Reinforced Concrete Shear Wall Analysis And Design
Reinforced Concrete Shear Wall Analysis and Design
Reinforced Concrete Shear Wall Analysis and DesignA structural reinforced concrete shear wall in a 5-story building provides lateral and gravity load resistance for theapplied load as shown in the figure below. Shear wall section and assumed reinforcement is investigated after analysisto verify suitability for the applied loads.Figure 1 – Reinforced Concrete Shear Wall Geometry and LoadingVersion: Aug-10-2017
Contents1. Minimum Reinforcement Requirements (Reinforcement Percentage and Spacing) .21.1. Horizontal Reinforcement Check .21.2. Vertical Reinforcement Check .22. Neutral Axis Depth Determination.33. Moment Capacity Check .44. Shear Capacity Check .55. Shear Wall Analysis and Design – spWall Software . 76. Design Results Comparison and Conclusions . 16Version: Aug-10-2017
CodeBuilding Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14)ReferenceReinforced Concrete Mechanics and Design, 7th Edition, 2016, James Wight, Pearson, Example 18-2Design Datafc’ 4,000 psi normal weight concretefy 60,000 psiSlab thickness 7 in.Wall thickness 10 in.Wall length 18 ftVertical reinforcement:#5 bars at 18 in. on centers in each face (As, vertical #5 @ 18 in.)Horizontal reinforcement: #4 bars at 16 in. on centers in each face (As, horizontal #4 @ 16 in.)1
1. Minimum Reinforcement Requirements (Reinforcement Percentage and Spacing)1.1. Horizontal Reinforcement Check t Av , horizontalh s2 2 0.2 0.002510 16ACI 318-14 (2.2) t 0.0025 t ,min 0.0025 (o.k)st ,max 3 h 3 10 smallest of 18 in. smallest of 18 in. l / 5 18 / 5 w ACI 318-14 (11.6.2(b)) 30 in. smallest of 18 in. 18 in. 43.2 in. ACI 318-14 (11.7.3.1)st , provided 16 in. st ,max 18 in. (o.k)1.2. Vertical Reinforcement Check l Av ,verticalh s1 2 0.31 0.0034410 18ACI 318-14 (2.2) hw 0.0025 0.5 2.5 t 0.0025 lw 0.0025 l ,min greater of l ,min hw 0.0025 0.5 2.5 0.0025 0.0025 greater of lw greater of 0.0025 ACI 318-14 (11.6.2(a)) 0.0025 0.0025 0.0025 l 0.00344 l ,min 0.0025 (o.k) 3 h 3 10 sl ,max smallest of 18 in. smallest of 18 in. l / 3 18 / 3 w ACI 318-14 (11.6.2(a)) 30 in. smallestof 18 in. 18 in. 72 in. ACI 318-14 (11.7.2.1)sl , provided 18 in. sl ,max 18 in. (o.k)2
2. Neutral Axis Depth DeterminationM base 35 54 32 43.5 26 33 18 22.5 10 12 4,670 kip-ftThe load factor for strength-level wind force 1.0M u ,base 1.0 4,670 4,670 kip-ftNu 0.9 ND 0.9 30 50 50 50 50 207 kips 1 0.85 l fyf c'0.05 f c' 4000 1000 0.00344 0.85 0.05 4000 4000 1000ACI 318-14 (Eq.5.3.1f) 0.85ACI 318-14 (Table 22.2.2.4.3)60 0.05164Nu207 0.0240'h lw f c 10 216 4 0.0240 0.0516 c lw 216 19.8 in. 0.85 0.85 2 0.0516 0.85 1 2 Assume the effective flexural depth (d) is approximately equal to 0.8lw 173 in.ACI 318-14 (11.5.4.2)c 19.8 in. d 173 in. Tension controlled section 0.90ACI 318-14 (Table 21.2.2)3
3. Moment Capacity CheckAst Av ,verticallw216 2 0.31 7.44 in.4sl , provided18 l c 216 19.8 T Ast f y w 7.44 60 405 kips 216 lw Taking into account the applied axial force and summing force moments about the compression force (C), themoment capacity can be computed as follows: l l c 216 216 19.8 M n T w Nu w 405 207 64, 000 kips-in. 5,340 kips-ft 2 2 2 2 M n 0.9 5,340 4,800 kips-ft M u 4,670 kips-ftSince ϕMn is greater than Mu, the wall has adequate flexural strength.To further confirm the moment capacity is adequate with detailed consideration for the axial compression, aninteraction diagram using spColumn can be created easily as shown below for the wall section. The location ofthe neutral axis, maximum tensile strain, and the phi factor can all be also verified from the spColumn modelresults output parameters. As can be seen from the interaction diagram a comprehensive view of the wallbehavior for any combination of axial force and applied moment.For a factored axial and moment of 207 kips and 4670 kip-ft the interaction diagram shows a capacity factor of1.139 (ϕMn 5,320 kip-ft for ϕPn Pu), see Figures 11 and 12.4
4. Shear Capacity CheckVu 35 32 26 18 10 121 kipsNu d ' 3.3 f c h d 4 lw N lw 1.25 f c' 0.2 u Vc lesser of lw h 0.6 f ' h dc M u lw Vu2 (d) (e) ACI 318-14 (Table 11.5.4.6)207, 000 173 3.3 1.0 4, 000 10 173 4 216 207, 000 216 1.25 1.0 4, 000 0.2Vc lesser of 216 10 10 173 0.6 1.0 4, 000 3,580 216 1212 402 kips Vc lesser of 214 kips 214 kips Where Mu/Vu ratio used in equation (e) was calculated at the critical section above the base of the wall (seeFigure 1). lw 2 hw distance to the critical section smaller of 2 one story height ACI 318-14 (11.5.4.7) 18 2 9 ft 54 distance to the critical section smaller of 27 ft 9 ft 2 12 ft The factored moment at the ultimate section is equals to:M u M u ,base Vu ,base lw 4, 670 121 9 3,580 kip-ft2 Vc Vc 0.75 214 161 kips5
