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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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3

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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5

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.

6

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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7

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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9

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Examples

Unbra

cedin

Y-dir

ection

&Braced

inX-

direct

ion

X

Y

Stiff shear walls

10

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Examples

Bracedin

X&Ydir

ection

s

X

Y

Stiff shear walls

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11

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Examples

Shear

wall+

Core

System

Bracedin

X&Ydir

ection

s

X

Y

Stiff shear wallsCore

12

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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13

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

14

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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15

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

16

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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17

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

18

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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19

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Design of Slender UnBraced Columns

Design for the greater moment of:M2 + MaddPu.emin

M2

M1

Mi

20

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

22

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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23

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Example1

24

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Example1

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25

RCDesign2-Dr.HanyNessim

Monday,

November26,

2012

Example1