FINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABS.

FINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABSFINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABS

IntroductionTests on steel plate bridge decks have shown that, if a load on the deck is increased beyond

the usual wheel load limits, or if the ratio of the deflection to the span of a ribs is relatively large, internal axial stresses begin to appear in the loaded ribs, in addition to the purely flexural stresses. An additional tension, due to membrane action of the deck plate, occurs in the directly loaded rib, and has to be balanced by an equally large compression in the adjoining ribs [8].

As the loads and the corresponding deflection increase, a complete redistribution of the stresses takes place in the system, and the membrane stresses almost entirely replace the flexural stresses which are predominant under working loads.

Thus with sufficiently large deflections, a steel plate deck behaves in a manner radically different from that predicted by the usual flexural theory which disregards the effect of the deformations of a system on its stresses. Most importantly, its strength has been found to be many times greater than predicted by the ordinary flexural theory.

The Aim of the ResearchThe main aim of this research is to use finite element approach in analyzing steel

fiber concrete slabs and steel deck plate allowing for membrane action. Then, study the effect of number of parameters on the structural behavior of the above structures.

ANALYSIS OF STEEL DECKPLATES ALLOWING FOR MEMBRANE ACTION

Comparison of small- and large-deflection theories using an approximate method

3

maxmax3 13

864

a

w

a

hE

a

w

a

Dpo Eq.1

An alternate form of Eq.1, obtained by taking =0.3, is:

2

maxmax4

65.0164 h

w

h

w

Dh

apo Eq.2

Fig.1: Maximum Deflections and Stresses Plates Having Large Deflections [78]

(a) Clamped edge (b) Simply supported

hh

Eh4Eh4

The variation of load deflection for a uniformly loaded circular plate with clamped edge, wmax/h and poa4/Eh4 are plotted in Fig.3. It is observed that the linear theory which, neglects the membrane action, is satisfactory for wmax<h/2 and the larger deflections produce greater error. When wmax=h, for example there is a 65 percent error in the load according to the bending theory alone[78].

Von-Karman assumptionsThe Von-Karmen assumptions for large deformation of plates and shells should take the

following forms when applying shells and plates [22]:1.The magnitude of the deflection (w) is of the order of the thickness (h).2.The thickness is much less than the length (L); (this hypothesis is not restrictive) since otherwise the displacements are not large.3.The slope is small everywhere 4. The tangent displacements (u, v) are small, only nonlinear term, which depend on have to be

retained in the strain-displacement relations.5.All strain components are small.

yx

wN

y

wN

x

wNp

Dy

w

yx

w

x

wxyyx

2

2

2

2

2

4

4

22

4

4

4

21

2

General equations for large deflections of platesThe general differential equation for a thin plate, subjected to combined lateral (p) and in-plane (Nx, Ny, and Nxy) forces [78]:

Eq.3

For a thin plate element, the x and y equilibria of direct forces are expressed by:

0

y

N

x

N xyx 0

y

N

x

N yxy Eq.4

2

2

1

x

w

x

ux

2

2

1

x

w

x

ux

y

w

x

w

y

u

x

vxy

Eq.5

The resultant strain components may be expressed as:

22

2 2

1

2

1

1 y

w

y

v

x

w

x

uEhN x

22

2 2

1

2

1

1 x

w

x

u

y

w

y

vEhN y

y

w

x

w

y

u

x

vEhN xy )1(2

The in-plane forces can be expressed as [86]:

Eq.6a

Eq.6b

Eq.6c

The non-linear stiffness matrix:

K=K+K Eq.7

Where: v

T DBdvBK Eq.8

Eq.9v

T dvGGK ]][[][

B:strain displacement matrixD: elasticity matrixv: volume

[G]: is a matrix with two rows and number of columns equal to the total number of element nodal variables. The first row contains the contribution of each nodal variable to the local derivative corresponding shape function derivatives( ) and the second row contains similar contributions for ( )

```

