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MK_L07-L08-1675x400 C13
General column design by PROKON. (GenCol Ver W3.1.09 - 28 Apr 2020)
Design code : ACI 318 - 2011
General design parameters:
Given:
Lo = 10.400 m
fc' = 70 MPa
fy = 390 MPa ACI 318 - 2011 Y
Ac = 643536 mm²
500
X X
Assumptions:
(2) The specified design axial loads include 0
the self-weight of the column.
1000
1500
2000
-500
500
Y
0
(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 4 ([Pier:MK]-[LCWP9A]-[L08]-[M1]) is critical.
Check column slenderness:
End fixity and bracing for bending about the Design axis:
The column is braced.
Effective length factor ß = 0.75 Table 3.21
Effective column height:
k Lu = ß . Lo
= .75 ×10.4
= 7.800 m
Column slenderness about weakest axis:
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k Lu
k Lu/r =
r
7.8
=
.11595
= 67.270
Minimum Moments for Design:
Check for mininum eccentricity:
Check that the eccentricity exceeds the minimum in the plane of bending:
10.10.6.5
eminx = 0.015 + 0.03 . h
= 0.015 + 0.03 ×1.675
= 0.0652 m
10.10.6.5
eminy = 0.015 + 0.03 . b
= 0.015 + 0.03 ×.4
= 0.0270 m
Mminx = eminx. N
= .027 ×4 296.2
= 115.997 kNm
Check if the column is slender: 10.10.1
Load case 4 ([Pier:MK]-[LCWP9A]-[L08]-[M1]) is critical.
kLux/r = 67.3 > 34 - 12× M1/M2 = 30.1 10.10.1
kLux/r = 67.3 > 34 - 12× M1/M2 = 30.1 6.2.5
Note that 34 - 12× M1/M2 is limited to a maximum value of 40.0
\ The column is slender.
Initial moments:
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The column is bent in single curvature about the X-X axis:
M1 = Smaller initial end moment = 107.6 kNm
M2 = Larger initial end moment = 956.5 kNm
The column is bent in single curvature about the Y-Y axis:
M1 = Smaller initial end moment = 73.4 kNm
M2 = Larger initial end moment = 295.3 kNm
Moment Magnification: 10.10.6
For bending about the weakest axis:
The bending moments M1 and M2 about the X-X and Y-Y axes are transformed to
moments about the weakest axis and summed to give resultant moments about the
weakest axis. Moment magnification is now performed and the slenderness in-
duced moments are transformed back to the X-X and Y-Y axes.
Weakest axis lies at an angle of -180.00° to the X-X axis
EsIs = Es . Ist
= 200 ×278.41
= 55.68×103 kNm²
10.10.6.1
Ec. Ig
+ Es. Ist
5
EI =
1 + ßd
39.323 ×8 652.7
+ 200 ×278.41
5
=
1 + .85
= 66.88×103 kNm²
(10-13)
p2 . EI
Pc =
k Lu2
p2 ×66882
=
7.8 2
= 10.85×103 kN
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Pu = 4296.2 kN
f = 0.650
Where no end moment or pin exists, the minimum moment emin× N = 116.0 kNm is used.
10.10.6
0.4 . M1
Cm = 0.6 -
M2
0.4 ×- 107.55
= 0.6 -
- 956.46
= 0.5550
But 10.10.6
Cm > = 0.4
Cm is based on the assumption that the maximum moment occurs
at mid height - see commentary on clause 10.10.6.4 ACI - 2011 code.
For checking top and bottom of the column, Cm is taken as 1.
