structural engineering parametric study of web shear cracking

Structural Engineering

Concrete Structures Kristian Edekling & Lars Rettne

Parametric Study of Web Shear Cracking

Lars Rettne

Based on the Master’s Project “Improved Design Method for Web Shear Tension Failure in Hollow Core Units” in the International Master’s Programme Structural Engineering



Web Shear Tension Failure in Hollow Core Units



Problem Description

”In the present standard the guidance on howto calculate shear tension capacity is not detailed enough and a more precise methodis needed”



Aim of the Project

• Create finite element (FE) models of single hollow core units

• Perform calculations using Yang’s methodof single hollow core units

• Compare the shear capacity and location of the critical point between the two methods



Critical Point= The point where web shear cracking starts



Collaboration

• This project was initiated by Strängbetong, which is the largest hollow core unit producer in Sweden



Hollow Core Floors

Hollow core floors consist of hollow core units

Hollow core floor Hollow core unit




Uncracked cross-section σ1 < fctm

σ1

σ1 = Principal stressfctm = Mean tensile strength of concrete




Web shear cracking σ1 = fctm

Immediately failure (brittle)



Shear Capacity with Respect to Web Shear Tension Failure

• Failure when the concrete tensile strength is reached, σ1 = fctm

• The principal stresses are dependent of the shear and normal stresses, σ1 = σ1(σx, τ)



Shear Stress Calculations in Prestressed Members

Yang’s (new)Traditional (present)

P0i P0i P0iP0i

x xσp



Shear Stress Calculations in Prestressed Members


)()()(

),(I cpw

cpcpcpcp zbI

xVzSzx =τ )(

)()()(

),( 0

I dxdPf

zbIxVzS

zx i

cpw

cpcpcpcp +=τ

The shape is taken into account



Shear Capacity Calculations in Prestressed Members


Assumed location of criticalpoint somewhere along line

Assumed location ofcritical point



Reference Case – Principal Sketch

Prestressing strand

Cross-section

Self weight and imposed load



Parametric Study

• Prestressing strand arrangement• Prestressing strand amount• Prestress• Concrete strength class• Concrete strength at strand release• Prestress transfer function• Type of cross-section



FE Model

Steel strands: Truss finite elementsStiff steel support plate: Solid finite elements

Concrete part: Solid finite elements



FE Model - Boundary Conditions

Roller support

Solid concrete part

Stiff support plate

Line where the boundary conditions were applied



FE Model - Boundary Conditions: Symmetry Planes

Boundary conditions along transversal symmetry plane

Boundary conditions along longitudinal symmetry plane



FE Model - LoadsSelf weight & Imposed load (pressure)

Initial stress from prestressing (initial condition)



FE Model - Mesh

dense mesh (25 mm)

Non-critical region coarse mesh (200 mm)

Critical region



Results – FE MethodPrincipal Stresses in the Reference case

Critical point



Results – FE MethodStress Field in the Reference Case

Short term response(28 days age)

Long term response(57 years age)



Results – Yang’s Method

Critical point

Principal Stresses in the Reference Case



Shear CapacitySupport Reaction at Web Shear Cracking

Lin Yang, 35° Critical Path from Mid Support

100

200

300

400

500

600

REFSTIFF

PSArPSAm8PSAm12 PS CC

CSAR

PTFTOCS

TOCS-PSAr

Supp

ort R

eact

ion

[kN

]

t=28 days t=57 years

Support Reaction at Web Shear CrackingFE Analyses

100

200

300

400

500

600

REFSTIFF


CSAR

PTFTOCS

TOCS-PSAr

Supp

ort R

eact

ion

[kN

]

t=28 days t=57 years



Shear CapacityRelative Support Reactions at Web Shear Cracking

RLin Yang 35°/RFE Analyses

0,90

0,95

1,00

1,05

1,10

REF

STIFF PSAr

PSAm8

PSAm12 PS CC

CSAR

PTF

TOCSTOCS-PS

Ar

RLi

n Y

ang

35°/R

Aba

qus [

]

t=28 dayst=57 years

Comparison between FEM and Yang’s Method

Yang’s method unconservative

Yang’s method conservative



Location of Critical PointPosition of Critical Point For the Reference Model (REF)

