COLUMN DESIGN CALCULATIONS
Project Name : 1
Client Name : Qatar Gas
Engineer Name : GG
Design File : D:\Scube\000 RCDC 2010\10.0.0\Queries\Worley Parsons\Validation sheets\Column.rcdx
Analysis File : \\inairwpdfs01v\Shares\Projects$\RPSC-SOR-4-FEED-UPDATE-AND-EARLY-DETAILED-ENGINEERING\11.0-Engineering\11.11 Structural\4.0 Calculations\Substation-806\STAAD\Substation-806.std
Analysis Last Modified : 2/18/2020 2:12:31 PM

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 10.10.5.2)
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 bc = Cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area Ash in 'mm'
15 c = Distance from extreme compression fiber to neutral axis in 'mm'
16 Cc = Clear cover to longitudinal reinforcement in 'mm'
17 Cm = Factor relating actual moment diagram to an equivalent uniform moment diagram
18 D = Depth / diameter of column in 'mm'
19 d = Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in 'mm'
20 d' = Distance from extreme compression fiber to centroid of longitudinal compression reinforcement,'mm'
21 Ec = Modulus of elasticity of concrete in 'N/sqmm'
22 EI = Flexural stiffness of compression member in 'Nsqmm'
23 f'c = Specified compressive strength of concrete cylinder in 'N/sqmm'
24 fy = Specified yield strength of reinforcement in 'N/sqmm'
25 fyt = Specified yield strength fy of transverse reinforcement in 'N/sqmm'
26 hw = Height of entire wall from base to top of wall segment considered in 'mm'
27 Icr = Moment of Inertia of concrete crack section
28 k = Effective length factor for compression member
29 lc = Length of compression member in a frame, measured center-to-center of the joints in the frame in 'mm'
30 lg = Moment of inertia of gross concrete section about centroidal axis neglecting reinforcement in 'mm4'
31 lw = Length of entire wall in 'mm'
32 lux = Un-supported length for compression member along D in 'mm'
33 luy = Un-supported length for compression member along B in 'mm'
34 MCap = Moment capacity of section for a given NA angle at design Pu in 'kNm '
35 Mcr = Cracking Moment
36 MRes = Resultant design moment at a given load angle to local major axis in 'kNm '
37 Mc = Factored moment amplified for the effects of member curvature used for design of compression member in 'kNm'
38 Mm = Factored moment modified to account for effect of axial compression in 'kNm'
39 Mux = Factored moment acting on a section along D in 'kNm' from Analysis (Momemt About Major Axis)
40 Muy = Factored moment acting on a section along B in 'kNm' from Analysis (Momemt About Minor Axis)
41 M1 = Smaller factored end moment on a compression member in 'kNm'
42 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'
43 M1s = Factored end moment on compression member at the end at which M1 acts, due to loads that cause appreciable sidesway in 'kNm'
44 M1sldr = Smaller factored end moment on a compression member due to slenderness effect in 'kNm'
45 M2 = Larger factored end moment on compression member in 'kNm'
46 M2min = Minimum value of moment M2 as per minimum eccentricity of column
47 M2ns = Factored end moment on compression member at the end at which M2 acts, due to loads that cause no appreciable sidesway in 'kNm'
48 M2s = Factored end moment on compression member at the end at which M2 acts, due to loads that cause appreciable sidesway in 'kNm'
49 M2sldr = Largest factored end moment on a compression member due to slenderness effect in 'kNm'
50 Mnb = Flexure Capacity for Beam
51 Mnc = Flexure Capacity for Column
52 Mnty = Nominal Flexure strength of column at top along depth in 'kNm'
53 Mnby = Nominal Flexure strength of column at bottom along depth in 'kNm'
54 Mntx = Nominal Flexure strength of column at top along width in 'kNm'
55 Mnbx = Nominal Flexure strength of column at bottom along width in 'kNm'
56 Nu = Factored axial force normal to cross section occurring simultaneously with Vu in 'kN'
57 Pc = Critical buckling load in 'kN'
58 pt = Ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement
59 Pω = Ratio of As to B x d
60 Q = Stability index for storey
61 r = Radius of gyration of cross section of a compression member in 'mm'
62 Vc = Nominal shear strength provided by concrete in 'kN'
63 Vj = Shear Force acting at the joint in 'kN'
64 Vn = Nominal shear strength in 'kN'
65 Vn' = Nominal shear strength at joint in 'kN'
66 Vus = Factored horizontal shear in a storey in 'kN'
67 Vux = Factored shear at section along B in 'kN' (From Analysis)
68 Vux1 = Shear induced due to column flexural capacity along width,'kN'
69 Vux2 = Shear due to enhanced earthquake factor along width, 'kN'
70 Vuy = Factored shear at section along D in 'kN' (From Analysis)
71 Vuy1 = Shear induced due to column flexural capacity along depth, 'kN'
72 Vuy2 = Shear due to enhanced earthquake factor along depth, 'kN'
73 y = Neutral axis depth.
74 β = It is a Neutral Axis angle corresponding to load angle to find out MCap