```

yyx

yxx

and

`` xw

`` yw

Eq.10

Material Nonlinearity The material nonlinearity deals (for steel deck plates) with elasto-plastic behavior and the

anisotropic affect in the yielding behavior.Flow theory of plasticity

The flow theory of plasticity [44,45] is employed as the nonlinear material model. For anisotropic material to be considered in this work is a generalization of the Huber-Mises law and can be written in general form as: F()=f()-Y() in which f() is some function of the deviatoric stress invariant and the yield level Y() can be a function of a hardening parameter, .Tangent stiffness matrix The tangential stiffness matrix of the material can be expressed as:

Eq.11

v v

epTT BdvDBdv

aB

a

PK

Eq.12

where Dep: is the elasto-plastic rigidity matrix and equal:

DaaH

DDaaDD

T

T

ep

`Eq.13

a: is the flow vector andH`: is the hardening parameter

Computer program (ANSYS software)ANSYS software is a general purpose FE-program for static, dynamic as well as multiphysics

analysis and includes a number of shell elements with corner nodes only and with corner and mid-side nodes.

From the available element library in ANSYS, SHELL93 element is used in this work.

Case studies 1.Steel deck plate

The results of a full scale loading test [8] of a 10 mm thick deck plate supported on ribs spaced 300 mm o.c. is analyzed by ANSYS software, Fig.2. It is represented and modeled as shown in Figs.3 and 4. The load deflection curves for both small displacement analysis and large displacement analysis (allowing for membrane action) are explained in Fig.5. Conservative solution was obtained in small displacement analysis but good agreement with experimental tests was gotten in case of large displacement analysis. The deflected shape at ultimate load is listed in Fig.6.

a

a=300 mm

a a

Loading

Point A

Rigid steel frame

16 0 m m

P/2

P/2

Point m

10

m m

Fig.2: Steel Deck Plate

Fig.3: Representation of Steel Deck Plate

Point A

Fig.4: FE-Model of Steel Deck Plate

-200-180-160-140-120-100-80-60-40-200cen tra l d e flc tio n (m m )

0

50

100

150

200

250

300ce

ntra

l poi

nt lo

ad (

ton)

ex p er im en ta l

la rge d efo rm a tio n

sm all d e fo rm a tio n

Fig.5: Load Deflection Relationships of Steel Deck Plate

central deflection (mm)

Fig.6: Deflected Shape of Steel Deck Plate

2. Steel deck plate with open ribsA steel deck plate with open ribs under a concentrated wheel load, which was conducted at the

Technological University in Darmstadt [8] (Germany), is analyzed using both large and small displacement analysis. The 5-span continuous test panel was a half-scale model of the deck plating intended for Save River Bridge in Belgrade, Fig.7. Also conservatives solution and good agreement compared with experimental test was shown in both small and large deformation analysis respectively, Fig10.

P

Load P Point A

Rubber bed4.5 mm deck plate

150 mmPL 250 mm x 4.5 mm

PL 70 mm x 4.5 mm

3750 mm

300 mm

P1480 mm

Ribs 70 mm x 4.5 mm

Fig.7: Steel Deck Plate with Open Ribs Fig.9: FE-Model of Steel Deck with Open Ribs Plate in ANSYS

Fig.8: Representation of Steel Deck Plate with Open Ribs

Fig.10: Load Deflection Relationships of Steel Deck Plate with Open Ribs

-50-45-40-35-30-25-20-15-10-50cen tra l d e flc tio n (m m )

0

5

10

15

20

25

30

cent

ral p

oint

load

(to

n)

ex p er im en ta l

la rg e d efo rm a tio n

sm a ll d e fo rm a tio n


Fig.11: Deflected Shape of Steel Deck Plate with Open Ribs

3. Steel deck plate with closed ribsA steel deck plate with closed (torsionally rigid) longitudinal stiffening ribs was tested at

the Technological University in Stuttgart. The dimensions of test panel with trapezoidal ribs, which may be regarded as a half scale model of an actual bridge penal, are illustrated in Fig. 12. the same previous notes for large and small displacements analysis can be observed in Fig.15.