Comparison Between FE Analyses / Yang

00,020,040,060,08

0,10,120,140,16

0 0,05 0,1 0,15 0,2 0,25

Horizontal Position from Mid Support [m]

Ver

tical

Pos

ition

from

-Bo

ttom

Uni

t [m

]

REF 28 days, FEM REF 57 years, FEMREF 28 days, Yang REF 57 years, Yang

Position of Critical Point For the Model with Stiffener (STIFF)Comparison Between FE Analyses / Yang

00,02

0,040,060,08

0,10,12

0,140,16

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Botto

m U

nit [

m]

STIFF 28 days, FEMSTIFF 57 years, FEMSTIFF 28 days, YangSTIFF 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Prestressing Strand Arrangement (PSAr)


PSAr 28 days, FEMREF 28 days, FEM

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

] PSAr 28 days, FEMPSAr 57 years, FEMPSAr 28 days, YangPSAr 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Prestressing Strand Amount (PSAm8)


PSAm8 28 days, FEMPSAm8 57 years, FEM

0

0,05

0,1

0,15

0,2

0,25

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

PSAm8 28 days, FEMPSAm8 57 years, FEMPSAm8 28 days, YangPSAm8 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Prestressing Strand Amount (PSAm12)


PSAm12 28 days, Yang

PSAm12 57 years, Yang

0

0,05

0,1

0,15

0,2

0,25

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]


Position of Critical Point For the Model with Changed Prestress (PS)Comparison Between FE Analyses / Yang

PS 28 days, FEM

PS 57 years, FEM

REF 28 days, FEM

REF 57 years, FEM

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0 0,05 0,1 0,15 0,2 0,25

Horizontal Position from Mid Support [m]V

ertic

al P

ositi

on fr

omB

otto

m U

nit [

m]

PS 28 days, FEMPS 57 years, FEMPS 28 days, YangPS 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Concrete Class (CC)


CC 28 days, FEMREF 28 days, FEM

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

CC 28 days, FEMCC 57 years, FEMCC 28 days, YangCC 57 years, YangREF 28 days, FEMREF 57 year, FEM

Position of Critical Point For the Model with Changed Concrete Strength at Strand Release (CSAR)


CSAR 57 years, FEM

CSAR 28 days, YangCSAR 57 years, Yang

REF 57 years, FEM

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0 0,05 0,1 0,15 0,2 0,25Horizontal Position from Mid Support [m]

Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

CSAR 28 days, FEMCSAR 57 years, FEMCSAR 28 days, YangCSAR 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Prestressing Transfer Fuction (PTF)


0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

PTF 57 years, FEMPTF 57 years, YangREF 57 years, FEM

Position of Critical Point For the Model with Changed Type of Cross-Section (TOCS)


TOCS 28 days, YangTOCS 57 years, Yang

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0 0,05 0,1 0,15 0,2 0,25


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

TOCS 28 days, FEMTOCS 57 years, FEMTOCS 28 days, YangTOCS 57 years, YangREF 28 days, FEMREF 57 years, FEM

Position of Critical Point For the Model with Changed Type of Cross-Section and Prestressing Strand Arrangement (TOCS-PSAr)


TOCS-PSAr 28 daYang

TOCS-PSAr 57 yeYang0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0 0,05 0,1 0,15 0,2 0,25


Ver

tical

Pos

ition

from

Bot

tom

Uni

t [m

]

TOCS-PSAr 2TOCS-PSAr 5TOCS-PSAr 2TOCS-PSAr 5REF 28 days, FREF 57 years,



Location of Critical PointFE Analyses

Horizontal and Vertical Location of Critical Point Independently of Web, t =28 days, FE Analyses

PSAm8

PSAm12

TOCS

REFPSAr

PSCCCSARSTIFF

TOCS-PSAr

0

0,05

0,1

0,15

0,2

0,25

0 0,05 0,1 0,15 0,2 0,25 0,3

Horizontal Distance from Middle Support [m]