(10-12)
Cm
db =
Pu
1 -
0.75 . Pc
.64498
=
4296×103
1 -
0.75 ×1085×104
= 1.366
With the proviso that (10-12)
db > = 1.0
(10-12)
1
db(top&bot) =
Pu
1-
0.75 . Pc
1
=
4296×103
1-
0.75 ×1085×104
= 2.118
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With the proviso that (10-12)
db > = 1.0
ds = 1.000 (10-12)
Additional moment at Top of column:
(10-12)
Madd = (db. Mb + ds. Ms ) - (Mb + Ms )
= (1.3664 ×- 956.46 + 1 ×0 ) - (- 956.46 + 0 )
= - 350.4469 kNm
Maddx = Madd. cos( - 180.00)
= 350.4 ×cos ( - 180.00)
= - 350.4000 kNm
Maddy = Madd. sin( - 180.00)
= 350.4 ×sin( - 180.00)
= 0.0000×100 kNm
Additional moment at Middle of column:
(10-12)
Maddt + Maddb
Madd =
2
350.4 + 39.402
=
2
= 194.901 kNm
Maddx = Madd. cos( - 180.00)
= 194.9 ×cos ( - 180.00)
= - 194.9000 kNm
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Maddy = Madd. sin( - 180.00)
= 194.9 ×sin( - 180.00)
= 0.0000×100 kNm
Additional moment at Bottom of column:
(10-12)
Madd = (db. Mb + ds. Ms) - (Mb + Ms )
= (1.3664 ×107.55 + 1 ×0 ) - (107.55 + 0 )
= 39.406 kNm
Maddx = Madd. cos( - 180.00)
= 39.402 ×cos ( - 180.00)
= -39.4020 kNm
Maddy = Madd. sin( - 180.00)
= 39.402 ×sin( - 180.00)
= 0.0000×100 kNm
Design ultimate load and moment:
Design axial load:
Pu = 4296.2 kN
For bending about the X-X axis, the maximum design moment is the greatest of: 10.10.7
(a)
Mtopx = Mtop + Madd
= - 956.46 + - 350.4
= -1 306.8600 kNm
(b)
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Mbotx = Mbot + Madd
= - 107.55 + -39.402
= - 146.9520 kNm
Moments about X-X axis( kNm)
Mx=1306.9 kNm
Mxtop=-956.5 kNm Mxadd=-350.4 kNm Mxmin=116.0 kNm
Mxadd=-194.9 kNm
+ =
Mxbot=107.6 kNm Mxadd=-39.4 kNm
Initial Additional Design
For bending about the Y-Y axis, the maximum design moment is the greatest of: 10.10.7
(a)
Mtopy = Mtop + Madd
= -73.381 + 0
= -73.3810 kNm
(b)
Mboty = Mbot + Madd
= - 295.28 + 0
= - 295.2800 kNm
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Moments about Y-Y axis( kNm)
My=295.3 kNm
Mytop=-73.4 kNm Mymin=280.3 kNm
+ =
Mybot=295.3 kNm
Initial Additional Design
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 4 lies at an angle of 183.21° to the X-axis
The safety factor for the critical load case 4 is 1.21
For bending about the design axis:
Interaction Diagram
26E3
Moment max = 1591 kNm @ 4012kN
24E3
22E3
20E3
18E3
16E3
14E3
Axial load (kN)
12E3
10E3
8000
6000
4296 kN
4000
-1800
-1600
-1400
-1200
-1000
1000
1200
1400
1600
1800
-800
-600
-400
-200
0.00
2000
200
400
600
800
1309 kNm
-2000
-4000
-6000
-8000
Bending moment (kNm)
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- moments
of the critical load case. This also determined the design axis direction
