

Project Name  :  a 
Client Name  :  a 
Engineer Name  :  a 
Design File  :  D:\Needhi (F Drive)\Working\RCDC Manual\Euro Intermediate Column Design\Euro_Slenderness_sample file_column C7_2m to 6m.rcdx 
Analysis File  :  D:\Needhi (F Drive)\Working\RCDC Manual\Euro Intermediate Column Design\STAAD file\Euro_Slenderness_sample fie_Final for testing.std 
Analysis Last Modified  :  11/6/2020 5:04:11 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  Ωwd  =  Volumetric ratio of confining reinforcement in boundary element 
2  μθ  =  Curvature ductility factor 
3  α1  =  Multiplier of horizontal design seismic action at formation of first plastic hinge in the system 
4  αcc  =  Coefficient taking account of long term effect on the compressive strength 
5  αcw  =  Coefficient taking account of the state of the stress in the compression chord 
6  αu  =  Multiplier of horizontal seismic design action at formation of global plastic in mechanism 
7  β  =  It is a Neutral Axis angle corresponding to load angle to find out MCap 
8  εc  =  Strain in Concrete 
9  εcu2  =  Ultimate strain of unconfined Concrete 
10  εcu2,c  =  Ultimate strain of confined Concrete 
11  εm  =  Average steel strain at level considered 
12  εs  =  Strain in Reinforcement 
13  εsc  =  Compressive Strain in Reinforcement 
14  ρw  =  Shear Reinforcement Ratio provided 
15  ρw min  =  Minimum Shear Reinforcement Ratio 
16  γ_{c}  =  Partial factor for concrete (Persistent and Transient) 
17  γ_{c acc}  =  Partial factor for concrete (Accidental) 
18  γ_{s}  =  Partial factor for reinforcing steel (Persistent and Transient) 
19  γ_{s acc}  =  Partial factor for reinforcing steel (Accidental) 
20  ω  =  Reinforcement ratio 
21  ωwd  =  Technical volumetric ratio of confining reinforcement 
22  φef  =  Creep coefficient 
23  Kφ  =  Factor for taking account of creep 
24  Nεd  =  Design value of axial load in kN 
25  1/r  =  Curvature value 
26  A (Slenderness)  =  Constant 
27  A_{c}  =  Cross Sectional Area of Concretein in mm^{2} 
28  Ash  =  Volume of confining hoops in mm^{3} 
29  As est  =  Estimated area of longitudinal reinforcement for slenderness check in mm^{2} 
30  Asw/s  =  Area of Shear reinforcement required in sqmm/m 
31  Aswmax/s  =  Maximum Area of Shear Reinforcement in sqmm/m 
32  b  =  Effective Width of Column in mm 
33  bj  =  Effective joint width along Column direction considered in mm 
34  B (General Data)  =  Width / Smaller Dimension of Column in mm 
35  B (Slenderness)  =  Constant 
36  bwo  =  Thickness of web of a wall in mm 
37  C (Slenderness)  =  Constant 
38  c  =  Factor depending on the curvature distribution 
39  D  =  Depth / Larger Dimension of Column OR Diameter of Circular Column in mm 
40  d  =  Effective Depth of Column in mm 
41  Dk  =  Diameter Of core measured to the outside of circular link in mm 
42  Ec  =  Modulus of elasticity of concrete in N/sqmm 
43  Es  =  Modulus of elasticity of Reinforcement in N/sqmm 
44  e2  =  Deflection to calculate second order moment in mm 
45  e0  =  Minimum eccentricity in mm 
46  fck  =  Characteristic Cylindrical strength of Concrete N/sqmm 
47  FcPerm  =  Permissible Stress in Concrete required in N/sqmm 
48  fctm  =  Mean value of axial tensile strength of Concrete in N/sqmm 
