10 slender columns
TRANSCRIPT
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Slender Columns
2
RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Definition Slender columns
are those subjectto buckling thatproducesadditionalmoment resultingin significant
reduction ofcolumn capacity.
P
P
e
Madd = P.
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Definition
If the column isunbraced, i.e.both ends canmove relative toeach other, thenthe additionalmoment is
greater.
P
P
e
Unbraced
P
4
RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Braced and Unbraced StructuresWhen the structure contains members to resist side-sway (lateralforces) then it is a braced structure.
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Braced and Unbraced Structures
When the structure does not contain members to resist side-sway(lateral forces) then it is an unbraced structure.
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Braced and Unbraced StructuresAccording to ECP 203Bracing of RC structures is usuallyprovided by shear walls or cores.
A building without shear walls or coresis considered an unbraced structures.
A building with a shear wall or a core isconsidered braced only if
4nfor0.1n0.20
4nfor0.60
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Braced and Unbraced Structures
Hb = Total height of the building (m) N = Sum of all unfactored vertical loadsEI = Sum of EI for all vertical stiffening
elements n = number of stories E = 4400 fcu
4nfor0.1n0.20
4nfor0.60
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Examples
Unbra
cedin
Y-dir
ection
&Braced
inX-
direct
ion
X
Y
Stiff shear walls
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Examples
Bracedin
X&Ydir
ection
s
X
Y
Stiff shear walls
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Examples
Shear
wall+
Core
System
Bracedin
X&Ydir
ection
s
X
Y
Stiff shear wallsCore
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Slenderness Ratio; Is the ratio between the effective length of
the column and its cross sectional dimensionsin the direction under consideration.
He = k.Ho
Ho = unsupported (clear) length of thecolumn b-column dimension in the direction of study
i
H
b
H eeb == ior
g
g
A
Ii =
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Limitations
35810Unbraced
501215Braced
iDb or tColumn Status
Columns are considered short columns (not slender) when
isless than values of the following table
Columns are considered slender when is greater than values inthe above table BUT less than the values in the following table
701823Unbraced
1002530Braced
iDbColumn Status
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Effective Height of ColumnsAccording to the support
Condition at each end ofThe column, the value of kIs determined, hence, He Ho
Column end is freeCase4
Column is connected to an element that cannotprevent rotation.
Case3
Column is connected to a slab or a beam shallowerthan the column dimension.
Case2
Column is connected to a beam with a depth
column dimension in this direction
Case1
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Values of k
0.900.800.75Case1
1.000.950.90Case3
0.950.850.80Case2
Case3Case2Case1End condition at top
End condition at bottom
k = He/Ho for Braced columns
k = He/Ho for Unbraced columns
--1.801.60Case3
1.601.301.20Case1
----2.20Case4
1.801.501.30Case2
Case3Case2Case1End condition at top
End condition at bottom
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Calculating Additional Moment For Braced Columns
Calculate column deflection,
Calculate additional moment, MaddMadd = P.
columnscircular2000
.
columnsrrectangula2000
.or
2000
.
2
22
D
tb
D
tb
=
=
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Design of Slender Braced Columns
Design for the greatest moment of:M2M1 + Madd/2Mi + Madd/2Pu.emin
Where:Mi= 0.4M1+0.6M2 0.4M2M2>M1M1 has a negative sign if it is atthe other side of the column.
M2
M1
Mi
M1
M2
Mi
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Calculating Additional Moment For UnBraced Columns
Calculate column deflection, Calculate average deflection per story, av
Where:N; total number of columns in a storyNeglect > 2av
Calculate additional moment, MaddMadd = P.av
n
av
=
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Design of Slender UnBraced Columns
Design for the greater moment of:M2 + MaddPu.emin
M2
M1
Mi
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Minimum Reinforcement
Minimum reinforcement ratio is:min = 0.25 + 0.015iormin = 0.25 + 0.052b
rectangular section
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Example
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Example1Design an RC rectangular column
in a ground floor of a bracedmultistory building, knowingthat:
Column is connected to a beamwith section (20x60)cm in bothdirections.
Pu = 1500kN
b = 250mm & Ho = 4.50m
fcu = 30N/mm2 & st. 360/520
t
250mm
y
x
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Example1
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Example1
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RCDesign2-Dr.HanyNessim
Monday,
November26,
2012
Example1