verify assumptions The loation of tension and ompression reinforement is dependent on the unit onfiguration U-Lintel and Knok-out Web units are non-standard and vary by manufaturer Speifi blok manufaturers should be onsulted Knok-out Web units an failitate grout ontinuity A value of χ = 0.7 may be used if neutral axis lies in region with horizontal grout ontinuity If speifying knok-out web units for ompression reinforement it is usually best pratie to have it throughout beam This will also ensure better grout flow in the beam 2018 Canada Masonry Design Centre 19

20 Review: CSA S304 Clauses 2018 Canada Masonry Design Centre 20

Flexure: Beam with Intermediate Reinforement (Page 261) Intermediate Reinforement Differentiated from Main Tension and Tied Compression Reinforement Primary purpose is rak ontrol for tall beams (over

21 Flexure: Beam with Intermediate Reinforement (Page 261) Intermediate Reinforement Differentiated from Main Tension and Tied Compression Reinforement Primary purpose is rak ontrol for tall beams (over 3-ourses) Rationale similar to skin reinforement for reinfored onrete Cl M bar at 400 mm for 15 m and 20 m blok 2 15M bars at 400 mm for 25 m and 30 m blok 2018 Canada Masonry Design Centre 21

22 Intermediate Reinforement Design Considerations Contributes as tension reinforement in the beam May not yield in tension Intermediate reinforement does not ontribute as ompression reinforement Beam Details 6-Course beam 20 m units, Type S mortar, 15 MPa blok strength Knok-out depth = 70 mm Minimum over = 40 mm Minimum learane = 13 mm U-Lintel on Bottom ourse 25M Tension Rebar (A s ) 15M Compression Rebar (A s ) 10M Compression Stirrups 15M Intermediate Reinforement d = 62 mm d 3 = 462 mm d 2 = 862 mm d 1 = 1,108.5 mm 2018 Canada Masonry Design Centre 22

23 Assumptions Main Tension Reinforement (A s1 ) Yielded in tension First Intermediate Bar (A s2 ) Under tension but has NOT yielded Seond Intermediate Bar (A s3 ) Under ompression but is NOT tied Compression Reinforement (A s ) Yielded in ompression and is tied 1: Strain Compatibility using Similar Triangles ε mu ε s ε mu ε s d 3 ε s3 ε s3 - d ε s2 d 2 - d 1 - ε s1 ε s2 ε ε d ε d 3 ε d 2 ε d 1 ε s Canada Masonry Design Centre 23

24 C s = ϕ s A s f y Conditions at Ultimate Moment Capaity 2 C = ϕ m χ (0.85f m )bβ 1 2: Fore Equilibrium (Summation of Internal Fores is zero) T 2 = ϕ s A s2 f s2 T 1 = ϕ s A s1 f y Variable Value (CSA S Referene if Appliable) Conditions at Ultimate Moment Capaity 2: Fore Equilibrium (Summation of Internal Fores is zero) ϕ m 0.6 (Cl ) χ 0.5 (Cl sine strethers are used grout is NOT ontinuous horizontally) f m 7.5 MPa (Table 4 for a fully-grouted 15 MPa blok) b β mm (For a 20 m unit and its atual dimensions) 0.8 (Cl sine f m < 20 MPa) ϕ s 0.85 (Cl ) 500 mm 2 (25M bar) A s1 f y A s A s2 f s2 400 MPa 200 mm 2 (15M bar) 200 mm 2 (15M bar) ε d Canada Masonry Design Centre 24

25 Verify Assumptions ε mu ε s ε mu ε s d 3 ε s3 ε s3 - d ε s2 d 2 - d 1 - ε s1 ε s2 ε ε d ε d 3 ε d 2 ε d 1 ε s1 C s = ϕ s A s f y C = ϕ m χ (0.85f m )bβ 1 Moment Moment Resistane Take moment about neutral axis T 2 = ϕ s A s2 f s2 β 1 M r T 1 d 1 T 2 d 2 C 2 Cs d T 1 = ϕ s A s1 f y 2018 Canada Masonry Design Centre 25

