Sachpazis_VERIFICATION OF THE ULTIMATE PUNCHING SHEAR RESISTANCE to EC2 1992-1-1-2004 with NA CEN.pdf

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VERIFICATION OF THE ULTIMATEPUNCHING SHEAR RESISTANCE

EUROCODE 2

GEODOMISI Ltd. - Dr. Costas Sachpazis

Civil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures.

Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944,

www.geodomisi.com - [email protected]


2/11

GEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company for

Structural Engineering, Soil Mechanics, Rock Mechanics,

Foundation Engineering & Retaining Structures.Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 -Mobile: (+30) 6936425722 & (+44) 7585939944,


Section

Civil & Geotechnical Engineering

Calc.

16/01/2016

INDEX

DESCRIPTION

CHECKS1.- Zone adjacent to the support or load (Persistent situations) 3

2.- Zone with punching shear reinforcement (Persistent situations) 5

3.- External zone to the punching shear reinforecement (Persistentsituations) 7

4.- Punching shear reinforcement (EN 1992-1-1:2004/AC:2008, 9.4.3(2)) 9

5.- Clear distance between two isolated consecutive bars 9

6.- Distance between the support's face and the first punching shearreinforcement 10

7.- Distance between transverse consecutive reinforcement perimeters 108.- Distance between two consecutive reinforcements in peripheral direction 11

9.- Distance between the support's external face and the outermost barinclined at 45 11


3/11

GEODOMISI Ltd. - Dr. Costas SachpaziCivil & Geotechnical Engineering Consulting Company for

Structural Engineering, Soil Mechanics, Rock Mechanics

Foundation Engineering & Retaining Structures.

Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461Mobile: (+30) 6936425722 & (+44) 7585939944,


DESCRIPTION

CHECKS

1.- Zone adjacent to the suppo

The worst case design forces occuThe following criteria must be sati

Where:

vEd: Design value of the sheevRd,max: Design value of thecontrol section considered.

The design value of the sheer strefrom the following expression (EN

Where:

VEd: Design value of the

Ed Rd,maxv v

Ed

Ed

0

Vv

u d

=

,

-

Section


Calc.

16/01/2016

alculation of the punching shear perimeters

Perimeter of th

u0:

Critical perime

u1:

xG:

yG:W1x:

W1 :

Punching shear

uout,ef:

xG:

yG:

Wout,ef,x:

Wout,ef,y:

rt or load (Persistent situations)

for load combination 1.35SW+1.35DL1+1.5 fied:

r stress along the control section considered.aximum punching shear resistance along the

ss along the control section considered is obtai1992-1-1:2004/AC:2008, 6.4.5):

applied shear force.

Page 3 - 11

e support (C1)

1600 mm

er

4362 mm

0 mm

0 mm19163.6 cm

19163.6 cm

reinforcement perimeter

5031 mm

0 mm

0 mm

51487.8 cm

51487.8 cm

LL1.

2.43 MPa 4.50 MPa

vEd: 2.43 MPa

vRd,max: 4.50 MPa

ed

vEd: 2.43 MPa

VEd: 756.75 kN


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Section


Calc.

16/01/2016

Page 4 - 11

: Coefficient which takes into account the effects of load eccentricity. (EN1992-1-1:2004/AC:2008, 6.4.3). : 1.13

kx: Coefficient which depends on the relationship between the dimensionscy(dimension in direction of the y-axis) and cx(dimension in direction of thex-axis) of the column (EN 1992-1-1:2004/AC:2008, Table 6.1). kx: 0.60

ky: Coefficient which depends on the relationship between the dimensions cx(dimension in direction of the x-axis) and cy(dimension in direction of the

y-axis) of the column (EN 1992-1-1:2004/AC:2008, Table 6.1). k :0.60

MEdx: Design moment around the x-axis, regarding the center of gravity ofthe critical perimeter u1. MEdx: 58.65 kNm

MEdy: Design moment around the y-axis, regarding the center of gravity ofthe critical perimeter u1. MEd : 12.30 kNm

MEdOx: Design moment around the x-axis, regarding the center of gravity ofthe column. MEdOx: 58.65 kNm

MEdOy: Design moment around the y-axis, regarding the center of gravity ofthe column. MEdO : 12.30 kNm

u1: Critical punching shear perimeter (EN 1992-1-1:2004/AC:2008, 6.4.2). u1: 4362 mm

W1x: 19163.6 cm

dl: Differential element of the critical perimeter length.

e : Distance from dl to the axis where the moment MEdxacts about.

