COLUMN DESIGN CALCULATIONS
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Client Name : Unassigned
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Design File : D:\Bentley\Common data\Bentley Communities\ACI\ACI_M_Validation Sheets\2014_Metric\Column_Regular_Flexural\STAAD file\Sample model_02-Column-1.rcdx
Analysis File : D:\Bentley\Common data\Bentley Communities\ACI\ACI_M_Validation Sheets\2014_Metric\Column_Regular_Flexural\STAAD file\Sample model_02.std
Analysis Last Modified : 2/20/2023 10:24:12 AM

Definitions Of Terms:
All forces in units 'kN' and 'm'
All reinforcement details like area, spacing in 'mm'
Neutral axis angle for resultant design moment is with respect to local major axis.
1 βdns = Ratio to account for reduction of stiffness of columns due to sustained axial loads
2 δns = Moment magnification factor for frames not braced against sidesway
3 Δo = First-order relative deflection between the top and bottom of the story due to Vu in 'kN'
4 ∑Pu = Total factored vertical load in 'kN'. (Clause 6.6.4.4)
5 δu = Design displacement in 'mm'
6 λ = Modification factor reflecting the reduced mechanical properties Of concrete
7 ac = Coefficient defining the relative contribution Of concrete strength To nominal wall shear strength
8 Ach = Cross-sectional area of a structural member measured to the outside edges of transverse reinforcement in 'sqmm'
9 Acv = Gross area of concrete section bounded by web thickness And length of section in the direction Of shear force considered in 'sqmm'
10 Aj = Effective cross-sectional area within a joint In a plane parallel To plane Of reinforcement generating shear In the joint in 'sqmm'
11 As = Area Of non-prestressed longitudinal tension reinforcement in 'sqmm'
12 Avmin = Minimum area Of shear reinforcement within spacing 's' in 'sqmm'
13 B = Width of column/ wall in 'mm'
14 beff = Effective Width of column/ wall in 'mm'
15 bc1 and dc1 = Cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area Ash in 'mm'
16 c = Distance from extreme compression fiber to neutral axis in 'mm'
17 Cc = Clear cover to longitudinal reinforcement in 'mm'
18 Cm = Factor relating actual moment diagram to an equivalent uniform moment diagram
19 D = Depth / diameter of column in 'mm'
20 deff = Effective Depth / diameter of column in 'mm'
21 d = Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in 'mm'
22 d' = Distance from extreme compression fiber to centroid of longitudinal compression reinforcement,'mm'
23 Ec = Modulus of elasticity of concrete in 'N/sqmm'
24 EI = Flexural stiffness of compression member in 'Nsqmm'
25 f'c = Specified compressive strength of concrete cylinder in 'N/sqmm'
26 fy = Specified yield strength of reinforcement in 'N/sqmm'
27 fyt = Specified yield strength fy of transverse reinforcement in 'N/sqmm'
28 hw = Height of entire wall from base to top of wall segment considered in 'mm'
29 Icr = Moment of Inertia of concrete crack section
30 k = Effective length factor for compression member
31 lc = Length of compression member in a frame, measured center-to-center of the joints in the frame in 'mm'
32 lg = Moment of inertia of gross concrete section about centroidal axis neglecting reinforcement in 'mm4'
33 lw = Length of entire wall in 'mm'
34 lux = Un-supported length for compression member along D in 'mm'
35 luy = Un-supported length for compression member along B in 'mm'
36 MCap = Moment capacity of section for a given NA angle at design Pu in 'kNm '
37 Mcr = Cracking Moment
38 MRes = Resultant design moment at a given load angle to local major axis in 'kNm '
39 Mc = Factored moment amplified for the effects of member curvature used for design of compression member in 'kNm'
40 Mm = Factored moment modified to account for effect of axial compression in 'kNm'
41 Mmx = Factored moment along D of column modified to account for effect of axial compression in 'kNm'
42 Mmy = Factored moment along D of column modified to account for effect of axial compression in 'kNm'
43 Mur = Sqrt (Mmy^2 + Mmx^2) for circular column in 'kNm'
44 Mux = Factored moment acting on a section along D in 'kNm' from Analysis (Momemt About Major Axis)
45 Muy = Factored moment acting on a section along B in 'kNm' from Analysis (Momemt About Minor Axis)
46 M1 = Smaller factored end moment on a compression member in 'kNm'
47 M1ns = Factored end moment on a compression member at the end at which M1 acts, due to loads that cause no appreciable sidesway in 'kNm'
48 M1s = Factored end moment on compression member at the end at which M1 acts, due to loads that cause appreciable sidesway in 'kNm'
49 M1sldr = Smaller factored end moment on a compression member due to slenderness effect in 'kNm'
50 M2 = Larger factored end moment on compression member in 'kNm'
51 M2min = Minimum value of moment M2 as per minimum eccentricity of column
52 M2ns = Factored end moment on compression member at the end at which M2 acts, due to loads that cause no appreciable sidesway in 'kNm'
53 M2s = Factored end moment on compression member at the end at which M2 acts, due to loads that cause appreciable sidesway in 'kNm'
54 M2sldr = Largest factored end moment on a compression member due to slenderness effect in 'kNm'
55 Mnb = Flexure Capacity for Beam
56 Mnc = Flexure Capacity for Column
57 Mnty = Nominal Flexure strength of column at top along depth in 'kNm'
58 Mnby = Nominal Flexure strength of column at bottom along depth in 'kNm'
59 Mntx = Nominal Flexure strength of column at top along width in 'kNm'
60 Mnbx = Nominal Flexure strength of column at bottom along width in 'kNm'
61 Nu = Factored axial force normal to cross section occurring simultaneously with Vu in 'kN'
62 Pc = Critical buckling load in 'kN'
63 pt = Ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement
64 Pω = Ratio of As to B x d
65 Q = Stability index for storey
66 r = Radius of gyration of cross section of a compression member in 'mm'
67 Vc = Nominal shear strength provided by concrete in 'kN'
68 Vj = Shear Force acting at the joint in 'kN'
69 Vn = Nominal shear strength in 'kN'
70 Vn' = Nominal shear strength at joint in 'kN'
71 Vs = nominal shear strength provided by shear reinforcement in 'kN'
72 Vs permissible = Maximum nominal shear strength provided by shear reinforcement in 'kN'
73 Vur = Factored resultant shear force acting on the column in 'kN'
74 Vus = Factored horizontal shear in a storey in 'kN'
75 Vux = Factored shear at section along B in 'kN' (From Analysis)
76 Vux1 = Shear induced due to column flexural capacity along width,'kN'
77 Vux2 = Shear due to enhanced earthquake factor along width, 'kN'
78 Vuy = Factored shear at section along D in 'kN' (From Analysis)
79 Vuy1 = Shear induced due to column flexural capacity along depth, 'kN'
80 Vuy2 = Shear due to enhanced earthquake factor along depth, 'kN'
81 y = Neutral axis depth.
82 β = It is a Neutral Axis angle corresponding to load angle to find out MCap
83 So = Center to center spacing of transverse reinforcement within the length lo in 'mm'
84 lo = Length, measured from joint face along axis of member, over which special transverse reinforcement must be provided in 'mm'


