COLUMN DESIGN CALCULATIONS
Project Name : Sample
Client Name : Sample
Engineer Name : Sample
Design File : D:\Bentley\Common data\Bentley Communities\IS\Shear Wall_Boundary Element\STAAD file\RCDC-Staad-Demo -with RCC wall-Column-1.rcdx
Analysis File : D:\Bentley\Common data\Bentley Communities\IS\Shear Wall_Boundary Element\STAAD file\RCDC-Staad-Demo -with RCC wall.std
Analysis Last Modified : 7/26/2020 2:46:06 PM

Definitions Of Terms:
All forces in units kN and m
All reinforcement details like area, spacing are mm
Grade Of steel for 6 mm dia. bars is Fe250. It is irrespective of the grade of steel defined by user in column design.
Neutral axis angle for resultant design moment is with respect to local major axis.
1 β = Stiffness proportion factor at joint ( column stiffness/sum of stiffness of all members connected at joint)
2 Δu = Elastically computed first order lateral deflection.(Relative deflections)
3 ε1 = Strain at level considered, Calculated ignoring the stiffening of the concrete in tension zone
4 εm = Average steel strain at level considered
5 acr = Distance from the point considered to the surface of the nearest longitudinal bar
6 Ag = Gross area of the column cross section
7 Ak = Area of confined concrete core
8 Ash = Area of link cross section
9 b = Effective Width of Column in mm
10 B = Width / Smaller Dimension of Column in mm
11 d = Effective Depth of Column in mm
12 D = Depth / Larger Dimension of Column OR Diameter of Circular Column in mm
13 Dk = Diameter Of core measured to the outside of circular link
14 Ec = Modulus of elasticity of concrete
15 Es = Modulus of elasticity of steel
16 FcPerm = Permissible Stress in Concrete required in N/ (sqmm)
17 Fst = Stress in steel
18 FstPerm = Permissible Stress in Steel required in N/ (sqmm)
19 Fck = Characteristic compressive strength of concrete cube in N/sqmm
20 Fy = Yield Stress Of Steel in N/sqmm
21 h = Longer dimension of rectangular link measured to its outer face
22 Hu = Total lateral force acting within the story(Story shear)
23 Hs = Height of the story (Floor height)
24 k = Reduction factor for slenderness moments
25 Max = Additional moment due to slenderness about major axis (Along D)
26 May = Additional moment due to slenderness about minor axis (Along B)
27 Mminx = Moment due to minimum eccentricity along D
28 Mminy = Moment due to minimum eccentricity along B
29 Muv = Moment capacity of web portion of wall as per clause 9.4.2 and Annes A of IS 13920 - 2016
30 Mux = Factored moment Along D (Momemt About Major Axis)
31 Muy = Factored moment Along B (Momemt About Minor Axis)
32 MCap = Moment capacity of section for NA angle at design Pu
33 MRes = Resultant design moment at angle to local major axis
34 Pb = Axial capacity of column along B as defined in 39.7.1.1
35 Pd = Axial capacity of column along D as defined in 39.7.1.1
36 Pu = Factored axial force
37 Puz = Axial load on column as defined in 39.6
38 Pu_Total = Sum of Axial loads on all column in the story (Gravity Load)
39 Q = Stability Index (factor for checking sway/ non sway condition for a given story)
40 S = Link Spacing
41 Shear Strength Enhancement Factor = Multiplying factor for shear strength of concrete as per 40.2.2
42 Vur = Factored resultant shear force acting on the column
43 Vux = Factored shear force Along B
44 Vuy = Factored shear force Along D
45 Wcr = Surface Crack Width
46 WcrPerm = Permissible Crack Width required in mm
47 β = It is a Neutral Axis angle corresponding to load angle to find out MCap


 
 

Code References:
IS 456
ELEMENT CLAUSE / table
1 Max area of reinforcement : 26.5.3.1-a & b
2 Min area of reinforcement : 26.5.3.1-a & b
3 Min number of bars : 26.5.3.1-c
4 Minimum Eccentricity Calc : 25.4 & 39.2
5 Effective Length : 25.2
6 Slenderness Moments : 25.3 & 39.7
7 Design for axial loads : 39.3
8 Design for axial loads And uniaxial bending : 39.5
9 Design for axial loads And Biaxial bending : 39.6
10 Design of horizontal links : 26.5.3.2
11 Design shear strength : 40.2
12 Stiffness Proportion Factor, β : E-1
13 Stability(Index, Q) : E -2
14 Crack width calculation : 3.8
15 Multiplying factor to Beam Stiffness for effective length calculation : SP 24 1983 APPENDIX D
 