Ver

tical

Dis

tanc

e fr

om

-B

otto

m E

dge

[m]

REF PSAr PSAm8 PSAm12PS CC CSAR PTFSTIFF TOCS TOCS-PSAr



Location of Critical PointYang’s Method

Horizontal and Vertical Location of Critical Point Independently of Web, t =28 days, Yang's Method

REF

PSAr

PSAm8

PSAm12PS

CCCSAR PTF STIFF

TOCSTOCS-PSAr

00,020,040,060,080,1

0,120,140,160,18

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Dist

ance

from

B

otto

m E

dge

[m]

REF PSAr PSAm8 PSAm12PS CC CSAR PTFSTIFF TOCS TOCS-PSAr



Location of Critical Point:Reference Case

Location of Critical Point For the Reference Case (REF)Comparison Between FE Analyses / Yang's Method

0

0,020,04

0,06

0,08

0,10,12

0,14

0,16

0 0,05 0,1 0,15 0,2 0,25


Ver

tical

Dis

tanc

e fr

om

-B

otto

m E

dge

[m]

REF 28 days, FEM REF 57 years, FEMREF 28 days, Yang REF 57 years, Yang



Location of Critical Point: Prestressing Strand Amount, PSAm8

Location of Critical Point For the Case with Changed Prestressing Strand Amount (PSAm8)

Comparison between FE Analyses / Yang's Method

PSAm8 28 days, FEMPSAm8 57 years, FEM

0

0,05

0,1

0,15

0,2

0,25

0 0,05 0,1 0,15 0,2 0,25 0,3


Ver

tical

Dist

ance

from

B

otto

m E

dge

[m]




Angle β for Different CasesAngle β** for Different Cases

FE Analyses

15

20

25

30

35

40

45

50

55

60

REF STIFF PSAr PSAm8 PSAm12 PS CC CSAR PTF TOCS TOCS-PSAr

Ang

le [D

egre

es]

t=28 dayst=57 years

β



Angle β** for Different CasesFE Analyses

15

20

25

30

35

40

45

50

55

60


Ang

le [D

egre

es]

t=28 dayst=57 years

Angle β for Different Cases

Recommended β from Yang (1994) β

Comparison between FEM and Yang’s Method



Angle β for Different Cases

Angle β** for Different CasesFE Analyses

15

20

25

30

35

40

45

50

55

60


Ang

le [D

egre

es]

t=28 dayst=57 years

Recommendations of New Angle

β

Suggested β for long term response and long transfer length

Suggested β for short term response and short transfer length



Relative Shear Capacity

Relative Support Reactions at Web Shear CrackingRYang Ne w Su gge stion s/RFE Analyse s

0,900

0,950

1,000

1,050

1,100

REFSTIFF


CSAR

PTFTOCS

TOCS-PSAr

RY

ang/R

Aba

qus [

]

t=28 dayst=57 years

New Recommended Angle is Used



Conclusions

• For long term response and long transfer length, the critical point was found along a path with a smaller inclination than 35°proposed by Yang (1994).

• For long term response and long transfer length, the capacity of web shear tension failure was reduced.

General from FE Analyses



Conclusions

• Decreased reinforcement amount had a great influence on the position of the critical point; the horizontal distance from the support to the critical point was increased. The capacity in web shear tension failure is reduced.

• Increased prestress from 1000 MPa to 1200 MPadid not affect the location of the critical point, but reduced the shear capacity.

Specific from FE Analyses



Conclusions

• The agreement between Yang’s method and FEM regarding the location of the critical point was, with some exceptions, good for short term response and short transfer length and less good for long term response and long transfer length.

• The agreement between Yang’s method and FEM regarding the web shear tension capacity was, with some exceptions, good for short term response and short transfer length and less good for long term response and long transfer length.

General from Comparison FEM – Yang’s Method



Recommendation

• Use β=35° for short term response and short transfer length with Yang’s method.

• Use β=25° for long term response and long transfer length with Yang’s method.

β



Thanks for your attention!

structural engineering parametric study of web shear cracking

Documents