Piont A

4000 mm

Edge beam

Rigid support

Rigid support

P

P

P

Edge beam

150 mm

150 mm

3 mm longitudinal ribs

5 mm deck plate

85 mm

3450 mm1800 mm

Fig.12: Steel Deck Plate with Closed Ribs

Fig. 13: Representation of Steel Deck Plate with Closed Ribs

Fig.14: FE-Model of Steel Deck with Closed Ribs

-800-700-600-500-400-300-200-1000cen tra l d e flc tio n (m m )

0

20

40

60

80

100

120

140

160

180

cent

ral p

oint

load

(to

n)

ex p er im en ta l

la rge d efo rm a tio n

sm all d e fo rm a tio n

Fig.15: Load Deflection Relationships of Steel Deck Plate with Closed Ribs central deflection (mm)

Fig.16: Deflected Shape of Steel Deck Plate with Closed Ribs

Computer ProgramTo analyze fibrous concrete slabs, a program which is coded by Hinton and Owen [40] and called

"conshell", is used. The program was modified by Al-Shather [11] to take into account the presence of steel fiber in concrete slab. This is done by introducing tension stiffening technique. In the present study the membrane action is introduced, and this done by using geometrical nonlinearity, and allowing for high strain limit m during the running of the program.

ANALYSIS OF FIBROUS CONCRETE SLABS ALLOWING FOR MEMBRANE ACTION

Case Studies To verify the computer program which is called "conshell program", number of fibrous concrete slabs, which were tested by Mohammed [61], are analyzed. The material parameters and are assumed to obtain good agreement with the experimental tests.

These specimens are also analyzed by ANSYS software. The so-called "SOLID65 element", which is favorable with the analysis of reinforced concrete structures, is used. Geometrical and material nonlinearities are adopted. The tested slabs [6] had dimensions of 1.0 m x 0.7 m and 25 mm thick with compressive strength as shown in table 1.Table 1: Compressive Strength of Fibrous Concrete

The steel fiber aspect ratio (lf/df) was 20. For slabs with reinforcement, they were reinforced with smooth wires of 2 mm diameter, with yield strength of 380.6 MPa. These steel wire reinforcement provided at shorter span were 0.076 mm2/m (x=0.33%) and 0.108 mm2/m ('x=0.49%) at positive and negative moment, respectively. Conversely at longer direction an amount of 0.036 mm2/m (y=0.17%) and 0.051 mm2/m ('y=0.23%) at positive and negative moment, respectively.

Volume fraction Vf %Compressive strength f'cf (MPa)

no fiber 28.60

0.5 29.31

1.0 30.49

1.5 31.15

1. Fibrous concrete slabs axially unrestrained at all edgesa. Without reinforcement

Fig.18: Load Deflection Relationships of Fibrous Concrete Slab Axially Unrestrained with Vf=0.5%

-25-20-15-10-50

cen tra l d e flec tio n (m m )

0

5

10

15

20

25

30

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)

e x p e rim e n ta l

A N S Y S

p re sen t (L eo n a rd )

p re sen t

uniformly distributed load (kN/m2)

Fig.19: Load Deflection Relationships of Fibrous Concrete Slab Axially Unrestrained with Vf=1.0%

-10-8-6-4-20


0

4

8

12

16

20

24

28

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t


Fig. 20: Load Deflection Relationships of Fibrous Reinforced Concrete Slab Axially Unrestrained with Vf=0.5%

-45-40-35-30-25-20-15-10-50


0

40

80

120

160

200

240

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t


b. With reinforcement

2. Fibrous concrete slabs axially restrained at all edgesa. Without reinforcement

Fig.21: Load Deflection Relationships of Plain Concrete Slab Axially Restrained

-16-14-12-10-8-6-4-20


0

10

20

30

40

50

60

70

80

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)


A N S Y S


p re sen t


Fig.22: Load Deflection Relationships of Fibrous Concrete slab Axially Restrained with Vf=0.5%

