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C13N-C8
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 (°)
+ 5.000
190.000
5.000 5.000
790.000
-5.000 5.000
-190.000
-5.000 -5.000
-790.000
+ 43.000 43.000
b 16
+ 157.000 43.000
b 16
+ 157.000 757.000
b 16
+ 43.000 757.000
b 16
+ 43.000 185.800
b 16.000
+ 157.000 185.800
b 16.000
+ 43.000 328.600
b 16.000
+ 157.000 328.600
b 16.000
+ 43.000 471.400
b 16.000
+ 157.000 471.400
b 16.000
+ 43.000 614.200
b 16.000
+ 157.000 614.200
b 16.000
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Loadcase Designation
Ultimate limit state design loads
P (kN) Mx top (kNm) My top (kNm) Mx bot (kNm) My bot (kNm)
1 Axial 1450
2 Axial + Mecc 1450 38 19
3 Axial + Mxx 1450 128 38
4 Axial + Myy 1450 38 19
5 Axial + Mxx + Myy1450 128 64
Design loads:
0
250
1000
750
500
250
0
X X
Y
Y
CP65 - 1999
General design parameters:Given: Lo = 3.600 m fcu = 35 MPa fy = 460 MPa Ac = 157537 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. (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 + Mxx + Myy) 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 3 (pinned). The column is braced.
Effective length factor ß = 1.00 Table 3.21
Effective column height:
=le ß Lo.
= 1 3.6×
= 3.600 m
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Column slenderness about weakest axis:
=max_s140lle
h
=3.6
.19997
= 18.003
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
=Mmin emin N.
= .01 1450×
= 14.500 kNm
Check if the column is slender: 3.8.1.3
le/h = 18.0 > 15∴ The column is slender.
Initial moments:
The initial end moments about the X-X axis:
M1 = Smaller initial end moment = 0.0 kNm
M2 = Larger initial end moment = 128.0 kNm
The initial moment near mid-height of the column : 3.8.3.2
=Mi 0.4 M1 0.6 M2. .- +
= 0.4 0 0.6 128× ×- +
= 76.800 kNm
=Mi2 0.4 M2.
= 0.4 128×
= 51.200 kNm
∴ Mi ≥ 0.4M2 = 76.8 kNm
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
The initial end moments about the Y-Y axis:
M1 = Smaller initial end moment = 0.0 kNm
M2 = Larger initial end moment = 64.0 kNm
The initial moment near mid-height of the column : 3.8.3.2
=Mi 0.4 M1 0.6 M2. .- +
= 0.4 0 0.6 64× ×- +
= 38.400 kNm
=Mi2 0.4 M2.
= 0.4 64×
= 25.600 kNm
∴ Mi ≥ 0.4M2 = 38.4 kNm
Deflection induced moments: 3.8.3.1
Design ultimate capacity of section under axial load only:
=Nuz 0.45 fcu Ac 0.87 fy Asc. . . . +
= 0.45 35 157.54 0.87 460 2.4127× × × × +
= 3 446.818 kN
Maximum allowable stress and strain:
Allowable compression stress in steel
=fsc 0.87 fy.
= 0.87 460×
= 400.200 MPa
Allowable tensile stress in steel
=fst 0.87 fy.
= 0.87 460×
= 400.200 MPa
Allowable tensile strain in steel
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
=eyfst
Es
=400.2
210000
= 0.0019
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 = 200mm
=KNuz N
Nuz Nbal
-
-
=3447×10
31450×10
3
3447×103
1119×103
-
-
= 0.8578
=ßa1
2000max_sl
2.
=1
200018.003
2×
= 0.1621
Where max_sl is the maximum slenderness ratio of the column as an equivalent rectangular column.
Therefore:
=Madd N ßa K h. . .
= 1450 .16205 .85793 .19997× × ×
= 40.312 kNm
∴ Maddx = Madd*cos(-90.00°) = 0.0 kNm ∴ Maddy = Madd*sin(-90.00°) = 40.3 kNm
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Design ultimate load and moment:Design axial load: Pu = 1450.0 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
=Mtop MtMadd
2 +
= 1280
2 +
= 128.000 kNm
(b) 3.8.3.2
=Mmid Mi Madd +
= 76.8 0 +
= 76.800 kNm
(c) 3.8.3.2
=Mbot MbMadd
2 +
= 00
2 +
= 0.0000×100
kNm
(d) 3.8.3.2
=M eminx N.