W1y: 19163.6 cm

ex: Distance from dl to the axis where the moment MEdyacts about.

u0: Verification critical punching shear perimeter of the area adjacent to thesupport or load (EN 1992-1-1:2004/AC:2008, 6.4.5). u0: 1600 mm

d: Nominal depth of the slab. d : 220 mm

The design value of the maximum punching shear resistance along the control section

considered is obtained from the following expression (EN 1992-1-1:2004/AC:2008,6.4.5):

vRd,max: 4.50 MPa

: 0.54

Where:

fck: Concrete compressive strength. fck: 25.00 MPa

EdyEdx 1 1x y

Ed 1x Ed 1y

MM u u1 k k

V W V W = + +

1u

1x y

0

W e dl=

1u

1y x

0

W e dl=

Rd,max cdv 0.5 f =

ckf0.6 1250

=


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fcd: Design value of thelongitudinal member axi

2.- Zone with punching shear r


Where:

vEd: Design value of the shee

vRd,cs: Design value of the pushear reinforcement along th


Where:

VEd: Design value of the: Coefficient which tak1992-1-1:2004/AC:200

kx: Coefficient which decy(dimension in directiothe x-axis) of the colum

ky: Coefficient which decx(dimension in directiothe y-axis) of the colum

MEdx: Design moment a

the critical perimeter u1.MEdy: Design moment athe critical perimeter u1.

MEdOx: Design momentof the column.

MEdOy: Design momentof the column.

u1: Critical punching sh

dl: Differential element

Ed Rd,csv v

Ed

Ed

1

Vv

u d

=

Edx

x

Ed

M u1 k

V W = +

1u

1x y

0

W e dl=

,

-

Section


Calc.

16/01/2016

concrete compression force in the direction of ts.

einforcement (Persistent situations)


r stress along the control section considered.

nching shear resistance of a slab with punchinge control section considered.


applied shear force.s into account the effects of load eccentricity. (, 6.4.3).

ends on the relationship between the dimension of the y-axis) and cx(dimension in directionn (EN 1992-1-1:2004/AC:2008, Table 6.1).

ends on the relationship between the dimension of the x-axis) and cy(dimension in directionn (EN 1992-1-1:2004/AC:2008, Table 6.1).

ound the x-axis, regarding the center of gravit

ound the y-axis, regarding the center of gravit

round the x-axis, regarding the center of gravi

round the y-axis, regarding the center of gravi

ar perimeter (EN 1992-1-1:2004/AC:2008, 6.

of the critical perimeter length.

Edy1 1y

1x Ed 1y

M uk

V W+

Page 5 - 11

hefcd: 16.67 MPa

LL1.

0.89 MPa 4.90 MPa

vEd: 0.89 MPa

vRd,cs: 4.90 MPa

ed

vEd: 0.89 MPa

VEd:756.75

kNEN

: 1.13

nsf

kx: 0.60

nsf

ky: 0.60

of

MEdx: 58.65 kNmof

MEdy: 12.30 kNm

tyMEdOx: 58.65 kNm

tyMEdOy: 12.30 kNm

.2). u1: 4362 mm

W1x: 19163.6 cm


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Section


Calc.

16/01/2016

Page 6 - 11

ey: Distance from dl to the axis where the moment MEdxacts about.

W1 : 19163.6 cm

ex: Distance from dl to the axis where the moment MEd acts about.


The design value of the punching shear resistance of a slab with punching shearreinforcement along the control section considered is obtained from the followingexpression (EN 1992-1-1:2004/AC:2008, 6.4.5):

vRd,cs: 4.90 MPa

Where:

vRd,c: 0.95 MPa

with a minimum value of:

vRd,c,min: 0.68 MPa

Where:

c: Concrete resistance reduction coefficient. c: 1.50

k: Coefficient which depends on the nominal depth of 'd'. k : 1.95


l: Geometric steel area of the main tensile longitudinalreinforcement. l: 0.0132

Where:lx: Ratio in X-direction. lx: 0.0132

ly: Ratio in Y-direction. ly: 0.0132

cp: Average axial stress on the critical verification surface (positivecompression), with a maximum value of cp,max. cp: 2.00 MPa

cp,max: 3.33 MPa

fcd: Design value of the concrete compression force in thedirection of the longitudinal member axis. fcd: 16.67 MPa