 
 

Code References:
ACI 318M - 14
Sr.No Element Clause / table
1 Minimum area of longitudinal reinforcement for column : 18.7.4
2 Maximum area of longitudinal reinforcement for column : 18.7.4
3 Minimum longitudinal and transverse reinforcement for wall : 18.10.2.1
4 Minimum diameter of transverse ties : 25.7.2
5 Minimum spacing of transverse ties : 25.7.2
6 Maximum spacing of longitudinal and transverse reinforcement for wall : 18.10.2.1
7 Applicability of boundary element : 18.10.6
8 Area and spacing of special confining reinforcement : 18.7.5
9 Slenderness Moments : 6.2.5
10 Shear Strength provided by concrete for column : 22.5.5
11 Design of shear for non-ductile wall : 11.5.4
12 Design of shear for ductile wall : 18.10.4.1
13 Minimum Flexural Strength of Columns : 18.7.3
14 Shear Check at Column Joint : 18.8.4.1
15 Shear Strength of Column : 18.3.3, 18.4 & 18.6.5
16 fs,perm : 10.6.4
17 fc,perm : 10.2.7.1
18 Wcr : Eq 4.2(a)
Sway Calculation (Stability Index)
For Global-X Direction
Level Load Combination
Analysis		 Storey Height (m) Gravity Load P (kN) Relative Displacements (mm) Storey Shear (kN) Stability Index (Q) Sway Condition
A B C D B x C / (A x D)
0 m to 6.2 m 13 6.2 4931.57 1.25 120.05 0.008 Non Sway


For Global-Y Direction
Level Load Combination
Analysis		 Storey Height (m) Gravity Load P (kN) Relative Displacements (mm) Storey Shear (kN) Stability Index (Q) Sway Condition
A B C D B x C / (A x D)
0 m to 6.2 m 14 6.2 4931.57 2.7 480.19 0.004 Non Sway