 
 

Code References:
ACI 318M - 2014
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)
-2m to 0.15m 312 2.15 50583.7 1.45 2122.21 0.016 Non Sway
0.15m to 1.377m 313 1.23 1605.02 0.47 264.61 0.002 Non Sway
1.377m to 2.73m 312 1.35 48182.07 3.47 2064.92 0.06 Sway
2.73m to 4.48m 313 1.75 911.26 2.96 211.23 0.007 Non Sway
4.48m to 5.63m 312 1.15 28412.91 1.3 1739.9 0.018 Non Sway
5.63m to 6.18m 313 0.55 271.87 3.35 61.19 0.027 Non Sway
6.18m to 6.48m 313 0.3 5396.22 2.4 554.77 0.078 Sway
6.48m to 7.88m 313 1.4 480.83 4.3 206.09 0.007 Non Sway
7.88m to 9.08m 313 1.2 10827.37 0.89 1130.25 0.007 Non Sway
9.08m to 9.58m 312 0.5 17245.18 0.96 1160.81 0.028 Non Sway
9.58m to 12.43m 313 2.85 1472.98 4.78 171.32 0.014 Non Sway
12.43m to 13.28m 312 0.85 5934.67 0.38 586.5 0.005 Non Sway
13.28m to 15.88m 312 2.6 6298.83 4.39 599.45 0.018 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)
-2m to 0.15m 315 2.15 50583.7 2.64 2734.86 0.023 Non Sway
0.15m to 1.377m 315 1.23 1559.94 0.35 115.35 0.004 Non Sway
1.377m to 2.73m 314 1.35 47977.8 6.88 2700.18 0.09 Sway
2.73m to 4.48m 315 1.75 874.15 0.61 123.04 0.002 Non Sway
4.48m to 5.63m 314 1.15 28268.69 10.82 2177.46 0.122 Sway
5.63m to 6.18m 315 0.55 281.73 7.11 22.47 0.162 Sway
6.18m to 6.48m 314 0.3 5705.93 8.06 680.46 0.225 Sway
6.48m to 7.88m 315 1.4 468.69 3.99 164.29 0.008 Non Sway
7.88m to 9.08m 314 1.2 10504.2 14.56 968.45 0.132 Sway
9.08m to 9.58m 314 0.5 17245.18 4.49 1420.53 0.109 Sway
9.58m to 12.43m 314 2.85 1415.93 7.86 243.49 0.016 Non Sway
12.43m to 13.28m 314 0.85 5909.96 2.03 680.77 0.021 Non Sway
13.28m to 15.88m 314 2.6 6298.83 3.95 653.09 0.015 Non Sway


General Data
Column No. : C4
Level : 7.88m To 9.08m
Frame Type = Lateral
Response Modification Coefficient = 3
Design Code = ACI 318M - 2014
Grade Of Concrete (f'c) = C40 N/sqmm
Grade Of Steel (fy) = Fy500 N/sqmm
Consider Ductile = Yes
Type of Frame = Intermediate
Column B = 500 mm
Column D = 600 mm
Clear Cover, Cc = 50 mm
Clear Floor Height @ lux = 2650 mm
Clear Floor Height @ luy = 2250 mm
No Of Floors = 1
No Of Columns In Group = 1