49  Fst  =  Stress in Reinforcement in N/sqmm 
50  FstPerm  =  Permissible Stress in Reinforcement required in N/sqmm 
51  Fyd  =  Design value of Reinforcement yield strength in N/sqmm 
52  fyd, h  =  Design value Of yield strength Of the horizontal web reinforcement in N/sqmm 
53  fctd  =  Tensile Strength of Concrete in N/sqmm 
54  fywd  =  Design yield stress for shear reinforcement in N/sqmm 
55  hcr  =  Height Of critical region above base Or basement story in m 
56  hjc  =  Distance between extreme layer of column reinforcement along Column direction considered in mm 
57  hjw  =  Distance between top and bottom reinforcement of Beam along Column direction considered in mm 
58  i  =  Radius of Gyration of uncracked section in mm 
59  K_{1}  =  Crack width coefficient For high bond bars (value = 0.8) 
60  K_{2}  =  Crack width coefficient For bending (value =0.5) 
61  K_{3}  =  Crack width constant (value =3.4) 
62  K_{4}  =  Crack width constant (value =0.5) 
63  Kr  =  Correction factor depending On the axial load 
64  kw  =  Factor reflecting the prevailing failure node In structural systems With walls 
65  lo  =  Effective length Of column in mm 
66  lw  =  Length Of crosssection Of wall in mm 
67  Med  =  Design bending moment from the analysis For the seismic design situation in kNm 
68  mgeoD  =  Moment due To geometric imperfections along D in kNm 
69  mgeoB  =  Moment due To geometric imperfections along B in kNm 
70  Mux  =  Factored moment Along D (Momemt About Major Axis) in kNm 
71  Muy  =  Factored moment Along B (Momemt About Minor Axis) in kNm 
72  MCap  =  Moment capacity Of section For NA angle at design Pu in kN 
73  MRes  =  Resultant design moment at angle To local major axis in kNm 
74  M2B  =  Additional moment due To slenderness about minor axis (Along B) in kNm 
75  M2D  =  Additional moment due To slenderness about major axis (Along D) in kNm 
76  M2  =  Nominal second order moment in kNm 
77  M01  =  First order End moments in kNm 
78  M02  =  First order End moments in kNm 
79  n  =  Relative axial force in kN 
80  nbal  =  Value Of n at maximum moment Of resistance in kN 
81  Ned  =  Design axial force from the analysis For the seismic design situation in kN 
82  q  =  Behavior factor 
83  qo  =  Basic value Of the behavior factor 
84  rm  =  Moment Ratio, M01 / M02 
85  sl,max  =  Maximum Longitudinal Spacing of stirrups in mm 
86  T1  =  Fundamental period Of the building In the horizontal direction Of interest in sec 
87  Tc  =  Corner period at the upper limit Of the constant acceleration region Of the elastic Spectrum in sec 
88  V_{Rd,max}  =  Maximum Shear resistance of Section in kN 
89  Vd  =  Normalized axial force in column above joint in kN 
90  VEd x  =  Design shear force at the ULS Long B in kN 
91  VEd y  =  Design shear force at the ULS Long D in kN 
92  v'ed  =  Shear force in a wall from the analysis for the seismic design situation in kN 
93  Vur  =  Factored resultant shear force acting on the column in kN 
94  Vjhd  =  Compressive strength of Concrete in the presence of transverse tensile strain in kN 
95  Wcr  =  Surface Crack Width in mm 
96  WcrPerm  =  Permissible Crack Width required in mm 
