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C13W25-L02-L07 STY
General column design by PROKON . (GenCol Ver W2.6.11 - 24 Apr 2014)
Design code : CP65 - 1999
Input tables
General design parameters:
CodeX/Radius or
Bar dia. (mm)Y (mm)
Angle (°)
+ 10.000
230.000
10.000 10.000
1955.000
-10.000 10.000
-230.000-10.000 -10.000
-1955.000
- 125.0 137.5
c 75.000
+ 47.500 47.500
b 25
+ 202.500 47.500
b 25
+ 202.500 1927.500
b 25
+ 47.500 1927.500
b 25
+ 47.500 218.409
b 25.000
+ 202.500 218.409
b 25.000
+ 47.500 389.318
b 25.000
+ 202.500 389.318
b 25.000
+ 47.500 560.227
b 25.000
+ 202.500 560.227
b 25.000
+ 47.500 731.136
b 25.000
+ 202.500 731.136
b 25.000
+ 47.500 902.045
b 25.000
+ 202.500 902.045
b 25.000
+ 47.500 1072.955
b 25.000+ 202.500 1072.955
b 25.000
Sheet Job Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016
8/16/2019 W25-L02-L07 STY
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+ 47.500 1243.864
b 25.000
+ 202.500 1243.864
b 25.000
+ 47.500 1414.773
b 25.000
+ 202.500 1414.773
b 25.000
+ 47.500 1585.682
b 25.000
+ 202.500 1585.682
b 25.000
+ 47.500 1756.591
b 25.000
+ 202.500 1756.591
b 25.000+ 125.000 47.500
b 25.000
+ 125.000 1927.500
b 25.000
Loadcase Designation
Ultimate limit state design loads
P (kN) Mx top (kNm) My top (kNm) Mx bot (kNm) My bot (kNm)
1 Axial 12500
2 Axial+Mxx 12500 350
3 Axial+Myy 12500 1004 Axial+Mxx+Myy 12500 350 100
5 Axial+Mecc 12500 850 850
Design loads:
0
2000
1500
1000
500
0
-500
X X
Y
Y
CP65 - 1999
General design parameters:Given: Lo = 5.000 m fcu = 50 MPa fy = 460 MPa Ac = 463116 mm²
Assumptions:
(1) The general conditions of clause 3.8.1 are applicable. (2) The specified design axial loads include the self-weight of the column. (3) The design axial loads are taken constant over the height of the column.
Design approach:The column is designed using an iterative procedure: (1) An area of reinforcement is chosen. (2) The column design charts are constructed. (3) The corresponding slenderness moments are calculated. (4) The design axis and design ultimate moment are determined .
(5) The design axial force and moment capacity is checked on the relevant design chart. (6) The safety factor is calculated for this load case. (7) The procedure is repeated for each load case.
Sheet Job Number
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Client
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Software Consultants (Pty) Ltd
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KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016
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(8) The critical load case is identified as the case yielding the lowest safety factor about the design axis
Through inspection: Load case 5 (Axial+Mecc) is critical.
Check column slenderness:End fixity and bracing for bending about the Design axis: At the top end: Condition 2 (partially fixed). At the bottom end: Condition 2 (partially fixed). The column is braced.
Effective length factor ß = 1.00 Table 3.21
Effective column height:
=le ß Lo.
= 1 5×
= 5.000 m
Column slenderness about weakest axis:
=max_s140lle
h
=5
.25311
= 19.754
Where h is an equivalent column depth derived from the radius of gyration*square root of 12
Minimum Moments for Design:Check for mininum eccentricity: 3.8.2.4 Check that the eccentricity exceeds the minimum in the plane of bending: Use emin = 20mm
= M min emin N .
= .02 12500×
= 250.000 kNm
Check if the column is slender: 3.8.1.3 le/h = 19.8 > 15∴ The column is slender.
Sheet Job Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016
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Initial moments:
The initial end moments about the X-X axis:
M1 = Smaller initial end moment = 0.0 kNm
M2 = Larger initial end moment = 850.0 kNm
The initial moment near mid-height of the column : 3.8.3.2
= M i 0.4 M 1 0.6 M 2. .- +
= 0.4 0 0.6 850× ×- +
= 510.000 kNm
= M i2 0.4 M 2.
= 0.4 850×
= 340.000 kNm
∴ Mi ≥ 0.4M2 = 510.0 kNm
The initial end moments about the Y-Y axis:
M1 = Smaller initial end moment = 0.0 kNm
M2 = Larger initial end moment = 850.0 kNm
The initial moment near mid-height of the column : 3.8.3.2
= M i 0.4 M 1 0.6 M 2. .- +
= 0.4 0 0.6 850× ×- +
= 510.000 kNm
= M i2 0.4 M 2.
= 0.4 850×
= 340.000 kNm
∴ Mi ≥ 0.4M2 = 510.0 kNm
Deflection induced moments: 3.8.3.1Design ultimate capacity of section under axial load only:
= N uz 0.45 f cu Ac 0.87 f y Asc. . . . +
= 0.45 50 463.12 0.87 460 12.763× × × ×+
= 15.53×103
kN
Maximum allowable stress and strain:
Allowable compression stress in steel
Sheet Job Number
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ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
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=sc 0.87 f y.
= 0.87 460×
= 400.200 MPa
Allowable tensile stress in steel
=st 0.87 f y.
