Seismic Behaviour of RC Shear Walls

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1 Ductile Detailing of RC Structures :: IS: Short Course on Seismic Design of RC Structures Durgesh C. Rai Department of Civil Engineering, IIT Kanpur The material contained in this lecture handout is a property of Professors Durgesh C. Rai, Sudhir K. Jain and C.V.R.Murty of IIT Kanpur, and is for the sole and exclusive use of the participants enrolled in the short course on Seismic Design of RC Structures conducted at Ahmedabad during Nov 25-30, It is not to be sold, reproduced or generally distributed. RC Building SYSTEMS Three common lateral load resisting systems in RC Buildings Seismic Behaviour of RC Shear Walls Front Views of Buildings Top Views of Buildings 4 Moment Resistant Frame Shear Wall Braced Frame shear wall SHEAR WALLS... What is a Shear Wall? Vertical plate-like RC Walls Generally starts at foundation Goes through full building height Slab RC Shear Wall Building Shear Walls also called Structural Walls Slab Column Beam Plan RC Walls Column Beam 5 Foundation RC Shear Wall 6 Foundation RC Shear Wall 1

2 SHEAR WALLS... SHEAR WALLS... Principal attributes Large Strength High Stiffness Ductility Shear wall can be detailed to have large ductility Strength H RC Shear Wall Building Role of Shear Walls Smooth transfer of seismic forces Vertically oriented wide beams Shear Wall Earthquake-generated forces at floor levels Floor Slab F 3 F 3 F 2 F 3 Shear Wall F 3 F 2 F RC Frame Building Deformability 8 F 1 F=F 1 +F 2 +F 3 Cumulative horizontal force from above increases downward SHEAR WALLS... Advantages of Shear Walls Very good earthquake performance, if properly designed In past earthquakes Large number of RC frame buildings damaged or collapsed Shear wall buildings performed very well We cannot afford to to build concrete buildings meant to to resist severe earthquakes without shear walls :: :: Mark Mark Fintel, Fintel, a a noted noted earthquake engineer in in USA USA SHEAR WALLS... Advantages of Shear Walls Easy to construct Straight-forward reinforcement detailing Easily implemented at site Effective in Reducing construction cost Minimising earthquake damage to Structural elements Non-Structural elements E.g., Glass Windows, Building Contents 9 10 SHEAR WALLS... Advantages of Shear Walls Lesser lateral displacement than frames Lesser Damage to structural and non-structural elements small large SHEAR WALLS... Current Use of Shear Walls Popular choice in many earthquake prone countries Chile, Canada, USA and New Zealand In general, used in medium and high rise buildings 10 storeys and higher 11 Shear Wall Moment Resistant Frame 12 2

3 Architectural Aspects Walls must be preferably in both directions in plan If provided only in one direction, a proper moment resisting frame must be provided in the other direction. Architectural Aspects... If provided only in one direction, a proper moment resisting frame must be provided in the other direction. Frame 1 Frame 2 Shear Wall Shear Wall Frame 3 Frame A B C D Architectural Aspects... Shear wall can extend over the full width of building, or even over partial width Architectural Aspects... Walls should be throughout the height Cannot be interrupted in lower levels RC Wall RC Wall 15 RC Wall of partial width RC Wall of full width 16 Discontinuity of wall not desirable Best Option: Wall all through!! Architectural Aspects... Walls should be throughout the height Cannot be interrupted in upper levels Architectural Aspects... Walls should be along perimeter of building Improves resistance to twist Shear walls along perimeter are more efficient RC Wall Discontinuity of wall not desirable RC Wall Best Option: Wall all through!! Shear walls close to center of building are less efficient

4 Architectural Aspects... Walls must be symmetrically placed in plan Symmetry of building in plan about one axis Architectural Aspects... Shear wall building should not be narrow Earthquakes cause significant overturning effects Special care is required in design of their foundations Unsymmetric location of shear walls not desirable Shear Walls only along one direction of the building Symmetry of building in plan about both axes 19 Symmetric location of shear walls desirable 20 Soil Local failure of soil Soil Architectural Aspects... Openings in walls must be As few as possible As small as possible As symmetric as possible RC Wall Seismic Behaviour Undesirable Modes of Failure Inclined Crack RC Wall Vertical Uplift Horizontal Slide 21 Large and randomly placed openings not allowed Small and symmetrically placed openings allowed 22 Overturning Failure Sliding Failure Shear Failure Seismic Behaviour... Undesirable Mode of Failure Seismic Behaviour... Desirable Mode of Failure 23 Flexure Compression Failure Crushing of Concrete 24 Flexure Tension Failure Horizontal cracks and yielding of steel bars 4

