

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$\RPSCSOR4FEEDUPDATEANDEARLYDETAILEDENGINEERING\11.0Engineering\11.11 Structural\4.0 Calculations\Substation806\STAAD\Substation806.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  =  Firstorder 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  =  Crosssectional 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 crosssectional area within a joint In a plane parallel To plane Of reinforcement generating shear In the joint in 'sqmm' 
11  As  =  Area Of nonprestressed 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  =  Crosssectional 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 centertocenter of the joints in the frame in 'mm' 
30  lg  =  Moment of inertia of gross concrete section about centroidal axis neglecting reinforcement in 'mm^{4}' 
31  lw  =  Length of entire wall in 'mm' 
32  lux  =  Unsupported length for compression member along D in 'mm' 
33  luy  =  Unsupported 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 nonductile 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 GlobalX 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 GlobalY 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(DOW)) +1.9 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(EZN))  
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  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 (UnBraced)  
Along B  
Q  =  0.007  
0.007< 0.05, Column shall be designed as nonsway frame (Braced) 
Slenderness Check  
Column Is UnBraced 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  Mdesignfinal 
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(DOW)) +1.9 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(EZN))  
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(DOW)) +1.9 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +1.1 (LOAD 4: SEISMIC LOAD(EZN))  
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(DOW)) +1.9 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +3 (LOAD 1: SEISMIC LOAD(EXP))  
Vuy2  =  283.98  kN  
Critical Analysis Load Combination  :  323  
Critical Load Combination  =  [58] : 0.99 (LOAD 5: DEAD LOADS(DOW)) +0.99 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 4: SEISMIC LOAD(EZN))  
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(DOW)) +1.9 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 9: FLOOR LIVE LOADS(LF)) +3 (LOAD 4: SEISMIC LOAD(EZN))  
Vux2  =  448.61  kN  
Critical Analysis Load Combination  :  320  
Critical Load Combination  =  [55] : 0.99 (LOAD 5: DEAD LOADS(DOW)) +0.99 (LOAD 6: DEAD LOADS(DUT)) +1.1 (LOAD 1: SEISMIC LOAD(EXP))  
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 