97  Xu  =  Neural axis Depth in mm 
98  z  =  Internal lever arm in mm 
Code References:  
EN 1992  1  1  2004 Base  
ELEMENT  CLAUSE / table  
1  Max area of reinforcement  :  Cl. 9.5.2 (3)  
2  Min area of reinforcement  :  Cl. 9.5.2 (2)  
3  Minimum Eccentricity Calc  :  6.1 (4)  
4  Slenderness Moments  :  5.8.8.2  
5  Design of horizontal links  :  6.2.3  
6  Determine shear capacity without shear reinforcement  :  6.2.2  
7  Crack width calculation  :  7.3.4  
BS EN 19981:2004 (E)  
ELEMENT  CLAUSE / table  
1  Spacing of special confining reinforcement  :  Cl.5.4.3.2.2 (8)  
2  C/s area of special confining reinforcement  :  Cl.5.2.3.4 (3)  
3  Shear resistance of ductile wall  :  Cl.5.5.2.4.1  
4  Ductile wall (Bending and Shear)  :  Cl.5.4.3.4  
5  Special provisions for ductile walls  :  Cl.5.4.2.4 and Cl.5.4.2.5  
6  Design for DCM  :  Cl.5.4  
7  Design for DCH  :  Cl.5.5  

General Data  
Column No.  :  C7  
Level  :  2 m To 6 m  
Design Code  =  EN 1992  1  1  2004 Base  
Type of Frame  =  Ductile Medium  
Grade Of Concrete (f_{ck}) (Cylindrical)  =  C50/60  N/sqmm 
Partial Factor for concrete, γ_{c} (Persistent and Transient)  =  1.5  
Partial Factor for concrete, γ_{c acc} (Accidental)  =  1.2  
Grade Of Steel (f_{yk})  =  Fy485  N/sqmm 
Partial Factor for reinforcing steel, γ_{s} (Persistent and Transient)  =  1.15  
Partial Factor for reinforcing steel, γ_{s acc} (Accidental)  =  1  
Column B  =  400  mm 
Column D  =  600  mm 
Clear Cover  =  50  mm 
Clear Floor Height @ B,loB  =  8700  mm 
Clear Floor Height @ D,loD  =  8500  mm 
No Of Floors  =  1  
No Of Columns In Group  =  1  
Column Type Along D  =  Braced  
Column Type Along B  =  UnBraced  
Minimum eccentricity check  =  Simultaneously (Both Axis)  
Effective Length Along D  =  0.59  
Effective Length Along B  =  1.25 
Load Data  
Analysis Reference No.  =  46  
Load Combination  =  [2] : 4.2 (LOAD 1: LOAD CASE 1) +4.25 (LOAD 2: LOAD CASE 2) +(LOAD 3: LOAD CASE 3)  
Critical Location  =  Mid Joint  
Ned(top joint)  =  2440.57  kN  
Mux(top joint)  =  333.18  kNm  
Muy(top joint)  =  296.75  kNm  
Vux(top joint)  =  26.11  kN  
Vuy(top joint)  =  47.7  kN  
Ned(bottom joint)  =  2630.64  kN  
Mux (bottom joint)  =  48.34  kNm  
Muy (bottom joint)  =  505.58  kNm  
Vux (bottom joint)  =  26.11  kN  
Vuy(bottom joint)  =  47.7  kN 
Minimum Eccentricity,  
Since Axial Force is compressive, Min. Eccentricity check to be performed  
Check,e0  
Minimum Eccentricity Along D:  =  D / 30  
Minecc (e0D)  =  20  mm  
Mmind  =  Ned x Minimum Eccentricity  
=  52.61  kNm  
Minimum Eccentricity Along B:  =  B / 30  
Minecc (e0B)  =  13.33  mm  
=  20  MM,Since < 20  
Mminb  =  Ned x Minimum Eccentricity  
=  52.61  kNm  
Geometric imperfection, ei  
θ0  =  0.005  
αn  =  0.707  
αm  =  1  
θ1  =  0.00354  Radian 
Eccentricity ,(ei) (along both the directions)  =  8.87  mm 
MgeoD  =  23.33  kNm 
MgeoB  =  23.33  kNm 
Slenderness Check  
Ast Prv  12868  sqmm  
ω  =  Ast prv x fyd / (B x D x fcd)  
=  0.62 
Calculation of SLENDERNESS CHECK 

Calculation of Slenderness Moment 

Note:  
deff, slenderness  =  Effective Depth of the section along the direction considered. 
D'  =  Depth of the section along the direction considered. 
