COLUMN DESIGN CALCULATIONS
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Design File : D:\Scube\000 RCDC 2010\10.0.0\Queries\Surendra Rao\RCDC-Staad-Demo -with RCC wall-Column-3.R3.rcdx
Analysis File : D:\Scube\000 RCDC 2010\10.0.0\Standard model for Demo\Staad\RCDC-Staad-Demo -with RCC wall.std
Analysis Last Modified : 12/31/2019 3:19:44 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 as defined in 39.7.1.1
35 Pu = Factored axial force
36 Pu_Total = Sum of Axial loads on all column in the story (Gravity Load)
37 Q = Stability Index (factor for checking sway/ non sway condition for a given story)
38 S = Link Spacing
39 Shear Strength Enhancement Factor = Multiplying factor for shear strength of concrete as per 40.2.2
40 Vur = Factored resultant shear force acting on the column
41 Vux = Factored shear force Along B
42 Vuy = Factored shear force Along D
43 Wcr = Surface Crack Width
44 WcrPerm = Permissible Crack Width required in mm
45 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)
0m to 4.2m LOAD 3: LOAD CASE 3 EQ-X 4.2 58606.007 1.143 1754.701 0.009 Non Sway
4.2m to 7.858m LOAD 3: LOAD CASE 3 EQ-X 3.658 51337.009 1.39 1690.676 0.012 Non Sway
7.858m to 12.058m LOAD 3: LOAD CASE 3 EQ-X 4.2 31804.197 1.704 1450.58 0.009 Non Sway
12.058m to 16.258m LOAD 3: LOAD CASE 3 EQ-X 4.2 13878.005 1.317 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)
0m to 4.2m LOAD 4: LOAD CASE 4 EQ-Y 4.2 58606.007 0.949 1754.701 0.008 Non Sway
4.2m to 7.858m LOAD 4: LOAD CASE 4 EQ-Y 3.658 51337.009 1.254 1690.676 0.01 Non Sway
7.858m to 12.058m LOAD 4: LOAD CASE 4 EQ-Y 4.2 31804.197 1.635 1450.58 0.009 Non Sway
12.058m to 16.258m LOAD 4: LOAD CASE 4 EQ-Y 4.2 13878.005 1.402 1015.406 0.005 Non Sway


General Data
Column No. : C1
Level : 0m To 4.2m
Frame Type = Non-Ductile
Response Reduction Factor = 3
Design Code = IS 456 + IS 13920 - 2016
Grade Of Concrete = M25 N/sqmm
Grade Of Steel = Fe415 N/sqmm
Column B = 700 mm
Column D = 700 mm
Clear Floor Height @ B = 3400 mm
Clear Floor Height @ D = 3400 mm
No Of Floors = 1
No Of Columns In Group = 1
Column Type : Braced
Minimum eccentricity check : One Axis at a Time
Code defined D/B ratio : 4
D/B Ratio : 1 <= 4 Hence, Design as Column


Flexural Design (Analysis Forces)
Analysis Reference No. = 1
Load Combination = [12] : 0.9 (LOAD 1: LOAD CASE 1) +1.5 (LOAD 4: LOAD CASE 4 EQ-Y)
Critical Location = Bottom Joint
Put (top joint) = 228.72 kN
Muxt (top joint) = 35.97 kNm
Muyt (top joint) = -65.96 kNm
Vuxt (top joint) = -64.73 kN
Vuyt (top joint) = -15.25 kN
Pub (bottom joint) = 275.04 kN
Muxb (bottom joint) = -28.06 kNm
Muyb (bottom joint) = 205.81 kNm
Vuxb (bottom joint) = -64.73 kN
Vuyb (bottom joint) = -15.25 kN


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 mm mm N/m N/m
Bottom 476.389 No Beam No Beam - - 1
Top 476.389 8000 x 400 x 800 No Beam 213.333 - 0.827
Sway Condition (as per Stability Index) = Non Sway
Effective Length Factor along Major Axis = 0.93

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 mm mm N/m N/m
Bottom 476.389 No Beam No Beam - - 1
Top 476.389 5710 x 400 x 800 No Beam 298.891 - 0.774
Sway Condition (as per Stability Index) = Non Sway
Effective Length Factor along Minor axis = 0.92