General Data
Column No. : C1
Level : 0 m To 6.2 m
Frame Type = Non-Ductile
Response Modification Coefficient = 3
Design Code = ACI 318M - 14
Grade Of Concrete (f'c) = C25 N/sqmm
Grade Of Steel (Main) = Fy420 N/sqmm
Grade Of Steel (Shear) = Fy420 N/sqmm
Grade Of Steel - Flexural Design = Fy420 N/sqmm
Grade Of Steel - Shear Design = Fy420 N/sqmm
Consider Ductile = No
Column B = 400 mm
Column D = 600 mm
Clear Cover, Cc = 50 mm
Clear Floor Height @ lux = 5000 mm
Clear Floor Height @ luy = 5400 mm
No Of Floors = 1
No Of Columns In Group = 1


Flexural Design (Analysis Forces)
Analysis Reference No. = 501
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
Put = 627.54 kN
Muxt = 361.04 kNm
Muyt = 300.79 kNm
Vuxt = 91.59 kN
Vuyt = -84.72 kN
Pub = 627.54 kN
Muxb = -164.06 kNm
Muyb = -266.94 kNm
Vuxb = 91.59 kN
Vuyb = -84.72 kN




Effective Length Calculation
Calculation Along Major Axis Of Column
Joint Column Stiffness Beam Sizes Beam Stiffness ψ
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 109.16 No Beam No Beam - - 1
Top 109.16 8000 x 450 x 800 No Beam 225.6 - 0.484
User Defined Effective Length Factor = 1.2

Calculation Along Minor Axis Of Column
Joint Column Stiffness
Beam Sizes
Beam Stiffness
 ψ
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 48.52 No Beam No Beam - - 1
Top 48.52 8900 x 400 x 1200 No Beam 608.36 - 0.08
User Defined Effective Length Factor = 1.2

Check For Stability Index
Along D
              Q = 0.008
0.008< 0.05, Column shall be designed as non-sway frame (Braced)
       
Along B
              Q = 0.004
0.004< 0.05, Column shall be designed as non-sway frame (Braced)

Slenderness Check
Column Is Braced Along D
Slenderness Check along D
k = 1.2
r = 173.2 mm
Kluy /r = 37.41
M1 = -164.06 kNm
M2 = 361.04 kNm
Min (40, 34 - 12 x (M1/M2)) = 39.45
37.41 < 39.45, Column not slender along D
Column Is Braced Along B
Slenderness Check along B
k = 1.2
r = 115.47 mm
Klux /r = 51.96
M1 = -266.94 kNm
M2 = 300.79 kNm
Min (40, 34 - 12 x (M1/M2)) = 40
51.96 > 40, Column slender along B
Moment Magnification:
For Non-sway frame:
       
Along B
βdns = 0.6
Ec = 23500 N/sqmm
Ig ( x 10 9) = 3.2 mm4
EI ( x 10 6) = 21708360 Nsqmm
M2min = 16.94 kNm
Cm = 0.25
Pc = 5951.47 kN
δns = 1
Mc1 = -266.94 kNm
1.4 MuyB = -373.72 kNm
Mc1 = Min (-266.94, -373.72) kNm
= -266.94 kNm
Mc2 = 300.79 kNm
1.4 MuyT = 421.1 kNm
Mc2 = Min (300.79, 421.1) kNm
= 300.79 kNm


Calculation of Design Moment
Direction Manalysis Msldr or Mc Mdesign-final
A B C
Major Axis Mux (top) 361.04 - 361.04
Major Axis Mux (bottom) -164.06 - -164.06
Minor Axis Muy (top) 300.79 300.79 300.79
Minor Axis Muy (bottom) -266.94 -266.94 -266.94

Where
A = Moments from analysis
B = Moment due to slenderness effect
C = Final design Moment = Maximum of (Manalysis, Maximum of (Msldr or Mc))
 

Final Critical Design Forces
Critical Case - Axial Load & BiAxial Bending
Pu = 627.54 kN
Mux = 361.04 kNm
Muy = 300.79 kNm


Φ Pn, Max Check
Critical Analysis Load Combination = 11
Load Combination = [1] : 1.5 (LOAD 1: LOAD CASE 1) +1.5 (LOAD 2: LOAD CASE 2)
Critical Location = Bottom Joint
Pu = 863.41 kN
Mux = -188.66 kNm
Muy = -37.88 kNm
Pt Calculated = 3.52
φ Pn, Max = 4404.72 kN
Pu < φ Pn, Max Hence, OK