5 Seismic Behaviour... Shear demand is more in lower storeys Seismic Behaviour... Shear demand is more in lower storeys Earthquake-generated forces at floor levels Floor Slab Cumulative horizontal force from above increases downward Earthquake-induced horizontal force at floor levels Building Height 25 Shear Wall Direct force flow through the wall 26 Total Horizontal Force Seismic Behaviour... At each section along the height, shear wall carries Axial Force P Shear Force V Bending Moment M V M P M V Region of Ductile Detailing Actions in Ductile Response Region (a) Formation of horizontal cracks (b) Yielding of vertical steel bars Tension Compression H w Ductile Response Region: Larger of L w and H w /6, but need not be more than 2L w L w Possible Geometry of Walls Possible Geometry of Walls C-Shaped Flanged Wall with more than two columns built together Barbell-Shaped L-Shaped Hollow:: Walls around Elevators 29 Rectangular 30 Wall with two columns built together 5

6 Primary Reinforcement in Walls Lapping of Vertical Reinforcement Bars Maximum spacing of vertical reinforcement not more than L w /5, t w or 450mm Proper anchoring of vertical reinforcement into foundation Maximum spacing of horizontal reinforcement not more than L w /5, t w or 450mm H w Staggering lapping of adjacent vertical bars: Minimum of 600mm Region over which lapping should be avoided: Larger of L w and H w /6, but need not be more than 2L w L w Detailing of Vertical and Horizontal Bars Confining Steel in Boundary Elements Closely spaced confining reinforcement in boundary elements Max. spacing of vertical reinforcement not more than L w /5, t w or 450mm Max. spacing of horizontal reinforcement not more than L w /5, t w or 450mm Confining reinforcement in boundary elements: 135 hooks, closely spaced ties Single curtain of reinforcement t w Anchoring of wall reinforcement in boundary element L w Two curtains of reinforcement Confining Wall Concrete Open-leg Ties Closed Loop Ties Curtains of Reinforcement One Two Single curtain of reinforcement Wall thickness t w Anchoring of ties around both vertical and horizontal wall reinforcement Closed stirrups with 135 hook ends Two curtains of reinforcement Wall length L w

7 Boundary Elements Boundary Elements without increased thickness Boundary Element Boundary Elements Single curtain of reinforcement Tension Compression Two curtains of reinforcement Boundary Elements with increased thickness Boundary Element Single curtain of reinforcement 37 Confining reinforcement in boundary elements: 135 hooks, closely spaced ties Two curtains of reinforcement Anchoring of wall reinforcement in boundary element 38 Boundary Element Slender and Squat Walls Seismic behaviour is controllable through design Influence of Boundary Elements on Strength For same amount of concrete and steel Strength of Section 2 > Strength of Section 1 Inclined Crack Vertical Uplift Horizontal Slide 1 1 Overturning Failure Sliding Failure Shear Failure Horizontal Cracks Boundary Element Flexure Failure 40 Slender and Squat Walls Effect of Axial Load on flexural strength Just as in columns P Coupled Shear Walls Size of opening Coupling Beam 0 M V M P 7

8 Coupled Shear Walls Coupling Beam Span-to-depth ratio is small Shear deformations are significant Ends have large rotational and vertical displacement Require very high ductility Coupled Shear Walls Coupling Beam Shear failure should not precede flexural yielding Diagonal reinforcement more effective Provide confinement throughout the beam Good anchorage of main bars into walls on either side Coupled Shear Walls Coupling Beam Diagonal and parallel reinforcement 9.1 General Requirements 1.5 l 1.5 d l d Thickness 150 mm (preferably) Thinner walls have a tendency to buckle out of plane Wall thickness t w l 1.5 d l d Wall Wall reinforcement not not shown shown Special confining reinforcement spacing > 100 mm centers 46 Wall length L w 9.1 General Provisions General Provisions Effective flange width, beyond face of web, smaller of Half distance to next wall web 1/10 of total wall height Minimum reinforcement in walls Vertical and horizontal direction 0.25% of gross area

9 9.1 General Provisions Minimum reinforcement in walls 9.1 General Provisions... Vertical 0.25% of of Gross Area Both faces together Horizontal 0.25% of of Gross Area Two curtains of reinforcement, if Factored shear stress > 0.25 f ck ; or Wall thickness > 200 mm Two curtains reduce fragmentation and early deterioration of concrete under cyclic response General Provisions Two curtains of reinforcement 9.1 General Provisions Diameter of bars 1/10th wall thickness Single curtain of reinforcement τ > f, or t v w ck > 200mm t w L w t w d b L w Two curtains of reinforcement General Provisions General Provisions Maximum reinforcement spacing Maximum reinforcement spacing l w 5 3t w 450 mm Vertical Maximum Maximum spacing spacing of of vertical vertical reinforcement reinforcement not not more more than than LL w /5, w /5, t w t or w or 450mm 450mm Horizontal Maximum Maximum spacing spacing of of vertical vertical reinforcement reinforcement not not more more than than L L w /5, w /5, t w t or w or 450mm 450mm

