COLUMN DESIGN CALCULATIONS
Project Name : Unassigned
Client Name : Unassigned
Engineer Name : Unassigned
Analysis File : D:\Bentley\000 RCDC\11.6.0\to Dhawal\Sample model_04_only column for cracked section.std
Analysis Last Modified : 10/14/2022 12:47:06 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 Aeff = Effective area of column / wall considered for shear check in sqmm
8 Ak = Area of confined concrete core
9 Ash = Area of link cross section
10 b = Effective Width of Column in mm
11 beff = Effective Width of Column in mm
12 B = Width / Smaller Dimension of Column in mm
13 d = Effective Depth of Column in mm
14 deff = Effective Depth of Column in mm
15 D = Depth / Larger Dimension of Column OR Diameter of Circular Column in mm
16 Dk = Diameter Of core measured to the outside of circular link
17 Ec = Modulus of elasticity of concrete
18 Es = Modulus of elasticity of steel
19 FcPerm = Permissible Stress in Concrete required in N/ (sqmm)
20 Fst = Stress in steel
21 FstPerm = Permissible Stress in Steel required in N/ (sqmm)
22 Fck = Characteristic compressive strength of concrete cube in N/sqmm
23 Fy = Yield Stress Of Steel in N/sqmm
24 h = Longer dimension of rectangular link measured to its outer face
25 Hu = Total lateral force acting within the story(Story shear)
26 Hs = Height of the story (Floor height)
27 k = Reduction factor for slenderness moments
28 Max = Additional moment due to slenderness about major axis (Along D)
29 May = Additional moment due to slenderness about minor axis (Along B)
30 Mminx = Moment due to minimum eccentricity along D
31 Mminy = Moment due to minimum eccentricity along B
32 Muv = Moment capacity of web portion of wall as per clause 9.4.2 and Annes A of IS 13920 - 2016
33 Mux = Factored moment Along D (Momemt About Major Axis)
34 Muy = Factored moment Along B (Momemt About Minor Axis)
35 MCap = Moment capacity of section for NA angle at design Pu
36 MRes = Resultant design moment at angle to local major axis
37 Pb = Axial capacity of column along B as defined in 39.7.1.1
38 Pd = Axial capacity of column along D as defined in 39.7.1.1
39 Pu = Factored axial force
40 Puz = Axial load on column as defined in 39.6
41 Pu_Total = Sum of Axial loads on all column in the story (Gravity Load)
42 Q = Stability Index (factor for checking sway/ non sway condition for a given story)
43 S = Link Spacing
44 Shear Strength Enhancement Factor = Multiplying factor for shear strength of concrete as per 40.2.2
45 Vur = Factored resultant shear force acting on the column
46 Vux = Factored shear force Along B
47 Vuy = Factored shear force Along D
48 Wcr = Surface Crack Width
49 WcrPerm = Permissible Crack Width required in mm
50 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
General Data
Column No. : C1
Level : 0 m To 4.2 m
Frame Type = Non-Ductile
Response Reduction Factor = 3
Design Code = IS 456 : 2000 + IS 13920 : 2016
Grade Of Concrete = M50 N/sqmm
Grade Of Steel (Main) = Fe500 N/sqmm
Grade Of Steel (Shear) = Fe500 N/sqmm
Grade Of Steel - Flexural Design = Fe500 N/sqmm
Grade Of Steel - Shear Design = Fe415 N/sqmm
Column B = 600 mm
Column D = 900 mm
Clear Cover = 50 mm
Clear Floor Height @ B = 2000 mm
Clear Floor Height @ D = 2000 mm
No Of Floors = 1
No Of Columns In Group = 1
Column Type : UnBraced
Minimum eccentricity check : One Axis at a Time
Code defined D/B ratio : 4
D/B Ratio : 1.5 <= 4 Hence, Design as Column


Flexural Design (Analysis Forces)
Analysis Reference No. = 501
Load Combination = [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2)
Critical Location = Bottom Joint
Pu = 1000.4 kN
Mux = -900.12 kNm
Muy = 50.01 kNm
Vux = 0 kN
Vuy = 0 kN