= .02 1450×
= 29.000 kNm
Thus 3.8.3.2
M = 128.0 kNm
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Mxtop=128.0 kNm
Moments about X-X axis( kNm)
Initial Additional Design
Mx=128.0 kNm
Mxmin=29.0 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
=Mtop MtMadd
2 +
= 6440.317
2 +
= 84.159 kNm
(b) 3.8.3.2
=Mmid Mi Madd +
= 38.4 40.317 +
= 78.717 kNm
(c) 3.8.3.2
=Mbot MbMadd
2 +
= 040.317
2 +
= 20.159 kNm
(d) 3.8.3.2
=M eminy N.
= .02 1450×
= 29.000 kNm
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Thus 3.8.3.2
M = 84.2 kNm
Madd/2=20.2 kNm
Mya
dd
/2=
-40
.3 k
Nm
Mytop=64.0 kNm
Moments about Y-Y axis( kNm)
Initial Additional Design
My=84.2 kNm
Mymin=14.5 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 33.32° to the X-axis The safety factor for the critical load case 5 is 1.62
For bending about the design axis:
Interaction Diagram
Mo
me
nt m
ax
= 3
56
.8kN
m @
10
85
kN
-800-600-400-200
200 400 600 800 100012001400160018002000220024002600280030003200
-35
0
-30
0
-25
0
-20
0
-15
0
-10
0
-50
.0
0.0
0
50
.0
10
0
15
0
20
0
25
0
30
0
35
0
40
0
Axi
al l
oa
d (
kN)
Bending moment (kNm)
1450 kN
15
3 k
Nm
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
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 = 153.2 kNm Near mid-height, Mx = 110.0 kNm At the bottom, Mx = 0.0 kNm
Stresses at the top end of the column for the critical load case 50
250
1000
750
500
250
0
X X
Y
Y
CP65 - 1999
33.3°
D
D
Summary of design calculations:
Design table for critical load case:
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015
Moments and Reinforcement for LC 5:Axial + Mxx + Myy
Top Middle Bottom
Madd-x (kNm) 0.0 0.0 0.0
Madd-y (kNm) 20.2 -40.3 0.0
Mx (kNm) 128.0 76.8 0.0
My (kNm) 84.2 78.7 0.0
Mmin (kNm) 14.5 14.5 0.0
M-design (kNm) 153.2 110.0 0.0
Design axis (°) 33.32 45.71 180.00
Safety factor 1.62 1.72 1.04
Asc (mm²) 2413 2413 2413
Percentage 1.51 % 1.51 % 1.51 %
AsNom (mm²) 630 630 630
Critical load case: LC 5
Design results for all load cases:
Load case Axis N (kN) M1 (kNm) M2 (kNm) Mi (kNm) Madd (kNm) Design M (kNm) M' (kNm)Safetyfactor
Load case 1 Axial
Load case 2 Axial + Mecc
Load case 3 Axial + Mxx
Load case 4 Axial + Myy
Load case 5 Axial + Mxx + Myy
X-XY-Y 1450.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 -40.3 Middle
0.0 40.3 40.3 1.679
X-XY-Y 1450.0
0.0 0.0
38.0 19.0
22.8 11.4
0.0 -40.3 Middle
38.0 51.7 56.5 1.826
X-XY-Y 1450.0
0.0 0.0
128.0 38.0
76.8 22.8
0.0 -40.3 Middle
128.0 63.1 99.4 1.816
X-XY-Y 1450.0
0.0 0.0
38.0 19.0
22.8 11.4
0.0 -40.3 Middle
38.0 51.7 56.5 1.826
X-XY-Y 1450.0
0.0 0.0
128.0 64.0
76.8 38.4
0.0 20.2 Top
128.0 84.2 153.2 1.616
Load case 5 (Axial + Mxx + Myy) is critical.
SheetJob Number
Job Title
Client
Calcs by Checked by Date
Software Consultants (Pty) Ltd
Internet: http://www.prokon.com
E-Mail : [email protected]
KTP/10/13
NEW FUTURA
M/s KTP CONSULATNTS PTE LTD
HT T&T OCT 2015