26 Review Reinforement depths are typially based on the knok-out web unit onfiguration It is diffiult to plae reinforement elsewhere in masonry Most effiient to plae it on the webs of knok-out web units Problems may be iterative Solution is dependent on the loation of neutral axis Intermediate reinforement should onentrate lose to the tension side of the beam Expliitly speified in the 2014 CSA S304 We took moment about the neutral axis to avoid hanging signs in our alulation If moment was alulated about the lowest tension steel, C, C s ats against A s2 moments Review: CSA S304 Clauses 2018 Canada Masonry Design Centre 26

27 Shear (Pages ) 2018 Canada Masonry Design Centre 27

based on 2004 standard See Supplemental elearning for a more detailed desription

28 Changes to the 2004 Design Standard Masonry beam shear design has adapted to the modified ompression field theorem used in reinfored onrete design Course work is based on 2004 standard See Supplemental elearning for a more detailed desription of designing with the 2014 standard Shear Failure 2018 Canada Masonry Design Centre 28

29 190 mm Beam Details 43 mm 11 mm 62 mm 3-Course beam 20 m units, Type S mortar, 20 MPa Blok strength Knok-out depth = 70 mm Minimum over = 40 mm Minimum learane = 13 mm U-Lintel on Bottom ourse 25M Tension Rebar (A s ) 15M Compression Rebar (A s ) 10M Compression Stirrups mm 11 mm 13 mm 45 mm Shear Resistane d V s C V m Aggregate interlok V s Shear Stirrups V s V m d d Shear Crak Length s Shear Stirrup Spaing V f s T 2018 Canada Masonry Design Centre 29

30 Conditions at Ultimate Shear Capaity Variable Value (CSA S Referene if Appliable) ϕ m 0.6 (Cl ) λ 1.0 (Conrete density over 2,000 kg/m 3, 0.85 or 0.75 for Lightweight, Cl ) f m 10.0 MPa (Table 4 for a fully-grouted 20 MPa blok) d V r V m V s 0.16ϕ m λ f d 400 m mm b w d ϕ sa v f y d s Masonry and Reinforement Contributions b w 190 mm (For a 20 m unit and its atual dimensions) ϕ s 0.85 (Cl ) A v f y s 100 mm 2 (10M bar) 400 MPa 200 mm Shear Reinforement Detailing Minimum shear reinforement Must be provided when V f > 0.5 V m A v > 0.35b w s/f y Maximum Spaing of Shear Reinforement s d/2 or 600 mm 2018 Canada Masonry Design Centre 30

31 Determining V f M f V max l 2 V f d V max l 2 Shear Detailing Stirrups are not required where V f < 0.5V m Limited options with masonry ompared with onrete design If ounting on stirrups as ompression ties then limited appliability 2018 Canada Masonry Design Centre 31

32 Review Shear may be resisted entirely by masonry if V f 0.5 V m Shear reinforement is very different from reinfored onrete Spaing generally limited to inrements of 200 mm to fit in ells V smax limits most beams to a single 10M stirrup Rarely is it ever pratial to hange shear reinforement over beam span Substantial hanges were made to shear design in 2014 standard Fous in elearning module Review: CSA S304 Clauses 2018 Canada Masonry Design Centre 32

33 2018 Canada Masonry Design Centre 33

34 Supplemental elearning 2018 Canada Masonry Design Centre 34

35 General Overview and Materials Changes from 2004 to 2014 CSA Masonry Material, Constrution and Design Standards Speialty Mortars, Clay Brik, Connetors and Stone Produts Case Studies and Diagnostis of Masonry Veneers Masonry Beams: Ultimate Limit States Modified Compression Field Theory and Shear Design of Masonry Beams using the 2014 Standard Support of Masonry and Bearing Design, Using Movement Joints for Strutural Appliations and Arhing of Masonry over Openings Design of Brik Beams, Deep Beams and Prestressed Beams 2018 Canada Masonry Design Centre 35

Purpose of reinforcement P/2 P/2 P/2 P/2

Purpose of reinforcement P/2 P/2 P/2 P/2 Department o Civil Engineering Purpose o reinorement Consider a simpl supported beam: P/2 P/2 3 1 2 P/2 P/2 3 2 1 1 Purpose o Reinorement Steel reinorement is primaril use beause o the nature o onrete