Column Design - EURO CODE

7/23/2019 Column Design - EURO CODE

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calc: SNchk: .

CONCRETE COLUMN DESIGN - EUROCODE BS EN 1992-1-1:2004

0.0 TOC

1.0 Introduction

1.1 References

2.0 Design data

2.1 General Dimensions

2.2 Reinforcement details

2.3 Material properties

2.4 Actions on columns

3.0 Column design - nominal curvature method

3.1 Effective length

3.2 First order moments

3.3 Nominal second order moment

3.4 Design values

3.5 Design of steel reinforcement using design charts

3.6 Check for biaxial bending

1.0 Introduction

Checking adequacy of RC column dimensions and reinforcement with respect to EUROCODES

1.1 References

[1] BS EN 1990:2002+A1:2005 Basis of structural design

[2] BS EN 1992-1-1:2004 Design of concrete structures - Part 1-1: General rules for building

2.0 Design data

2.1 Material Properties

Characteristic compressive

strength f ck 12MPa

Yield strength of reinforcement f yk 500MPa

Partial factor for concrete - [2] 2.4.2.4 γc 1.5

Partial factor for steel - [2] 2.4.2.4 γs 1.15

Design strength of concrete f cd

f ck

γc

f cd 8 MPa

Design strength of reinforcement f yd

f yk

γs

f yd 434.8 MPa

Elastic modulus of reinforcement E

s

200GPa

Column design -- EURO code.xmcd 04/06/2015 1 of 8



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2.2 General Dimensions

Column breadth b 0.3m

Column depth h 0.4m

Column height lc 3.5m

Assumed effective cover ceff 30mm

Effective depth deff h ceff deff 370 mm

Cross sectional area of concrete Ac b h Ac 120000 mm2

Second moment of area, about y dir Iy b h

3

12 Iy 1 .6 10

9 mm

4

Radius of gyration, about y dir r y

Iy

Ac

r y 115 mm

Second moment of area, about z dir Iz b

3h

12 Iz 900 10

6 mm

4

Radius of gyration, about z dir r z

Iz

Ac

r z 87 mm

2.3 Reinforcement details

Provided rebar diameter d 16mm Bar diameter should not be less

than 12mm

Number of bars n 4

Total area of reinforcement provided Asprov n π

4 d

2

Asprov 804.25 mm2

2.4 Actions on cloumns

Design axial load NEd 250kN

Ultimate moment at top, about y dir Mtopy 38.5kN m

Ultimate moment at bottom, about y dir M boty 38.5 kN m

Factored moments without

effect of geometrical

imperfections

Ultimate moment at top, about z dir Mtopz 20kN m

Ultimate moment at bottom, about z dir M botz 30kN m




calc: SNchk: .

2.5 First order moments -

[2] - 5.8.8.2 - 2

Y direction

First order moment-1 M01y min Mtopy M boty maxh

3020mm

lc

400

NEd

M01y 43.5 kN m

First order moment-2 M02y max Mtopy M boty maxh

3020mm

lc

400

NEd

M02y 43.5 kN m

Equivalent first order end moment about

y dir

M0ey max 0.6 M02y 0.4 M01y 0.4 M02y

M0ey 43.5 kN m

Z direction

First order moment-1 M01z min Mtopz M botz max b

3020mm

lc

400

NEd

M01z 25 kN m

First order moment-2 M02z max Mtopz M botz max b

3020mm

lc

400

NEd

M02z 35 kN m

Equivalent first order end moment about

z dir M0ez max 0.6 M02z 0.4 M01z 0.4 M02z

M0ez 31 kN m

3.0 Column design - Nominal curvature method

3.1 Effective length

[2] Refer Figure 5.7




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Effective length factor τ 0.7

Effective length lo τ lc lo 2.45 m

[2] - 5.8.3.1 & 5.8.3.2 Acr 0.7

Bcr 1.1

r my

M01y

M02y

M01y 0 M02y 0 M01y 0 M02y 0 if

M01y

M02y

otherwise

r my 1

r mz

M01z

M02z

M01z 0 M02z 0 M01z 0 M02z 0 if

M01z

M02z

otherwise

r mz 0.71

Cy 1.7 r my Cy 0.7For braced columns

Cz 1.7 r mz Cz 0.99

Cy 0.7For unbraced columns toggle

these valuesCz 0.7

Relative normal force nf

NEd

Ac f cd nf 0.26

Cy 1.7 r myLimiting slenderness ratio about y dir λ limy 20 Acr Bcr

Cy

nf

λ limy 21.12

Limiting slenderness ratio about z dir λ limz 20 Acr Bcr Cz

nf

λ limz 29.75

NOTE

EN DIN 1992-1-1 gives a simpler and conservative check for limiting slenderness ratio as follows

λ= 25 when relative normal force nf 0.41




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nf nf .