Flexural Design (Analysis Forces)
Analysis Reference No. = 98
Critical Analysis Load Combination : 315
Load Combination = [50] : 1.9 (LOAD 5: DEAD LOADS(D-OW)) +1.9 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(E-ZN))
Critical Location = Top Joint
Put = 1833.12 kN
Muxt = -719.17 kNm
Muyt = -16.7 kNm
Vuxt = -5.26 kN
Vuyt = 208.39 kN
Pub = 1879.47 kN
Muxb = -0.43 kNm
Muyb = 1.44 kNm
Vuxb = -5.26 kN
Vuyb = 208.39 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
Nm mm mm Nm Nm
Bottom 948.68 No Beam No Beam - - 1
Top 948.68 No Beam 7965 x 500 x 1200 - 1143.42 2.821
Sway Condition (as per Stability Index) = Sway
Effective Length Factor along Major Axis = 2.24

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
Nm mm mm Nm Nm
Bottom 658.81 No Beam No Beam - - 5.913
Top 658.81 No Beam 6000 x 300 x 800 - 269.85 8.301
Sway Condition (as per Stability Index) = Non Sway
Effective Length Factor along Minor axis = 1

Check For Stability Index
Along D
              Q = 0.132
0.132> 0.05, Column shall be designed as sway frame (Un-Braced)
       
Along B
              Q = 0.007
0.007< 0.05, Column shall be designed as non-sway frame (Braced)

Slenderness Check
Column Is Un-Braced Along D
Slenderness Check along D
K = 2.24
r = 173.2 mm
Kluy /r = 29.1
Permissible slenderness ratio = 22
29.1 > 22, Column slender along D
Column Is Braced Along B
Slenderness Check along B
K = 1
r = 144.34 mm
Klux /r = 18.36
M1 = 1.44 kNm
M2 = -16.7 kNm
Min (40, 34 - 12 x (M1/M2)) = 35.04
18.36 < 35.04, Column not slender along B
Moment Magnification:
For Sway Frame:
Along D
δns x M1s = -598.36 kNm
δns x M2s = -46 kNm
M1ns = -199.55 kNm
M2ns = 39.52 kNm
δns = 1.15
M1sldr = -797.91 kNm
1.4 MuxT = -1006.84 kNm
M1sldr = Min (-797.91, -1006.84) kNm
= -797.91 kNm
M2sldr = -0.6 kNm
1.4 MuxB = -0.6 kNm
M2sldr = Min (-0.6, -0.6) kNm
= -0.6 kNm


Calculation of Design Moment
Direction Manalysis Msldr or Mc Mdesign-final
A B C
Major Axis Mux (top) -719.17 -797.91 -797.91
Major Axis Mux (bottom) -0.43 -0.6 -0.6
Minor Axis Muy (top) -16.7 - -16.7
Minor Axis Muy (bottom) 1.44 - 1.44

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 = 1833.12 kN
Mux = -797.91 kNm
Muy = -16.7 kNm


Φ Pn, Max Check
Critical Analysis Load Combination = 315
Load Combination = [50] : 1.9 (LOAD 5: DEAD LOADS(D-OW)) +1.9 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(E-ZN))
Critical Location = Bottom Joint kN
Pu = 1879.47 kN
Mux = -0.43 kNm
Muy = 1.44 kNm
Pt Calculated = 1.63
φ Pn, Max = 6489.44 kN
Pu < φ Pn, Max Hence, OK


Minimum Ast Calculation
Critical Analysis Load Combination = 315
Load Combination = [50] : 1.9 (LOAD 5: DEAD LOADS(D-OW)) +1.9 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(E-ZN))
Pu = 1879.47 kN
φ Pn = 6489.44 kN
Pt min for φ Pn = 0.5 %
Pt min (User Defined) = 1 %
Final Pt = 1 %


Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated = 1.63
Reinforcement Provided = 4-#25 + 10-#19
Load Angle = Tan-1(Muy/Mux)
= 1.2 deg
MRes = 798.09 kNm
( φ ) MCap = 838.85 kNm
Capacity Ratio = MRes/ MCap
= 0.951 < 1