-30-25-20-15-10-50


0

20

40

60

80

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)


A N S Y S


p re sen t

p re sen t (sm ea red )


Fig.23: Load Deflection Relationships of Fibrous Concrete Slab Axially Restrained with Vf=1.0%

-30-25-20-15-10-50


0

20

40

60

80

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)


A N S Y S


p re sen t




Fig.24: Load Deflection Relationships of Reinforced Concrete Slab Axially Restrained

-30-20-100


0

40

80

120

160

200

240un

ifor

mly

dis

trib

uted

(kN

/m^2

)


A N S Y S


p re sen t


Fig.25: Load Deflection Relationships of Fibrous Reinforced Concrete Slab Axially Restrained with Vf=0.5%

-50-40-30-20-100


0

40

80

120

160

200

240

280

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t



-40-30-20-100


0

40

80

120

160

200

240

280

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t



-50-40-30-20-100


0

40

80

120

160

200

240

280

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t


3. Fibrous concrete slabs axially restrained at two longer edges a. Without reinforcement

Fig.28: Load Deflection Relationships of Fibrous Concrete Slab Axially Restrained at Two Longer Edges with Vf=0.5%

-25-20-15-10-50

cen tra l d e fle c tio n (m m )

0

5

10

15

20

25

30

35

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)


A N S Y S


p re sen t



Fig.29: Load Deflection Relationships of Fibrous Concrete Slab Axially Restrained at Two Longer Edges with Vf=1.0%

-25-20-15-10-50

cen tra l d e fle c tio n (m m )

0

5

10

15

20

25

30

35

40

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)


A N S Y S


p re sen t




Fig.30: Load Deflection Relationships of Fibrous Reinforced Concrete Slab Axially Restrained at Two Longer Edges with Vf=0.5%

-20-16-12-8-40


0

40

80

120

unif

orm

ly d

istr

ibut

ed (

kN/m

^2)


A N S Y S


p re sen t


THE EFFECT OF SOME PARAMETERS ON THE BEHAVIOR OF STEEL DECK PLATES

The effect of a number of parameters on the behavior of steel deck plates are studied. ANSYS software is used to perform analyses of the considered steel deck plate, using SHELL93 element to model the considered problems. Large deformation analysis is adopted to take into account the membrane action as well as material nonlinearity.

Four types of the structures are studied in this work. These are: steel rectangular plate, steel deck plate with open rips running in one direction, steel deck plate with open ribs supported by transverse floor I-beams, and steel deck plate with closed ribs running in one direction. Two types of loading conditions are used, they are central point load and uniformly distributed load above the entire structure.

Dimensions of deck plate

2000 mm

1500

mm

S

ymm

etry

Symmetry

Dimensions of deck plate with open ribs

Sym

met

ry

2250

m

m

2250 mm Symmetry

PL 70mm x 5 mm as ribs spaced 150mm o.c.

Dimensions of deck plate with open ribs and

stiffened by floor beams

Sym

met

ry

2625

mm

2250 mm Symmetry

PL 70 mm x 5 mm as ribs spaced 150 mm o.c.

PL

70

mm

x 5

mm

.

PL 250 mm x 5 mm.

Dimensions of deck plate with closed ribs

Sym

met

ry 2250

m

m

2250 mm Symmetry

PL 5 mm

150 mm

63.1 mm

100 mm

Deck plate 5 mm thick

Fig. 31: Types of Steel Deck Plates

1. Effect of Changing Thickness of Rectangular or Top Plate of Steel Deck Plate

a. Steel rectangular plate

b. Steel deck plate with one-way open ribs

Fig.32: Load Deflection Relationships of Rectangular Plate with Varying Plate Thickness

under Central Point Load

-350-300-250-200-150-100-500cen tra l d e flec tio n in (m m )

0

40

80

120

160

200

cent

ral p

oint

load

in (

ton)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5

-80-60-40-200cen tra l d e flec tio n in (m m )