Where 0.75 for shearACI 318-14 (Table 21.2.1) Vc 161 kips Vu 121 kipsThus, it is not required to calculate the additional shear strength provided by the horizontal reinforcement (Vs)0.5 Vc 80.5 kips Vu 121 kipsSince 0.5ϕVc is less than Vu, ρl shall be at least the greater of Equation 11.6.2 in the Code and 0.0025 but neednot to exceed ρt required by Equation 11.5.4.8. and ρt shall be at least 0.0025.ACI 318-14 (11.6.2)(Those requirements were checked in step 1).6
5. Shear Wall Analysis and Design – spWall SoftwarespWall is a program for the analysis and design of reinforced concrete shear walls, tilt-up walls, precast wall andinsulate concrete form (ICF) walls. It uses a graphical interface that enables the user to easily generate complexwall models. Graphical user interface is provided for: Wall geometry (including any number of openings and stiffeners) Material properties including cracking coefficients Wall loads (point, line, and area), Support conditions (including translational and rotational spring supports)spWall uses the Finite Element Method for the structural modeling, analysis, and design of slender and nonslender reinforced concrete walls subject to static loading conditions. The wall is idealized as a mesh ofrectangular plate elements and straight line stiffener elements. Walls of irregular geometry are idealized toconform to geometry with rectangular boundaries. Plate and stiffener properties can vary from one element toanother but are assumed by the program to be uniform within each element.Six degrees of freedom exist at each node: three translations and three rotations relating to the three Cartesianaxes. An external load can exist in the direction of each of the degrees of freedom. Sufficient number of nodaldegrees of freedom should be restrained in order to achieve stability of the model. The program assembles theglobal stiffness matrix and load vectors for the finite element model. Then, it solves the equilibrium equations toobtain deflections and rotations at each node. Finally, the program calculates the internal forces and internalmoments in each element. At the user’s option, the program can perform second order analysis. In this case, theprogram takes into account the effect of in-plane forces on the out-of-plane deflection with any number ofopenings and stiffeners.In spWall, the required flexural reinforcement is computed based on the selected design standard (ACI 318-14 isused in this example), and the user can specify one or two layers of shear wall reinforcement. In stiffeners andboundary elements, spWall calculates the required shear and torsion steel reinforcement. Shear wall concretestrength (in-plane and out-of-plane) is calculated for the applied loads and compared with the code permissibleshear capacity.For illustration and comparison purposes, the following figures provide a sample of the input modules and resultsobtained from an spWall model created for the reinforced concrete shear wall in this example.7
Figure 2 –Defining Loads for Shear Wall (spWall)8
Figure 3 – Assigning Boundary Conditions for Shear Wall (spWall)9
Figure 4 –Factored Axial Forces Contour Normal to Shear Wall Cross-Section (spWall)10
Figure 5 – Shear Wall Lateral Displacement Contour (spWall)11
Figure 6 – Shear Wall Axial Load Diagram (spWall)12
Figure 7 – In-plane Shear Diagram (spWall)13
Figure 8 – Shear Wall Moment Diagram (spWall)14
Elements along the wall base As,vertical 7.56 in.2Figure 9 – Shear Wall Vertical Reinforcement (spWall)Figure 10 – Concrete Shear Strength and Shear Wall Cross-Sectional Forces (spWall)15
6. Design Results Comparison and ConclusionsTable 1 – Comparison of Shear Wall Analysis and Design ResultsWall Cross-Sectional l Section(kip-ft)StrengthRequired (in.2)Hand4,6702071213,580161Governed by Min.7.44Reference4,6702071213,580161Governed by Min.7.44spWall4,6652071213,576164Governed by Min.7.56The results of all the hand calculations and the reference used illustrated above are in precise agreement with theautomated exact results obtained from the spWall program. It is worth noting that the minimum area of steel isgoverned by the minimum reinforcement ratio stipulated by the code. The same can be seen in spWall output forelements 9 through 18.In the hand calculations and the reference, a simplified procedure to calculate the nominal flexural strength was used(A. E. Cardenas et al.). In this procedure, several broad assumptions are made to avoid tedious detailed calculations: All steel in the tension zone yields in tension. All steel in the compression zone