1u

1y x

0

W e dl=

swywd,ef

r

Rd,cs Rd,c

1

Af sin

sv 0.75 v 1.5

u

= +

( )1/3

Rd,c l ck cp

c

0.18v k 100 f 0.1= +

3 / 2 1 /2

Rd,c,min ck cpv 0.035 k f 0.1= +

200k 1 2

d

= +

l lx ly 0.02 =

cp,max cd0.20 f =


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Asw: Total area of puncconcentric with the supp

sr: Radial distance betw

: Angle between the sh

Reference

111

111

fywd,ef: Effective design strength o

fywd: Design yield strength o

(EN 1992-1-1:2004/AC:2008

u1: Critical punching shear perim

3.- External zone to the punchi


Where:

vEd: Design value of the shee

vRd,c: Design value of the pushear reinforcement along th


Where:

VEd: Design value of the

: Coefficient which tak1992-1-1:2004/AC:200

ywd,ef ywdf 250 0.25 d f = +

ywd ywkf 0.8 f =

Ed Rd,cv v

Ed

Ed

out,ef

Vv

u d

=

Edx

x

Ed

M u1 k

V W = +

,

-

Section


Calc.

16/01/2016

ing shear reinforcement within a permieterort or loaded area.

een two concentric perimeters of reinforcement

ear reinforcement and the plane of the slab.

Asw(mm)

sr(mm)

(degrees)

2262 80 45.0

2262 80 45.0

f the punching shear reinforcement.

the shear reinforcement.

, 6.2.3(3))

ter (EN 1992-1-1:2004/AC:2008, 6.4.2).

ng shear reinforecement (Persistent situat


r stress along the control section considered.

ching shear resistance of a slab without punchie control section considered.


applied shear force.

s into account the effects of load eccentricity. (

, 6.4.3).

Edyout,ef out,ef

y

out,ef,x Ed out,ef,y

M uk

V W+

Page 7 - 11

.

Asw/sr(cm/m)

282.8

282.8

fywd,ef: 305.00 MPa

fwd: 320.00 MPa

fywk: 400.00 MPa

u1: 4362 mm

ions)

LL1.

0.72 MPa 0.95 MPa

vEd: 0.72 MPa

ngvRd,c: 0.95 MPa

ed

vEd: 0.72 MPa

VEd: 756.75 kN

EN

: 1.05


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Section


Calc.

16/01/2016

Page 8 - 11

kx: Coefficient which depends on the relationship between the dimensionscy(dimension in direction of the y-axis) and cx(dimension in direction ofthe x-axis) of the column (EN 1992-1-1:2004/AC:2008, Table 6.1). kx: 0.60

ky: Coefficient which depends on the relationship between the dimensionscx(dimension in direction of the x-axis) and cy(dimension in direction ofthe y-axis) of the column (EN 1992-1-1:2004/AC:2008, Table 6.1). k : 0.60

MEdx: Design moment around the x-axis, regarding the center of gravity ofthe critical perimeter uout,ef. MEdx: 58.65 kNm

MEdy: Design moment around the y-axis, regarding the center of gravity ofthe critical perimeter uout,ef. MEd : 12.30 kNm

MEdOx: Design moment around the x-axis, regarding the center of gravityof the column. MEdOx: 58.65 kNm

MEdOy: Design moment around the y-axis, regarding the center of gravityof the column. MEdOy: 12.30 kNm

uout,ef: Critical punching shear perimeter outside the reinforced zone (EN1992-1-1:2004/AC:2008, 6.4.5). uout,ef: 5031 mm

Wout,ef,x: 51487.8 cm

dl: Differential element of the critical perimeter length.

e : Distance from dl to the axis where the moment MEdxacts about.

Wout,ef,y: 51487.8 cm

ex: Distance from dl to the axis where the moment MEdyacts about.


The design value of the punching shear resistance of a slab without punching shearreinformcement along the control section considered is obtained from the followingexpression (EN 1992-1-1:2004/AC:2008, 6.4.4):

vRd,c: 0.95 MPa

with a minimum value of:

vRd,c,min: 0.68 MPa

Where:

c: Concrete resistance reduction coefficient. c: 1.50

k: Coefficient which depends on the nominal depth of 'd'. k : 1.95


l: Geometric steel area of the main tensile longitudinal reinforcement. l: 0.0132

out,efu

out,ef,x y

0

W e dl=

out,efu

out,ef,y x

0W e dl=

( )1/ 3

Rd,c l ck cp

c

0.18v k 100 f 0.1= +

3 / 2 1 /2

Rd,c,min ck cpv 0.035 k f 0.1= +

200k 1 2

d

= +


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Where:

lx: Ratio in X

l : Ratio in Y

cp: Average axial strescompression), with a m

fcd: Design value othe longitudinal me

4.- Punching shear reinforcem

Where shear reinforcement is requ(9.11).