At the top, Mx = 1308.9 kNm
Near mid-height, Mx = 650.5 kNm
At the bottom, Mx = 329.8 kNm
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Stresses at the top end of the column for the critical load case 4
ACI 318 - 2011 Y 500
183.2°
183.2° D
M
X X
M
D
0
1000
1500
2000
-500
500
Y
0
Summary of design calculations:
Design table for critical load case:
Moments and Reinforcement for LC 4:[Pier:MK]-[LCWP9A]-[L08]-[M1]
Top Middle Bottom
Madd-x (kNm) -350.4 -194.9 39.4
Madd-y (kNm) 0.0 0.0 0.0
Mx (kNm) -1306.9 -616.9 147.0
My (kNm) -73.4 -206.5 295.3
Mmin (kNm) 106.4 106.4 106.4
M-design (kNm) 1308.9 650.5 329.8
Design axis (°) 183.21 198.51 243.54
Safety factor 1.21 3.71 6.50
As (mm²) 26465 26465 26465
Percentage 3.95 % 3.95 % 3.95 %
AsNom (mm²) 6435 6435 6435
Critical load case: LC 4
Design results for all load cases:
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Safety
Load case Axis N (kN) M1 (kNm) M2 (kNm) Mi (kNm) Madd (kNm) Design M (kNm) M' (kNm) factor
Load case 1 X-X -82.6 -743.4 -479.1 -43.5 786.9
Y-Y 3183.2
[Pier:MK]-[LCWM4B]-[L08]-[M1] -9.4 -233.7 -144.0 0.0 Top 233.7 786.9 2.061
Load case 2 X-X -36.3 -281.1 -183.2 0.0 281.1
Y-Y 2158.5
[Pier:MK]-[LCWM19B]-[L08]-[M1] -97.6 -211.1 -165.7 0.0 Top 211.1 351.5 9.904
Load case 3 X-X -36.3 -282.4 -183.9 0.0 282.4
Y-Y 2138.4
[Pier:MK]-[LCWM20B]-[L08]-[M1] -111.1 -197.1 -162.7 0.0 Top 197.1 344.4 9.831
Load case 4 X-X -107.6 -956.5 -616.9 -350.4 1306.9
Y-Y 4296.2
[Pier:MK]-[LCWP9A]-[L08]-[M1] -73.4 -295.3 -206.5 0.0 Top 295.3 1308.9 1.210
Load case 5 X-X -107.4 796.8 435.1 0.0 796.8
Y-Y 4379.4
[Pier:MK]-[LCWM4A]-[L07M]-[M1] -299.2 -530.9 -438.2 0.0 Bottom 530.9 957.4 3.940
Load case 6 X-X -82.6 621.9 340.1 0.0 621.9
Y-Y 3257.8
[Pier:MK]-[LCWM4B]-[L07M]-[M1] -233.7 -457.4 -367.9 0.0 Bottom 457.4 772.0 5.218
Load case 7 X-X -107.3 794.5 433.8 0.0 794.5
Y-Y 4414.5
[Pier:MK]-[LCWM5A]-[L07M]-[M1] -275.5 -458.5 -385.3 0.0 Bottom 458.5 917.4 3.784
Load case 8 X-X -36.3 226.2 121.2 0.0 226.2
Y-Y 2233.1
[Pier:MK]-[LCWM19B]-[L07M]-[M1] 20.7 -97.6 -50.3 0.0 Bottom 97.6 227.2 7.036
Load case 9 X-X -107.6 797.8 435.7 0.0 797.8
Y-Y 4395.6
[Pier:MK]-[LCWP9A]-[L07M]-[M1] -295.3 -515.2 -427.2 0.0 Bottom 515.2 949.7 3.902
Load case 10 X-X -67.2 494.7 269.9 0.0 494.7
Y-Y 2849.9
[Pier:MK]-[LCWP11B]-[L07M]-[M1] -225.9 -425.9 -345.9 0.0 Bottom 425.9 652.7 6.494
Load case 11 X-X -36.8 231.3 124.0 0.0 231.3
Y-Y 2235.6
[Pier:MK]-[LCWP12B]-[L07M]-[M1] 3.8 -101.2 -59.2 0.0 Bottom 101.2 231.3 6.830
Load case 12 X-X -80.1 644.8 354.8 0.0 644.8
[Pier:MK]-[LCEQXY1A 3942.2
Y-Y MAX]-[L07M]-[M1]
-314.0 -419.8 -377.5 0.0 Bottom 419.8 769.4 4.685
Load case 4 ([Pier:MK]-[LCWP9A]-[L08]-[M1]) is critical.