Minimum Eccentricity Check
Since Axial Force is compressive, Min. Eccentricity check to be performed
Most critical case is with Min. Eccentricity check in X-direction
Minimum Eccentricity Along D:
Minimum Eccentricity = Unsupported Length / 500 + D / 30
                = 30.13 mm
Minimum Eccentricity > 20 mm
Mminx (top) = Pu x Minimum Eccentricity
= 6.89 kNm
Mminx (bottom) = Pu x Minimum Eccentricity
= 8.29 kNm
Slenderness Check
Max Slenderness Ratio(L/B) = 4.86
< 60 (Hence Ok)
Column Is Braced Along D
Slenderness Check Along D:
               Effective Length Factor = 0.93
               Slenderness Ratio = Effective Length / D
= 4.52, Column not Slender Along D
Column Is Braced Along B
Slenderness Check Along B:
               Effective Length Factor = 0.92
               Slenderness Ratio = Effective Length / B
= 4.47, Column not Slender Along B


Calculation of Design Moment
Direction Manalysis Mmin (Abs) Mdesign Minit Mslndx (Abs) Mdesign-final
A B C D E F
Major Axis Mux (top) 35.97 6.89 35.97 --- 0 35.97
Major Axis Mux (bottom) -28.06 8.29 -28.06 --- 0 -28.06
Minor Axis Muy (top) -65.96 --- -65.96 --- 0 -65.96
Minor Axis Muy (bottom) 205.81 --- 205.81 --- 0 205.81

Where
A = Moments directly from analysis
B = Moments due to minimum eccentricity
C = Maximum of analysis moment and min. eccentricity = Max (A,B)
D = Initial moment = 0.4 x Min (top, bottom) ± 0.6 x Max (top, bottom) [As per sign requirement]
E = Moment due to slenderness effect
F = Final design Moment = Max(C- Top Bottom , D- Top Bottom) + E
 


Final Critical Design Forces
Pu = 275.04 kN
Mux = -28.06 kNm
Muy = 205.81 kNm

Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated = 0.46
Reinforcement Provided = 20-T12
Load Angle = Tan-1(Muy/Mux)
= 82.24 deg
MRes = 207.72 kNm
MCap = 325.91 kNm
Capacity Ratio = MRes/ MCap
= 0.64 <= 1
Shear Design (Analysis Forces)
Design for shear along D
Critical Load Combination = [11] : 0.9 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X)
Design shear force, Vuy = -73.9613 kN
Pu = 435 kN
Deff = 644 mm
Design shear stress, Tvy = Vuy / (Bx Deff) N/sqmm
= 0.1641 N/sqmm
Pt = 0.231 %
Design shear strength, Tc = 0.3523 N/sqmm
Shear Strength Enhancement Factor = 1 + 3 x Pu / ( B x D x Fck)
= 1.1065
Shear Strength Enhancement Factor (max) = 1.5
Shear Strength Enhancement Factor = 1.1065
Enhanced shear strength, Tc-e = 0.3898 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 Load Combination = [13] : 0.9 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y)
Design shear force, Vux = 81.8265 kN
Pu = 495.49 kN
Beff = 644 mm
Design shear stress, Tvx = Vux / (D x Beff) kN
= 0.1815 N/sqmm
Pt = 0.231 %
Design shear strength, Tc = 0.3523 N/sqmm
Shear Strength Enhancement Factor = 1 + 3 x Pu / (B x D x Fck)
= 1.1213
Shear Strength Enhancement Factor (max) = 1.5
Shear Strength Enhancement Factor = 1.1213
Enhanced shear strength, Tc-e = 0.395 N/sqmm
Design shear check = Tvx < Tc x Enhancement factor
Link for Shear Design along B are not required


Design Of Links
Links in the zone where special confining links are not required
Normal Links
Diameter of link = 8 mm
  > Max. longitudinal bar dia / 4
  = 3 mm
Criterion for spacing of normal links
Min. Longitudinal Bar dia X 16 = 192 mm
Min. dimension of column = 700 mm
Max. 300 mm = 300 mm
Provided spacing = 175 mm
 
 
Table For Links
Required Provided
Normal Design Shear Design Ductile Design Normal Zone Ductile Zone
Link Dia. 8 --- --- 8 ---
Spacing 175 --- --- 175 ---