Calculation of Design Moment 
Direction  Manalysis  Mmin  Mgeo  Mdesign  M2  Mdesignfinal 
A  B  C  D  E  F  
Major Axis  Mux (top)  333.18  48.81  21.65  354.81    354.81 
Major Axis Mux (bottom)  48.34  52.61  23.33  71.66    71.66 
Major Axis Mux (mid)             
Minor Axis Muy (top)  296.75  48.81  21.65  318.39  812.59  724.68 
Minor Axis Muy (bottom)  505.58  52.61  23.33  528.9  812.59  935.2 
Minor Axis Muy (mid)            1024.15 
Where  
A  =  Moments directly from analysis 
B  =  Moments due to minimum eccentricity 
C  =  Moments due to geometrical imperfection 
D  =  Max of (Manalysis+MGeo) , Mmin 
E  =  Moment due to slenderness effect 
F Top.Bottom  =  Mdesign+ M2 /2 
F Mid  =  Moe+M2 
Final Critical Design Forces  
Critical Case  Axial Load & BiAxial Bending  
Pu  =  2630.64  kN 
Mux  =  0  kNm 
Muy  =  1024.15  kNm 
Resultant Moment (Combined Action)  
Moment Capacity Check  
Pt Calculated  =  5.36  
Reinforcement Provided  =  16T32  
Load Angle  =  Tan^{1}(Muy/Mux)  
=  90  deg  
MRes  =  1024.15  kNm 
MCap  =  1043.49  kNm 
Capacity Ratio  =  MRes/ MCap  
=  0.98 < 1  
Biaxial Bending Check  
λD/λB  =  0.3074  
λB/λD  =  3.2527  
eD(top)  =  134.8769  mm 
eD(bot)  =  27.2416  mm 
eB(top)  =  275.4766  mm 
eB(bot)  =  355.5013  mm 
(eD top/D)/(eB top/B)  =  0.33  mm 
(eB top/B)/(eD top/D)  =  3.06  mm 
(eD bot/D)/(eB bot/B)  =  0.05  mm 
(eB bot/B)/(eD bot/D)  =  19.57  mm 
Check for Biaxial bending  Consider Biaxial  
Check For Minimum Vertical Reinforcement  
Minimum pt1(User Defined)  =  0.2  
As,min1(as per user defined pt1)  =  Minimum pt1 x Ac / 100  
=  480  sqmm  
Load Combination  =  [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2)  
Ned  =  619.06  kN 
fyd  =  421.74  N/sqmm 
Minimum pt2 (as per Ned)  =  0.1 x Ned / ( fyd x Ac)  
=  0.0612  %  
As,min2 (as per Ned)  =  Minimum pt2 x Ac / 100  
=  146.79  sqmm  
As,min  =  Max (As,min1 , As,min2)  
=  480  sqmm  
As provided  =  12867.96  sqmm 
As provided  >  As,min Hence, OK  
Design Of Shear  
ϒ_{RD}  =  1.1  
Along D  
Shear from Moment Capacity:  
Luy  =  8500  mm 
N_{Ed} Top  =  2630.64  kN 
M_{RC}t  =  1555.45  kNm 
N_{Ed} Bottom  =  2440.57  kN 
M_{RC}b  =  1550.5  kNm 
Vuy1  =  401.95  kN 
Critical Load Combination  =  [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2)  
Design shear force, Vuy2  =  14.55  kN 
N_{Ed}  =  573.8  kN 
V_{uy}  =  Maximum(Vuy, Vuy1)  
=  401.95  kN  
Design shear stress ,V_{Ed}  =  1.8818  N/mm^{2} 
Calculation for Concrete Strut Capacity V_{Rdmax}  
lever arm, z  =  534  mm 
v1  =  0.48  
v_{Rd,max cot θ = 2.5}  =  4.97  N/mm^{2} 
v_{Rd,max cot θ = 1}  =  7.2  N/mm^{2} 
V_{Rd,max}  =  1060.58  kN 
Check  V_{Rd,max} > V_{uy} Hence, OK  
VRD,c  =  268.39  kN 
As tension(50%)  =  6434  sqmm 
CRdc  =  0.18/γc  
=  0.12  
deff  =  534  mm 
k  =  MIN(1 + SQRT(200 / deff),2)  
=  1.612  
ρ1  =  Asmain / (b x deff)  
=  0.02  %  
k1  0.15  
σcp  =  NEd / (B x D)  
=  2.3908  N/mm^{2}  
Shear check  Shear Reinforcment Required  
Since VRD,C < Vuy  
Calculation for spacing of shear reinforcement  
θ  =  21.8  degree 
no of legs for stirrups  =  4  legged 
Shear reinforcement bar dia .∅link  =  8  mm 
Area of Shear reinforcement ,Asw  =  862.15  mm^{2} 
Design yeild stress for shear reinforcement,fywd  =  388  N/mm^{2} 
Spacing of Reinforcement required,s  =  233  mm 
Provided Spacing ,sprov.  =  150  mm 
Area of Shear reinforcement provided ,Asw,prov  1340.41  mm^{2}  
Check maximum area for Shear reinforcement provided.  
Maximum area of shear reinforcement, Asw.max  =  8247.42  sqmm 
Check minimum ratio & maximum longitudinal spacing for Shear reinforcement provided.  