10 9.2 Shear Strength 9.2 Shear Strength Shear Strength to provide same shear design provisions as in IS: for beams 9.2 Shear Strength... c τ τ < τ v v c,max c τ < τ < τ c,max < τ v MinimumReinforcement Design Reinforcement Redesign Section Uniformly distributed vertical reinforcement Horizontal reinforcement calculated for shear Particularly important for walls with height-to-width ratio of 1.0 or less W H Flexural Strength 9.3 Flexural Strength Flexural strength Flexural strength similarly calculated as for columns under axial loads (IS:456). Can use Annex A equations for assessing flexural strength under uniform distribution of reinforcement

11 9.3 Flexural Strength Flexural strength Annex A Pu f th ck ε c = Flexural Strength Cracked flexural strength > Uncracked flexural strength Avoid brittle behaviour M f u 2 ckth Flexural Strength Boundary Elements If no boundary elements Provide 4 bars of 12 mm diameter In two layers at either end Good to have more reinforcement near wall ends 9.4 Boundary elements improve Flexural strength Shear strength Ductility Boundary Element 9.4 Boundary Elements Boundary Elements Boundary elements required When extreme fiber compressive stress > 0.2f ck May discontinue boundary element When extreme fiber compressive stress < 0.2f ck No No boundary element <0.2fck Boundary element >0.2fck

12 9.4 Boundary Elements Boundary Elements Boundary element to carry axial Gravity load P w (its own share proportional to area) Vertical load P eq induced by EQ Vertical force couple caused by EQ overturning moment P eq = (M u -M uw )/C w Boundary Elements... Example Given Gravity Seismic Axial Load P on boundary element 400 kn ±50 kn Moment M u on entire wall - 10,000 knm M u resisted by web = 6,000 knm M ub resisted by boundary elements = 10,000-6,000 = 4,000 knm C/c distance of boundary element = 5 m Axial force induced by 4,000 knm moment = 4, 000 ± = ± 800 kn Boundary Elements When gravity load adds to strength Load factor is 0.8 (as against 1.2 or 1.5) Example: Let load factor be 1.2 for gravity. Design factored axial force Compression: 1.2( )=1,500kN Tension: ( )-(1.2 50)-( )=-700kN 9.4 Boundary Elements Boundary Elements Vertical reinforcement in boundary element 0.8 % gross area of boundary element 6% (practically 4%) Just like a column Confinement reinforcement required throughout height of boundary element

13 9.4 Boundary Elements Confinement reinforcement 9.4 Boundary Elements... Closely spaced confining reinforcement in boundary elements If entire wall is confined, boundary element not required. Open-leg Ties Closed Loop Ties Anchoring of ties around both vertical and horizontal wall reinforcement Closed stirrups with 135 hook ends 9.5 Coupled Shear Walls Coupling beams to be ductile Coupling beams to be ductile When shear stress in coupling beam exceeds given value, entire seismic shear and flexure to be taken by diagonal reinforcement (preferably) Coupling beams to be ductile l 1.5 d l d Wall Wall reinforcement not not shown shown Special confining reinforcement spacing > 100 mm centers 78 13

14 9.5.2 C u and T u intersect at mid-span Moment resisted at mid-span by diagonal bars is zero V = 2T sinα u u u T = f A y sd V u =1. 74fy Asdsinα Vu A sd = 1. 74fy sinα C u T u C u T u T u T u M u V u V u M u α C u α α V u M u V u V u M u α C u α α V u T u C u T u C u Diagonal/horizontal bars Diagonal/horizontal bars Anchored in wall by 1.5L dt 1.5 l 1.5 d l d 1.5 l 1.5 d l d ACI : Coupling Beams Diagonal reinforcement effective ACI : Diagonal/horizontal bars Detailing option 1 l n h < 4 for l n < 2 h 83 necessary to reinforced with two intersecting group of diagonally placed bars 84 Confinement of individual diagonals 14

15 ACI : Diagonal/horizontal bars Detailing option 1 ACI : Diagonal/horizontal bars Detailing option Full confinement of diagonally reinforced beam section ACI : Diagonal/horizontal bars Detailing option Openings in Walls Shear strength to be checked along planes passing through openings Critical Section Openings in Walls Openings in Walls Reinforcement at openings L dt Replacement steel steel Reinforcement interrupted by opening to be provided along edges Vertical edge reinforcement to extend full storey height Horizontal edge reinforcement to have development length in tension Interrupted bars bars