= 0.87 460×
= 400.200 MPa
Allowable tensile strain in steel
=e y f st
E s
=400.2
205000
= 0.0020
Allowable compressive strain in concrete
ec = 0.0035
For bending about the weakest axis: Weakest axis lies at an angle of -90.00° to the X-X axis Overall dimension perpendicular to weakest axis h = 253mm
=K N uz N
N uz N bal
-
-
=1553×10
41250×10
4
1553×104
4856×103
-
-
= 0.2839
=a1
2000max_sl
2.
=1
200019.754
2×
= 0.1951
Where max_sl is the maximum slenderness ratio of the column as an equivalent rectangular column.
Therefore:
Sheet Job Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
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KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
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= M add N ß a K h. . .
= 12500 .19511 .28373 .25311× × ×
= 175.148 kNm
∴ Maddx = Madd*cos(-90.00°) = 0.0 kNm ∴ Maddy = Madd*sin(-90.00°) = 173.0 kNm
Design ultimate load and moment:Design axial load: Pu = 12500.0 kN
Moments as a result of imperfections added about Design axis 5.8.9 2)
For bending about the X-X axis, the maximum design moment is the greatest of: 3.8.3.2
(a) 3.8.3.2
= M top M t M add
2 +
= 8500
2+
= 850.000 kNm
(b) 3.8.3.2
= M mid M i M add +
= 510 0+
= 510.000 kNm
(c) 3.8.3.2
= M bot M b M add
2+
= 0 02
+
= 0.0000×100
kNm
(d) 3.8.3.2
= M eminx N .
= .02 12500×
= 250.000 kNm
Thus 3.8.3.2
Sheet Job Number
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Client
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Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
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M = 850.0 kNm
Mxtop=850.0 kNm
Mxbot=0.0 kNm
Moments about X-X axis( kNm)
Initial Additional Design
Mx=850.0 kNmMxmin=250.0 kNm
+ =
Moments as a result of imperfections added about Design axis 5.8.9 2)
For bending about the Y-Y axis, the maximum design moment is the greatest of: 3.8.3.2(a) 3.8.3.2
= M top M t M add
2+
= 850172.99
2+
= 936.495 kNm
(b) 3.8.3.2
= M mid M i M add +
= 510 172.99+
= 682.990 kNm
(c) 3.8.3.2
= M bot M b M add
2 +
= 0172.99
2 +
= 86.495 kNm
(d) 3.8.3.2
Sheet Job Number
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Client
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ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016
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= M eminy N .
= .02 12500×
= 250.000 kNm
Thus 3.8.3.2
M = 936.5 kNm
Myadd/2=86.5 kNm
Myadd/2=86.5 kNm
M y a d d = - 1 7 3 . 0
k N m
Mytop=850.0 kNm
Mybot=0.0 kNm
Moments about Y-Y axis( kNm)
Initial Additional Design
My=936.5 kNm
Mymin=156.2 kNm
+ =
Design of column section for ULS:
The column is checked for applied moment about the design axis. Through inspection: the critical section lies at the top end of the column.
The design axis for the critical load case 5 lies at an angle of 47.77° to the X-axis The safety factor for the critical load case 5 is 1.02
Sheet Job Number
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Client
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ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
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For bending about the design axis:
Interaction Diagram
M o m e n t m a x = 3 3 3 5 k N m @ 3
9 0 1
k N
-4000-3000-2000-1000
10002000300040005000600070008000900010E311E312E313E314E3
- 3 5 0 0
- 3 0 0 0
- 2 5 0 0
- 2 0 0 0
- 1 5 0 0
- 1 0 0 0
- 5 0 0
0 . 0
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
3 0 0 0
3 5 0 0
A x i a l l o a d ( k N )
Bending moment (kNm)
12500 kN
1 2 6 5 k N m
Moment distribution along the height of the column for bending about the design axis:
The final design moments were calculated as the vector sum of the X- and Y- momentsof the critical load case. This also determined the design axis direction
At the top, Mx = 1264.7 kNm Near mid-height, Mx = 852.4 kNm At the bottom, Mx = 156.2 kNm
Stresses at the top end of the column for the critical load case 5
Sheet Job Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016
8/16/2019 W25-L02-L07 STY
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Load case Axis N (kN) M1 (kNm) M2 (kNm) Mi (kNm) Madd (kNm) Design M (kNm) M' (kNm)Safetyfactor
Load case 2 Axial+Mxx
Load case 3 Axial+Myy
Load case 4 Axial+Mxx+M
Load case 5 Axial+Mecc
X-XY-Y 12500.0
0.00.0
350.00.0
210.00.0
0.0-173.0 Middle
350.0173.0 272.1 1.093
X-XY-Y 12500.0
0.00.0
0.0100.0
0.060.0
0.0-173.0 Middle
0.0233.0 233.0 1.022
X-XY-Y 12500.0
0.00.0
350.0100.0
210.060.0
0.0-173.0 Middle
350.0233.0 313.7 1.093
X-XY-Y 12500.0
0.00.0
850.0850.0
510.0510.0
0.086.5 Top
850.0936.5 1264.7 1.016
Load case 5 (Axial+Mecc) is critical.
Sheet Job Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/20/13
ECHELON@Alexandra View
Ms KTP Consultants Pte Ltd
T&T T&T May 2016