Shear Reinforcement Ratio  =  0.0034  
Minimum Shear Reinforcement Ratio ,ρw  =  0.0012  
Hence safe for minimum ratio  
Along B  
Shear from Moment Capacity:  
Lux  =  8500  mm 
N_{Ed} Top  =  2630.64  kN 
M_{RC}t  =  1043.49  kNm 
N_{Ed} Bottom  =  2440.57  kN 
M_{RC}b  =  1034.06  kNm 
Vux1  =  268.86  kN 
Critical Load Combination  =  [1] : (LOAD 1: LOAD CASE 1) +(LOAD 2: LOAD CASE 2)  
Design shear force, Vux1  =  3.59  kN 
N_{Ed}  =  573.8  kN 
V_{ux}  =  Maximum(Vux, Vux1)  
=  268.86  kN  
Design shear stress ,v_{Ed}  =  1.3108  N/mm^{2} 
Calculation for Concrete Strut Capacity V_{Rd,max}  
lever arm, z  =  334  mm 
v1  =  0.48  
v_{Rd,max cot θ = 2.5}  =  4.97  N/mm^{2} 
v_{Rd,max cot θ = 1}  =  7.2  N/mm^{2} 
V_{Rd,max}  =  995.04  kN 
Check  V_{Rd,max} > V_{ux} Hence, OK  
VRD,c  =  269.86  kN 
As tension(50%)  =  6434  sqmm 
CRdc  =  0.18/γc  
=  0.12  
beff  =  334  mm 
k  =  MIN((1 + SQRT(200 / beff)),2)  
=  1.7738  
ρ1  =  Asmain / (d x beff)  
=  0.02  %  
k1  =  0.15  
σcp  =  NEd / (B x D)  
=  2.3908  N/mm^{2}  
Shear check  No Shear Reinforcement Required  
Since VRD,C > Vux 
Design Of Links  
Links in the zone where special confining links are not required or End Zone  
Normal Links  
Diameter of link Provided  =  8  mm 
Check for minimum diameter of link  
Main Reinforcement (Bundled / Single)  =  Single  
Number of Rebars in Bundled  =  1  
Maximum diameter of Vertical Reinforcement  =  32  mm 
Effective diameter of Vertical Reinforcement  =  32  mm 
Minimum dia1 (6mm)  =  6  mm 
Minimum dia2  =  Effective diameter / 4  
=  8  mm  
Minimum dia  =  Max (Minimum dia1, Minimum dia2)  
=  8  mm  
Diameter of link Provided  >  Minimum dia Hence, OK  
Criterion for spacing of normal links  
Min. Longitudinal Bar dia X 20  =  640  mm 
Min. dimension of column  =  400  mm 
Max. Permissible  =  400  mm 
Max. Permissible (User Input)  =  300  mm 
Provided spacing  =  150  mm 
Special confining reinforcement as per BS EN 19981:2004  
Links at End Zone  
Criterion for spacing of End Zone links  
0.6 x Min. Longitudinal Bar dia X 20  =  384  mm 
0.6 x Min. dimension of column  =  240  mm 
0.6 x Max. Permissible  =  240  mm 
Max. Permissible (User Input)  =  300  mm 
Provided spacing, s  =  150  mm 
Volume of confining hoops, Ash  
diameter of link  10  mm  
dbl  =  32  mm 
ωwd  =  (30 x μ∅ x Vd x εsyd x (bc/bo)  0.035) / α  
=  0.08  
α=αn x αs  =  0.6321  
αn  =  0.9777  
αs  =  0.6466  
bc  =  400  mm 
hc  =  600  mm 
bo  =  310  mm 
ho=Do  510  
bi  =  150  mm 
μφ  =  1.1  
Ned  =  573.8003  
Vd  =  Ned /(Ac x fcd)  
=  0.0717  
εsyd  =  0.0025  
Volume Of confining link per m  =  1517.53  sqmm/m 
Zone for special confining links  criterion  
Max. Size of column, D  =  600  mm 
Clear height/6  =  1416.67  mm 
Minimum value  =  450  mm 
Hence length of confining zone  =  1450  mm 
Table For Links 
Required  Provided  
Normal Design  Shear Design  Ductile/End Zone  Normal Zone  Ductile/End Zone  
Link Dia.  8    10  8  10 
Spacing  150    150  150  150 