IS 13920 - 2016
ELEMENT CLAUSE / table
1 Spacing of special confining reinforcement : 10.4 and 7.6
2 C/s area of special confining reinforcement : 7.6.1
3 Applicability of boundary element : 10.4.1
4 Muv-Moment Capacity of Web : Annex
5 Additional Compressive Force in BE : 10.4.2
6 Check for BE in tension and compression : 10.4.2.1 and 10.4.3
7 Shear include due to Beam : 7.5
8 Minimum Flexural Strength of Column : 7.2
9 Shear Check at Column Joint : 9.1
10 Length of wall to thickness ratio : 10.1.3
11 Type of wall & Minimum reinforcement : 10.1.4
12 Largest diameter of longitudinal steel bar : 10.1.8
13 Shear reinforcement in RC wall : 10.2.3
14 Special confinement reinforcement in Boundary Element : 10.4.4
15 Minimum vertical reinforcement across horizontal construction joint : 10.7
Sway Calculation (Stability Index)
For Global-X Direction
Level Load Name Storey Height (m) Gravity Load P (kN) Relative Displacements (mm) Storey Shear (kN) Stability Index Sway Condition
A B C D B x C / (A x D)
0 m to 4.2 m LOAD 3: LOAD CASE 3 EQ-X 4.2 58589.743 1.11 1754.701 0.009 Non Sway
4.2 m to 7.858 m LOAD 3: LOAD CASE 3 EQ-X 3.658 51324.946 1.366 1690.676 0.011 Non Sway
7.858 m to 12.058 m LOAD 3: LOAD CASE 3 EQ-X 4.2 31795.793 1.677 1450.58 0.009 Non Sway
12.058 m to 16.258 m LOAD 3: LOAD CASE 3 EQ-X 4.2 13873.803 1.302 1015.406 0.004 Non Sway


For Global-Y Direction
Level Load Name Storey Height (m) Gravity Load P (kN) Relative Displacements (mm) Storey Shear (kN) Stability Index Sway Condition
A B C D B x C / (A x D)
0 m to 4.2 m LOAD 4: LOAD CASE 4 EQ-Y 4.2 58589.743 0.986 1754.701 0.008 Non Sway
4.2 m to 7.858 m LOAD 4: LOAD CASE 4 EQ-Y 3.658 51324.946 1.303 1690.676 0.011 Non Sway
7.858 m to 12.058 m LOAD 4: LOAD CASE 4 EQ-Y 4.2 31795.793 1.698 1450.58 0.009 Non Sway
12.058 m to 16.258 m LOAD 4: LOAD CASE 4 EQ-Y 4.2 13873.803 1.449 1015.406 0.005 Non Sway



General Data
Wall No. : C7
Frame Type = Ductile
Level : 4.2 m To 7.858 m
Design Code = IS 456 - 2000 + IS 13920 - 2016
Grade Of Concrete = M25 N/sqmm
Grade Of Steel = Fe415 N/sqmm
Wall B = 300 mm
Wall D = 1500 mm
Clear Cover = 50 mm
Clear Floor Height @ B = 2858 mm
Clear Floor Height @ D = 2858 mm
No Of Floors = 1
No Of Walls In Group = 1
Wall Type : UnBraced
Minimum eccentricity check : One Axis at a Time
Code defined D/B ratio : 4
D/B Ratio : 5 >= 4 Hence, Design as Wall


Flexural Design (Analysis Forces)
Analysis Reference No. = 611
Critical Analysis Load Combination : 19
Load Combination = [9] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y)
Critical Location = Top Joint
Pu = 2261.28 kN
Mux = -12.08 kNm
Muy = 158.44 kNm
Vux = 82.43 kN
Vuy = 1.05 kN


Check For Requirement Of Boundary Element
Check For Maximum Compressive Stress
Having maxstress in between level's (4.2 m - 16.258 m)
At level (4.2 m)
Load Combination = [7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X)
Maximum Stress = 11.34
0.2 x Fck = 5
Maximum Stress in Wall > 0.2 x Fck
Hence Boundary Element is applicable
 
At level (7.858 m)
Load Combination = [7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X)
Maximum Stress = 7.55
0.15 x Fck = 3.75
Maximum Stress in Wall > 0.15 x Fck
Hence Boundary Element is applicable
Effective Length Calculation
Calculation Along Major Axis Of Column
Joint Column Stiffness       Beam Sizes Beam Stiffness Beta
Beam 1
(Length x Width x Depth)
Beam 2
(Length x Width x Depth)
Beam 1 Beam 2
N-m x 10^6 mm mm N-m x 10^6 N-m x 10^6
Bottom 2306.588 8000 x 450 x 800 8000 x 450 x 800 240 240 0.9
Top 2306.588 8000 x 450 x 800 8000 x 450 x 800 240 240 0.9
Sway Condition (as per Stability Index) = Non Sway
Effective Length Factor along Major Axis = 0.92