16 9.7 Discontinuous Walls 9.7 Discontinuous Walls Special confinement reinforcement 9.7 Special confinement reinforcement required over full height of columns supporting walls Development length of longitudinal bar in column Special confining reinforcement: closely spaced transverse ties throughout the short column Region over which special confining reinforcement must extend into the column above Regular floor RC Wall Construction Joints 9.8 Construction Joints Construction Joints Vertical Vertical bars bars across across construction joint joint 9.8 Minimum vertical reinforcement across the construction joint Construction Joint Joint Development, Splice & Anchorage Requirement 9.9 Development, Splice & Anchorage Req Splicing of vertical reinforcement to be avoided in critical regions Staggering lapping of adjacent vertical bars: Minimum of 600mm H w Region over which lapping should be avoided: Larger of L w and H w /6, but need not be more than 2L w L w 16

17 9.9 Development, Splice & Anchorage Req Development, Splice & Anchorage Req Lateral tie requirements for lapped spliced bars Welded splices and mechanical connections as per IS: Example Example: RC Shear Wall Design Design a shear wall for a two-storey building as shown in Figure. The materials are M20 concrete and Fe415 steel. The example shows design for load combination 1.2(DL + LL +EL) only. In practice all other combinations should also be considered. The unfactored forces in the panel between the ground level and first floor are obtained by analysis as IITK GSDMA: Explanatory Examples for Ductile Detailing of RC Buildings Example Example Factored bending moment on the section, M u = 1.2 ( ) = 6490 knm The maximum factored shear force, V u =1.2 ( ) = 863 kn Effective depth d e = 3380+(380/2)+(380/2) = 3760 mm Vu Shear stress, τ v = = d t e w Let the minimum vertical reinforcement = 0.25% provided in the web

18 As per Table 19 of IS: , τ c = 0.36 N/mm 2. Shear carried by concrete, V = τ d t = 311 kn 103 Shear DESIGN uc c e Shear to be resisted by horizontal reinforcement, V us = V u - V uc = ( ) = 552 kn V us = f A d S y h e v Ah = S v Minimum horizontal reinforcement (0.25%) requires this ratio to be For t w > 200 mm, the reinforcement shall be in 2 layers Provide horizontal reinf. of 8mm dia. bars at 175 mm c/c in 2 layers 104 Shear DESIGN at opening Effective depth of wall on each side of opening = ( /2) = 1280 mm τ v =1.47 N/mm 2 Shear to be resisted by reinforcement on each side of opening V us = 326 kn. Provide 8 mm diameter 2-legged stirrups at 140 mm c/c on each side of opening Flexural Strength of web Vertical reinf. in web is 0.25 percent L w = 4140 mm and t w = 230 mm Axial compression will increase moment capacity of wall Factored axial force - P u = = 1845 kn Assuming this axial load to be uniformly distributed, load on web = = 1059 kn The moment of resistance of a slender rectangular shear wall section with uniformly distributed vertical reinf. can be estimated as per IS 13920: 1993 (Annex A) Flexural Strength of web where (1) Flexural Strength of web where Value of x u / l w calculated from the quadratic equation (2) Flexural Strength of web As x u /l w < x u */l w, we get the value as: λ= 0.056, φ = 0.045, x u /l w = 0.233, x u */l w = 0.660, and β = Moment of resistance of the web M uv = 3296 knm Remaining moment will be resisted by reinf. in boundary elements (M u - M uv ) = ( ) = 3194 knm

19 Boundary elements Due to combined axial load and bending, axial compression at the extreme fibre = 6.81 N/mm 2 Cl > 0.2f ck Boundary elements are mandatory IS Center to center dist. b/w the boundary elements, C w = 3760 mm Axial force on the boundary element due to earthquake loading = (M u -M uv )/C w = 3194/3.76 = 849 kn Maximum factored compression on the boundary element [ ( )] = 1406 kn Factored tension on the boundary element, [0.213 ( ) -849] = -587 kn Boundary elements Assuming short column action the axial load capacity of the boundary element with min. reinf. of 0.8% = 2953 kn Cl IS bars of 16 mm diameter will be adequate to take the compression as well as tension Also, provide special confining reinf. as per Cl Reinforcement Around opening Opening size = 1200 mm by 1200 mm Area of vertical and horizontal reinforcement in the web (0.25%) that is interrupted by it is 690 mm 2 Provide area of bars equal to the respective interrupted bars Cl IS Reinforcement Details Thus, one bar of 16 mm diameter should be provided per layer of reinforcement on each side of the opening The vertical bar should extend for the full storey height The horizontal bar should be provided with development length in tension beyond the sides of the opening Cl IS Thank you 19

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