ReferenceAsw

(mm

111 113

111 113

where:

Asw: the area of a link leg (or

: is the angle between the s= 90 and sin = 1).

sr: is the spacing of shear lin

st: is the spacing of shear lin

fck: is in MPa

5.- Clear distance between two

The horizontal and vertical clear ssmin(EN 1992-1-1:2004/AC:2008,

l lx ly 0.02 =

cp,max cd0.20 f =

( ) ( ),min 1,5 sin cos / 0,08sw r ts s +

( ) ( )( )

,min

,min

1,5 sin cos /

0,08 /

w sw r t

w ck yk

A s s

f f

= + =

l mind s

,

-

Section


Calc.

16/01/2016

direction.

direction.

on the critical verification surface (positiveximum value of cp,max.

f the concrete compression force in the directiomber axis.

nt (EN 1992-1-1:2004/AC:2008, 9.4.3(2))

ired the area of a link leg (or equivalent), Asw,m

)sr

(mm)st

(mm)

(degrees)w w,mi

80 33 45.0 0.0757 0.001

80 33 45.0 0.0757 0.001

equivalent).

ear reinforcement and the main steel (i.e. for

s in the radial direction.

s in the tangential direction.

isolated consecutive bars

acing dlbetween two consecutive bars should8.2(2)):

( ) ( )/ 9.11ck yk f f

Page 9 - 11

lx: 0.0132

l : 0.0132

cp: 2.00 MPa

cp,max: 3.33 MPa

offcd: 16.67 MPa

in, is given by Expression

n ww,min

0

0

ertical links

fck: 25.00 MPa

e greater than or equal to

21 mm 20 mm


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Where:

smin: Maximum value of s1, s

Where:

d : Maximum size of ag

max: Diameter of the t

111

111

6.- Distance between the supp

The distance between the face of tnot be greater than smax(EN 1992

Where:

d: Nominal depth of the slab.

7.- Distance between transver

The distance dlbetween consecuti1992-1-1:2004/AC:2008, 9.4.3):

Where:

1 maxs =

2 gs 5 d= +

3s 20mm=

l maxd s

maxs 0.5 d=

l maxd s

,

-

Section


Calc.

16/01/2016

2, s3.

regate.

ickest bar of the transverse reinforcement.

dl(mm)

smin(mm)

max(mm)

21 20 12

21 20 12

rt's face and the first punching shear rein

he support or loaded area and the first punchin1-1:2004/AC:2008, 9.4.3):

.

e consecutive reinforcement perimeters

e transverse reinforcement perimeters should

Page 10 - 11

smin: 20 mm

s1: 12 mm

s2: 17 mm

s3: 20 mm

d : 12 mm

max: 12 mm

orcement

g shear reinforcement should

80 mm 110 mm

smax: 110 mm

d : 220 mm

be, at most, equal to smax(EN

80 mm 165 mm


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8.- Distance between two cons

The distance dlbetween two cons1-1:2004/AC:2008, 9.4.3):

Where:


9.- Distance between the supp

This combination does not proceesupport.

maxs 0.75 d=

l maxd s

= maxs 1.5 d

,

-

Section


Calc.

16/01/2016

.

ecutive reinforcements in peripheral direct

cutive perimeter reinforcements should not be

.

rt's external face and the outermost bar i

since the reinforcement is located between th

GEODOMISI Ltd.Civil & Geotechnical Engi

Structural Engineering, Soil M

Engineering &Tel.: (+30) 210 5238127, 210 57

(+30) 69364257

www.geodomisi.co

Page 11 - 11

smax: 165 mm

d : 220 mm

ion

greater than smax(EN 1992-

33 mm 330 mm

smax: 330 mm

d : 220 mm

clined at 45

external faces of the

- Dr. Costas Sachpazisneering Consulting Company for

chanics, Rock Mechanics, Foundation

Retaining Structures.11263 - Fax.:+30 210 5711461 - Mobile:

2 & (+44) 7585939944,

- [email protected]

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Sachpazis_VERIFICATION OF THE ULTIMATE PUNCHING SHEAR RESISTANCE to EC2 1992-1-1-2004 with NA CEN.pdf