Calculation Along Minor Axis Of Column
Joint Column Stiffness
Beam Sizes
Beam Stiffness
Beta
Beam 1
(Length x Width x Depth)
Beam 2
(Length x Width x Depth)
Beam 1 Beam 2
N-m x 10^6 mm mm N-m x 10^6 N-m x 10^6
Bottom 92.264 8900 x 450 x 800 5710 x 450 x 800 215.73 336.252 0.238
Top 92.264 8900 x 450 x 800 5710 x 450 x 800 215.73 336.252 0.238
Sway Condition (as per Stability Index) = Non Sway
Effective Length Factor along Minor axis = 0.57

Minimum Eccentricity Check
Since Axial Force is compressive, Min. Eccentricity check to be performed
Most critical case is with Min. Eccentricity check in Y-direction
Minimum Eccentricity Along B :
Minimum Eccentricity = Unsupported Length / 500 + B / 30
                = 15.72 mm
Mminy = Pu x Minimum Eccentricity
= 45.23 kNm
Slenderness Check
Max Slenderness Ratio(L/B) = 9.53
< 60 (Hence Ok)
Column Is Unbraced Along D
Slenderness Check Along D:
               Effective Length Factor = 0.92
               Slenderness Ratio = Effective Length / D
= 1.75, Wall not Slender Along D
Column Is Unbraced Along B
Slenderness Check Along B:
               Effective Length Factor = 0.57
               Slenderness Ratio = Effective Length / B
= 5.43, Wall not Slender Along B


Calculation of Design Moment
Direction Manalysis Mmin (Abs) Mdesign Mslndx (Abs) Mdesign-final
A B C E F
Major Axis - Mux   -12.08 --- -12.08 0 -12.08
Minor Axis - Muy 158.44 45.23 158.44 0 158.44

Where
A = Moments directly from analysis
B = Moments due to minimum eccentricity
C = Maximum of analysis moment and min. eccentricity = Max (A,B)
E = Moment due to slenderness effect
F = Final design Moment = Max(C- Top Bottom , D- Top Bottom) + E
 


Final Critical Design Forces
Pu = 2261.28 kN
Mux = -12.08 kNm
Muy = 158.44 kNm
Minimum % steel
User defined pt min1 = 0.25
Vertical reinforcement as per type of wall
hw = 3658 mm
Lw = 1500 mm
hw/Lw = 2.44
Type of wall = 2.44 > 2, hence, Slender wall
tw = 300 mm
Ph = 0.0025
Pvweb = 0.0025
Ptv min2 = 0.52 %
Ptmin = Max ( 0.25 , 0.52 )
= 0.52 %

Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated = 1.03
Reinforcement Provided = 20-T16 + 8-T10
Load Angle = Tan-1(Muy/Mux)
= 85.64 deg
MRes = 158.9 kNm
MCap = 286.96 kNm
Capacity Ratio = MRes/ MCap
= 0.55 <= 1
Check For Boundary Element
Calculation of vertical reinforcement in BE zone
A = 450000 sqmm
Z = 112500000 mm^3
Maximum Compressive Force in BE
Most Favouring Pu = [7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X)
P = 2370.99 kN
M = -257.13 kN-m
P/A = 5.27 N/sqmm
M/Z = -2.29 N/sqmm
Stress Slope,S1 = ((P/A + M/Z) - (P/A - M/Z)) / Lw
= -3.05 N/sqmm
Stress - 1 = (P/A + M/Z) - S1 X (BE length) / 2
= 3.55 N/sqmm
Stress - 2 = (P/A - M/Z) + S1 X (BE length) / 2
= 6.98 N/sqmm
Maximum compressive force = Maximum (Stress-1, Stress-2) x BE length
= 785.6 KN
Pt required = 0 %
Maximum Tensile Force in BE
Most Un-favouring Pu = 0.8 DL--1.5 EQ
P = 1265.43 kN
M = -255.6 kN-m
P/A = 2.81 N/sqmm
M/Z = -2.27 N/sqmm
Stress Slope,S1 = ((P/A + M/Z) - (P/A - M/Z)) / Lw
= -3.03 N/sqmm
Stress - 1 = (P/A + M/Z) - S1 X (BE length) / 2
= 1.11 N/sqmm
Stress- 2 = (P/A - M/Z) + S1 X (BE length) / 2
= 4.52 N/sqmm
Maximum Tensile force = Minimum (Stress-1, Stress-2) x BE length
= 124.66 KN
Pt required = 0 %
Design pt in BE
Minimum pt = 0.8 %
Pt required in BE = Maximum (0,0,0.8)
= 0.8 %
Check For Compression Capacity Of BE
PT provided in BE = 1.79
Ast provided in BE = 2010.62 mm2
Capacity of BE in compression = 0.4 x Fck x Aconcrete + 0.67 x Fy x Ast
= 1664.79 kN
1664.79 > 785.6
1664.79 Hence OK
Check For Tension Capacity Of BE
PT provided in BE = 1.79 %
Ast provided in BE = 2010.62 mm2
Capacity of BE in Tension = 0.87 x Fy x Ast
= 727.06 kN
727.06 > 124.66
727.06 Hence OK
Wall Configuration
  Boundary Element Mid Boundary Element
Length (mm) 375 750 375
Reinforcement 10-T16 8-T10 10-T16
Ast provided 2010.62 628.32 2010.62
Pt as % of entire wall 0.45 % 0.14 % 0.45 %
Pt as % of zone 1.79 % 0.28 % 1.79 %
Shear Design (Analysis Forces)
Design for shear along D
Critical Analysis Load Combination : 20
Critical Load Combination = [10] : 0.9 (LOAD 1: LOAD CASE 1) +1.5 (LOAD 3: LOAD CASE 3 EQ-X)
Design shear force, Vuy = 120.5658 kN
Pu = 1382.45 kN
= 0.3349 N/sqmm
Pt (20% of vertical reinforcement) = 0.207 %
Design shear strength, Tc = 0.3356 N/sqmm
Shear Strength Enhancement Factor = 1 + 3 x Pu / ( B x D x Fck)
= 1.3687
Shear Strength Enhancement Factor (max) = 1.5
Shear Strength Enhancement Factor = 1.3687
Enhanced shear strength, Tc-e = 0.4593 N/sqmm
Design shear check = Tvy < Tc x Enhancement factor
Link for Shear Design along D are not required
 
Design for shear along B
Critical Analysis Load Combination : 23
Critical Load Combination = [13] : 0.9 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y)
Design shear force, Vux = 73.5342 kN
Pu = 1338.35 kN
Design shear stress, Tvx = Vux / (B x 0.8 xD) kN
= 0.2043 N/sqmm
Pt (20% of vertical reinforcement) = 0.207 %
Design shear strength, Tc = 0.3356 N/sqmm
Shear Strength Enhancement Factor = 1 + 3 x Pu / (B x D x Fck)
= 1.3569
Shear Strength Enhancement Factor (max) = 1.5
Shear Strength Enhancement Factor = 1.3569
Enhanced shear strength, Tc-e = 0.4553 N/sqmm
Design shear check = Tvx < Tc x Enhancement factor
Link for Shear Design along B are not required


Design Of Links
 Main Links
Links in the zone where special confining links are not required
Normal Links
Horizontal reinforcement as per type of wall
hw = 3658 mm
Lw = 1500 mm
hw/Lw = 2.44
Type of wall = 2.44 > 2, hence, Slender wall
tw = 300 mm
Ph = 0.0025
Pvweb = 0.0025
Pth min = 0.52 %
Diameter of main horizontal steel = 8 mm
Thus, Spacing = 125 mm
 Spacing of horizontal reinforcement is minimum of following
D / 5 = 300 mm
3 x B = 900 mm
Maximum = 450 mm
Spacing considered = 125 mm
       
Special confining reinforcement as per IS 13920 - 2016
Min. Lateral dimension of column, B = 300 mm
B/3 = 100 mm
6 X Smallest Longitudinal Bar Dia = 60 mm
Spacing = 150 mm
Hence Link spacing, Sv = 100 mm
Hoop dimension, h 116.33
Area of special confining link, Ash = 0.05 x Sv x h x (Fck/Fy)
  = 35.04 sqmm
Diameter of special confining link = 8 mm
= > Max. longitudinal bar dia / 4
  = 4 mm
Area of horizontal steel provided = Area of bar provided x 1000 x 2 / spacing
= 1005.4 (sqmm)/ m height
= 0.3351 %
= > min. steel required 0.25%
Special confining links to be provided along full height in BE.
 
Table For Links
Note: Ductile Design Of Links Is Applicable Only For Boundary Elements
Required Provided
Normal Design Shear Design Ductile Design Normal Zone Ductile Zone
Link Dia. 8 --- 8 8 8
Spacing 125 --- 100 125 100

Secondary Links:
T8@100c/c
T8@125c/c