yields in compression. The tension force acts at mid-depth of the tension zone. The total compression force (sum of steel and concrete contributions) acts at mid-depth of thecompression zone.To investigate the exact shear wall cross section capacity, a detailed interaction diagram can be easily generated byspColumn conforming to the provisions of the Strength Design Method and Unified Design Provisions with allconditions of strength satisfying the applicable conditions of equilibrium and strain compatibility.For illustration and comparison purposes, following figures provide a sample of the input and output of the exactresults obtained from an spColumn model created for the reinforced concrete shear wall in this example. spColumncalculates the exact values of strain at each layer of steel (in tension and compression zones) with exact location ofthe total tension and compression forces leading to exact value for nominal and design strengths (axial and flexuralstrengths).16
Figure 11 – Shear Wall Interaction Diagram (X-Axis, In-Plane) (spColumn)17
Figure 12 – Load & Moment Capacities Output from spColumn18
Figure 13 – Shear Wall Interaction Diagram (Y-Axis, Out-of-Plane) (spColumn)19
Figure 14 – Wall Section Interaction Diagram – 3D (spColumn)20
Using the spColumn results output, further comparison can be made for the shear wall capacity parameters assummarized below:Table 2 – Comparison of Flexural Capacity Based on Method of Solutionc, in.εt, in./in.ϕMn, 028115,319100%Solution MethodspWallspColumn*Calculated from spWall plate reinforcement by summing the capacity of each element along the wall cross-sectionThe last column in the table above compares the hand calculated capacity estimated by approximate methods to theexact values generated by spWall and spColumn. The impact of simplifying assumptions is illustrated in the figurebelow showing the value of incorporating the exact value and location of steel and concrete strains and forces.Figure 15 – Strains, Forces, and Moment Arms for simplified and Actual Methods21
5. Shear Wall Analysis and Design – spWall Software spWall is a program for the analysis and design of reinforced concrete shear walls, tilt-up walls, precast wall and insulate concrete form (ICF) walls. It uses a graphical interface that enables the user to easily generate complex wall models. Graphical user interface is provided for:
3. Mid Ply Shear Wall 4. RC Hollow Concrete Block Masonry Wall 5. Steel Plate Shear Wall C. RC Shear Wall Reinforced concrete (RC) shear walls are considered as effective lateral force resisting system that has been widely used in the last decades. RC walls can provide the required
Keywords: RC Shear walls; Single layer reinforced; Double layer reinforced; In-plane shear strength; Ductility 1 Introduction Reinforced concrete shear walls (RCSW) are key lateral load resisting elements in concrete buildings; adequate capacity and ductility of these walls are central to the safety of the shear wall dominated buildings.
If shear reinforcement is provided, the concrete contribution to shear strength in a reinforced concrete member is a function of both the aggregate interlock and the dowel action between the concrete and reinforcement. Once a shear crack forms, the shear reinforcement engages, providing the remaining shear capacity of the section V s. For
1. Special reinforced concrete shear walls 14.2 5 21/ 2 5 NL NL 160 160 100 2. Ductile Coupled reinforced concrete shear wallsq 14.2 8 21/ 2 8 NL NL 160 160 100 3. Ordinary reinforced concrete shear walls 14.2 4 21/ 2 4 NL NL NP NP NP qStructural height, h n, shall not be less than 60 ft (18.3 m).
2.1 Analysis and Design of Frame-Shear Wall Systems 5 2.2 The Scope of the Reported Research .« 6 3. ANALYSIS OF THE FRAME-SHEAR WALL SYSTEMS 9 3.1 Description of the Frames 9 3.2 Frame-Shear Wall Configurations 9 3.3 Analysis 10 3.4 Frame-Cracked Shear Wall Systems 13 3.4.1 Damage Mechanism 14 3.4.2 Structural Idealization and Soft Story 16
wall section 3 2.1 Common structural systems for tall buildings 11 2.2 Coupled shear wall in Continuous Connection Method 15 2.3 Equivalent frame model of coupled shear wall 16 2.4 Braced wide column analogy of a planar shear wall 17 2.5 Finite element model of a shear wall 18 2.6 Concrete damage plasticity model a) compression behaviour b)
70 H. Naderpour et al./ Journal of Soft Computing in Civil Engineering 6-1 (2022) 66-87 Table 2 The shear capacity equations of a concrete shear wall. Models Concrete shear resistance Vc, Reinforcement shear resistance Vs ACI w318-14-11 [6] '' '' '' 4 4 V0.2 0.05 1 2 u c w u d
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