Shear Design (Analysis Forces)
Design for shear along D
Shear from Moment Capacity:
Luy = 2250 mm
Pu Top = 1879.47 kN
Mnty = 853.24 kNm
Pu Bottom = 1833.12 kN
Mnby = 848.68 kNm
Vuy1 = 756.41 kN
Shear from Load combinations with Enhanced Eq factor:
Load Combination = 1.9 (LOAD 5: DEAD LOADS(D-OW)) +1.9 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +3 (LOAD 1: SEISMIC LOAD(E-XP))
Vuy2 = 283.98 kN
Critical Analysis Load Combination : 323
Critical Load Combination = [58] : 0.99 (LOAD 5: DEAD LOADS(D-OW)) +0.99 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 4: SEISMIC LOAD(E-ZN))
Nu = 995.34 kN
Muy = 620.77 kNm
Vuy3 = 174.66 kN
Design Shear, Vuy = Maximum(Vuy1, Vuy2, Vuy3)
= 756.41 kN
λ = 1
φ = 0.75
deff = 537.3 mm
ρw (50% of As provided) = 0.018
Mm = 389.02 kNm
φVcy = 269.05 kN
Vuy > φVcy     Hence, Shear links required
       
Design of Shear Links Along D
Vsy = (Vuy - φVcy) / φ
= 649.81 kN
Vsy Permissible = 0.66 x sqrt(f'c) x b x deff
= 1121.4 kN
Vsy < Vsy permissible     Hence OK
Check for Minimum Shear Reinforcement
0.5 x φVcy = 134.53 kN
Vuy > 0.5 x φVcy     Hence , Minimum Shear reinforcement required
Av/s minimum = 466.81 sqmm/m
Av/s shear = 2879.5 sqmm/m
Av/s required = max (Av/s minimum , Av/s shear)
= 2879.5 sqmm/m
Link Rebar Number = 13
Diameter of link = 12.7
Numbers of legs provided = 4
Spacing of Link Provided = 175 mm
Av/s provided = 2895.54 sqmm/m
Av/s required < Av/s provided     Hence OK
 
Design for shear along B
Shear from Moment Capacity:
Lux = 2650 mm
Pu Top = 1879.47 kN
Mntx = 704.03 kNm
Pu Bottom = 1833.12 kN
Mnbx = 702.93 kNm
Vux1 = 530.93 kN
Shear from Load combinations with Enhanced Eq factor:
Load Combination = 1.9 (LOAD 5: DEAD LOADS(D-OW)) +1.9 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +3 (LOAD 4: SEISMIC LOAD(E-ZN))
Vux2 = 448.61 kN
Critical Analysis Load Combination : 320
Critical Load Combination = [55] : 0.99 (LOAD 5: DEAD LOADS(D-OW)) +0.99 (LOAD 6: DEAD LOADS(D-UT)) +1.1 (LOAD 1: SEISMIC LOAD(E-XP))
Nu = 765.22 kN
Mux = 207.79 kNm
Vux3 = -108.02 kN
Design Shear, Vux = Maximum(Vux1, Vux2, Vux3)
= 530.93 kN
λ = 1
φ = 0.75
deff = 437.3 mm
ρw (50% of As provided) = 0.019
Mm = 58.31 kNm
φVcx = 447.48 kN
Vux > φVcx     Hence, Shear links required
       
Design of Shear Links Along B
Vsx = (Vux - φVcx) / φ
= 111.26 kN
Vsx Permissible = 0.66 x sqrt (f'c) x d x beff
= 1095.23 kN
Vsx < Vsx permissible     Hence OK
Check for Minimum Shear Reinforcement
0.5 x φVcx = 223.74 kN
Vux > 0.5 x φVcx     Hence , Minimum Shear reinforcement required
Av/s minimum = 560.17 sqmm/m
Av/s shear = 605.79 sqmm/m
Av/s required = max (Av/s minimum , Av/s shear)
= 605.79 sqmm/m
Link Rebar Number = 13
Diameter of link = 12.7
Numbers of legs provided = 5
Spacing of Link Provided = 175 mm
Av/s provided = 3619.43 sqmm/m
Av/s required < Av/s provided     Hence OK


Design Of Links
Links in the zone where special confining links are not required
Normal Links
Link Rebar Number = 13
Diameter of link = 12.7
  > Max. longitudinal bar dia / 4
  = 6.4 mm
Criterion for spacing of normal links
Min. Longitudinal Bar dia X 16 = 305.6 mm
48 x diameter of links = 609.6 mm
Provided spacing = 175 mm
       
Criterion for spacing of Ductile links:
Min. Longitudinal Bar dia x 8 = 152.8 mm
24 x diameter of links = 304.8 mm
B / 2 = 250 mm
Spacing = 300 mm
Provided Spacing = 150 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 13 --- 13 13 13
Spacing 175 --- 150 175 150