Slenderness ratio about y direction λ y

lo

r y

λ y 21.22

Slenderness ratio about z direction λ z

lo

r z λ z 28.29

Columntypeydir "Slender column about y dir" λ y λ limyif

"Short Column about y dir" otherwise

Columntypeydir "Slender column about y dir"

Columntypezdir "Slender column about z dir" λ z λ limzif

"Short Column about z dir" otherwise

Columntypezdir "Short Column about z dir"

3.3 Nominal second order moment

[2] - 5.8.8.2 (3) & 5.8.8.3 ωAsprov f yd

Ac f yd ω 0.01

n bal 0.4

nu 1 ω nu 1.01

k r min 1n

u n

f

nu n bal

k r 1

β 0.35f ck

200 MPa

λ y

150 β 0.27

Effective creep

ratioϕef 0.3

k ϕ 1 β ϕef k ϕ 1.08

Deflection - y direction e2y

0.1k r k ϕ f yd

0.45 deff Es

l

o

2 e

2y 8.5 mm

Nominal second order

moment - y directionM2y NEd e2y M2y 2.1 kN m

Deflection - z direction e2z 0.1k r k ϕ f yd

0.45 b ceff Es

lo

2 e2z 11.6 mm

Nominal second order

moment - y directionM2z NEd e2z M2z 2.9 kN m

3.4 Design values

Design axial load NEd 250 kN




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[2] - 5.8.8.2 (1)

Design moment in y direction

MEdy M0ey M2y Columntypeydir "Slender column in y dir"=if

M0ey otherwise

MEdy 43.5 kN m

Design moment in z direction

MEdz M0ez M2z Columntypezdir "Slender column in z dir"=if

M0ez otherwise

MEdz 31 kN m

Cirtical moment to be selected for design MEd max MEdy MEdz MEd 43.5 kN m

3.5 Design of steel reinforcement using design charts

Parameters for using graph

Cover to height ratio ceff

h0.08

X axis parameter XMEd

b h2

f cd

X 0.11

Y axis parameter Y NEd

b h f cd Y 0.26

From graph P1 0.6 P1 indicates As*fyd

b*h

Required area of steel Asreq

P1 b h f cd

f yd

Asreq 13.25 cm2

Assumed diameter of bars d 16 mm

Percentage of reinforcement provided pAsprov

Ac

p 0.67 %

Check for maximum/minimum longitudinal reinforcement

Maximum percentage of long rfn pmax 4%

[2] - 9.5.2 (3)

Minimum percentage of long rfn pmin max 0.1 NEd

f yd Ac % 0.2%

pmin 0.2 %

[2] - 9.5.2 (2)

Details of transverse reinforcement

Provide links T12@150

dmin max 6mm d

4

dmin 6 mmMinimum link diameter




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Maximum spacing of links smax max 12 d 0.6 min b h( ) 240mm( ) smax 240 mm

3.6 Check for biaxial bending

[2] - 5.8.9 (4)

Axial load capacity of the

column NRd Ac f cd Asprov f yd

NRd 1309.67 kN

Moment capacity to be evaluated from

interaction curvesAsprov f yd

b h f cd 0.36

Y axis parameter NEd

b h f cd

0.26

ceff

h0.08

From the chart, X axis parameter P3 0.3 P3 indicates M/bh2f cd

Moment capacity in y-direction MRdy P3 b h2

f cd MRdy 115.2 kN m

Moment capacity in z-direction MRdz P3 b2

h f cd MRdz 86.4 kN m

Ratio of axial load capacity to axial

load resistance of columnα

NEd

NRd

α 0.19

Exponenta α( ) 1

0.5 α 0.1( )

0.6 0.1 α 0.7if

1.5 0.5 α 0.7( )

0.3 otherwise

Check for biaxial bending MEdyMRdy

a α( )

MEdzMRdy

a α( )

0.59[2] - Equation 5.39




calc: SNchk: .

0.1906 0.1907 0.1908 0.1909 0.191 0.19111.074

1.075

1.076

1.077

a α( )

α


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Column Design - EURO CODE