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
                = 34 mm
Minimum Eccentricity > 20 mm
Mminx = Pu x Minimum Eccentricity
= 34.01 kNm
Slenderness Check
Max Slenderness Ratio(L/B) = 3.33
< 60 (Hence Ok)
Column Is Unbraced Along D
Slenderness Check Along D:
               Effective Length Factor = 1
               Slenderness Ratio = Effective Length / D
= 2.22, Column not Slender Along D
Column Is Unbraced Along B
Slenderness Check Along B:
               Effective Length Factor = 1
               Slenderness Ratio = Effective Length / B
= 3.33, Column 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   -900.12 34.01 -900.12 0 -900.12
Minor Axis - Muy 50.01 --- 50.01 0 50.01

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 = 1000.4 kN
Mux = -900.12 kNm
Muy = 50.01 kNm

Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated = 3.28
Reinforcement Provided = 22-T32
Load Angle = Tan-1(Muy/Mux)
= 3.18 deg
MRes = 901.51 kNm
MCap = 2729.94 kNm
Capacity Ratio = MRes/ MCap
= 0.33 <= 1
Shear Calculation Along D Along B
Critical Load Combination [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2) [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2)
Design shear force, Vu (kN) 0 0
Pu (kN) 1000.4 1000.4
Deff , Beff (mm) 834 534
Aeff (sqmm) 500400 480600
Design shear stress, Tv Vu / (B x Deff) Vu / (D x Beff)
Tv (N/sqmm) 0 0
Pt (%) 1.638 1.638
Design shear strength, Tc (N/sqmm) 0.8411 0.8411
Shear Strength Enhancement Factor (Compressive Force) 1 + 3 x Pu / ( B x D x Fck)
  1.12 1.1249
Shear Strength Enhancement Factor (Tensile Force) - -
Shear Strength Enhancement Factor (max) 1.5 1.5
Shear Strength Enhancement Factor 1.12 1.1249
Enhanced shear strength, Tc-e (N/sqmm) 0.942 0.9461
Design shear check Tv < Tc x Enhancement factor Tv < Tc x Enhancement factor
Shear Links Design Shear Links Not Required Shear Links 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
  = 8 mm
Criterion for spacing of normal links
Min. Longitudinal Bar dia X 16 = 512 mm
Min. dimension of column = 600 mm
Max. 300 mm = 300 mm
Provided spacing = 300 mm
 
 
Table For Links
Required Provided
Normal Design Shear Design Ductile Design Normal Zone Ductile Zone
Link Dia. 8 --- --- 8 ---
Spacing 300 --- --- 300 ---

Crack Width Check as per IS 456 + IS 13920 - 2016
Location Bottom Top
Critical Load Combination 10001 10001
Member Force
       P (kN) 1000.3998 1000.3998
       Mx (kNm) 900.1209 900.1209
       My (kNm) 50.0067 50.0067
Reinforcement-Total 22-T32 22-T32
Corner Reinforcement - Dia 32 32
Ast - corner reinforcement - mm2 804.2477 804.2477
Neutral Axis Angle (Deg) 86.8202 86.8202
Neutral axis location from compressive corner (mm) 343.9969 343.9969
acr (mm) 77.3381 77.3381
Check for Stress in Steel
        Fst ( N/sqmm) -128.451 -128.451
        FstPerm ( N/sqmm) 275 275
Check for Stress in Concrete
        Fc ( N/sqmm) 15.2226 15.2226
        FcPerm ( N/sqmm) 16.6667 16.6667
Crack Width Check
        Epsilon-deff, ε1 0.0007 0.0007
        Wcr (mm) 0.1235 0.1235
        WcrPerm (mm) 0.2 0.2
Stress Limit Check as per IS 456 + IS 13920 - 2016
Location Bottom Top
Critical Load Combination 10001 10001
Member Force
       P (kN) 1000.3998 1000.3998
       Mx (kNm) 900.1209 900.1209
       My (kNm) 50.0067 50.0067
Reinforcement - Total 22-T32 22-T32
Corner Reinforcement - Dia 32 32
Ast - corner reinforcement - mm2 804.2477 804.2477
Neutral Axis Angle (Deg) 86.8202 86.8202
Neutral axis location from compressive corner (mm) 343.9969 343.9969
Check for Stress in Steel
        Fst ( N/sqmm) -128.451 -128.451
        FstPerm ( N/sqmm) 275 275
Check for Stress in Concrete
        Fc ( N/sqmm) 15.2226 15.2226
        FcPerm ( N/sqmm) 16.6667 16.6667