Minimum Ast Calculation
Critical Analysis Load Combination = 11
Load Combination = [1] : 1.5 (LOAD 1: LOAD CASE 1) +1.5 (LOAD 2: LOAD CASE 2)
Pu-max from all Combinations = 863.41 kN
Pt required for Pu-max = 0 %
Pt min (User Defined) = 1 %
Minimum Pt required = 1 %


Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated = 3.52
Reinforcement Provided = 4-#32 + 8-#29
Load Angle = Tan-1(Muy/Mux)
= 39.8 deg
MRes = 469.92 kNm
( φ ) MCap = 475.54 kNm
Capacity Ratio = MRes/ MCap
= 0.988 < 1



Shear Calculation (Analysis Forces) Along D Along B
lu (mm) 5400 5000
Column Dimension (D , B) (mm) 600 400
Check lu > 5 x D lu > 5 x B
Shear from Moment Capacity
Critical Analysis Load Combination 17 19
Critical Load Combination [7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X) [9] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y)
Nu (kN) 634.15 627.54
Mu (kNm) 543.21 300.79
Vu3 (kN) -152.45 91.59
λ 1 1
φ 0.75 0.75
Deff (mm) 533.85 333.85
ρw (50% of As provided) 0.02 0.021
Mm (kNm) 395.28 201.47
φVc (kN) 139.22 128.37
Check Vu > φVc Vu < φVc
Link For Shear Design Required Not Required
Shear Links Design
Vs (kN) (Vu - φVc) / φVc
17.64 -
Vs Permissible (kN) 0.66 x sqrt(f'c) x b x deff
704.68 -
Vs Permissible Check Vs < Vs permissible; Hence, OK -
Check for Minimum Shear Reinforcement -
0.5 x φVc (kN) 69.61 -
Minimum Shear Reinforcement Check Vu > 0.5 x φVc; Hence, Minimum Shear reinforcement required -
Av/s minimum (sqmm/m) 333.33 -
Av/s shear (sqmm/m) 78.67 -
Av/s required (sqmm/m) max (Av/s minimum , Av/s shear)
333.33 -
Link Rebar Number 10 -
Diameter of link (mm) 9.5 -
Numbers of legs provided 3 -
Spacing of Link Provided (mm) 250 -
Av/s provided (sqmm/m ) 850.56 -
Av/s provided check Av/s required < Av/s provided; Hence, OK -


Design Of Links
Links in the zone where special confining links are not required
Normal Links
fyt = 420 N/sqmm
Along D
Av/s min-1 = 0.062 x Sqrt(f'c) x B x 1000 / fyt
= 295.24 sqmm/m
Av/s min-2 0.35 x B x 1000 / fyt
= 333.33 sqmm/m
Av/s min = Max ( Av/s min-1, Av/s min-2)
= 333.33 sqmm/m
 
Along B
Av/s min-1 = 0.062 x Sqrt(f'c) x D x 1000 / fyt
= 442.86 sqmm/m
Av/s min-2 0.35 x B x 1000 / fyt
= 500 sqmm/m
Av/s min = Max ( Av/s min-1, Av/s min-2)
= 500 sqmm/m
Maximum Longitudinal Diameter = Dia Of Rebar
Rebar Number of bundled bar, D1 = 32
Diameter of bundled bar, D1 = 32.3 mm
Bundled Rebar = No
Minimum diameter of link >= 9.5 mm
Provided Link Rebar Number = 10
Provided Diameter of link = 9.5 mm
   
Criterion for spacing of normal links
Min. Longitudinal Bar dia X 16 = 459.2 mm
48 x diameter of links = 456 mm
Min. Dimension of column = 400 mm
 
Spacing Criteria as per Vs & 0.33*Sqrt (f'c)*Aeff
Along D
Vs = 17.64 kN
0.33*Sqrt (f'c)*Aeff = 352.34 kN
Check Vs <= 0.33*Sqrt (f'c)*B*d
d/2 = 266.92 mm
600 = 600 mm
 
Provided spacing = 250 mm
 
 
Numbers of legs provided along D = 3
Av/s provided along D = 850.56 sqmm/m
Numbers of legs provided along B = 5
Av/s provided along B = 1417.6 sqmm/m
Hence, OK
Provided spacing = 250 mm
       
 
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 Rebar Number 10 --- --- 10 ---
Spacing 250 --- --- 250 ---