0

50

100

150

200

250

300

350

unif

orm

lay

dist

ribu

ted

load

(kN

/m^

2)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5

Fig.33: Load Deflection Relationships of Rectangular Plate with Varying Plate Thickness

under Uniformly Distributed Load

-250-200-150-100-500

cern tra l d eflec tio n (m m )

0

20

40

60

80

100

cent

ral p

oint

load

(to

n)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5

Fig.34: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Varying

Thickness of the Top Plate under Central Point Load


Fig.35: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Varying

Thickness of the Top Plate under Uniformly Distributed Load

-800-600-400-2000

cern tra l d e flec tio n (m m )

0

200

400

600

800

1000

1200

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5


c. Steel deck plate with open ribs and stiffened by transverse floor I-beams

d. Steel deck plate with closed ribs

Fig.36: Load Deflection Relationships of Steel Deck plate with One-Way Open Ribs Stiffened by Floor I-Beams and Varying Thickness of the Top

Plate under Central Point Load

-200-160-120-80-400cen tra l d e flec tio n (m m )

0

20

40

60

80

100

cent

ral p

oint

load

(to

n)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5

Fig.37: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-Beams and Varying Thickness of the Top

Plate under Uniformly Distributed Load

-120-100-80-60-40-200cen tra l d e flec tio n (m m )

0

50

100

150

200

250

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5

Fig.38: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Varying

Thickness of the Top Plate under Central Point Load

-300-250-200-150-100-500

cern tra l d eflec tio n (m m )

0

20

40

60

80

100

120

140

160

180

200

cent

ral p

oint

load

(to

n)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5


Fig.39: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Varying

Thickness of the Top Plate under Uniformly Distributed Load

-600-500-400-300-200-1000


0

200

400

600

800

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick = 5

th ick = 6

th ick = 7

th ick = 8

th ick = 9

th ick = 1 0

th ick = 1 1

th ick = 1 2

th ick = 1 3

th ick = 1 4

th ick = 1 5


2. Effect of Changing the Length of Thickening Edge Plate a. Steel rectangular plate


-250-200-150-100-500

cen tra l d e flc tio n (m m )

0

1

2

3

4

5

cent

ral p

oint

load

(to

n)

su p o rt= 0 .0 0 L

su p o rt= 0 .0 5 L

su p o rt= 0 .1 0 L

su p o rt= 0 .1 5 L

su p o rt= 0 .2 0 L

su p o rt= 0 .2 5 L

su p o rt= 0 .3 0 L

Fig.40: Load Deflection Relationships of Steel Rectangular Plate with Varying Lengths of Thickening Plate under Central Point Load

Fig.41: Load Deflection Relationships of Steel Rectangular Plate with Varying Lengths of

Thickening Plate under Uniformly Distributed Load

-100-80-60-40-200


0

20

40

60

80

100

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

su p o rt= 0 .0 0 L

su p o rt= 0 .0 5 L

su p o rt= 0 .1 0 L

su p o rt= 0 .1 5 L

su p o rt= 0 .2 0 L

su p o rt= 0 .2 5 L

su p o rt= 0 .3 0 L

Fig.42: Load Deflection Relationships of Steel Deck Plate with One Way-Open Ribs and Varying Lengths

of Thickening Plate under Central Point Load

-250-200-150-100-500


0

10

20

30

40

cent

ral p

oint

load

(to

ns)

su p o r t= .0 0L

su p o rt= .0 5L

su p o rt= .1 0L

su p o rt= .1 5L

su p o rt= .2 0L

su p o rt= .2 5L

su p o rt= .3 0L

Fig.43: Load Deflection Relationships of Steel Deck Plate with One Way-Open Ribs and Varying Lengths

of Thickening Plate under Uniformly Distributed Load

-600-500-400-300-200-1000


0

100

200

300

400

500

600

700

800

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

su p p o rt= .0 0 L

su p p o rt= .0 5 L

su p p o rt= .1 0 L

su p p o rt= .1 5 L

su p p o rt= .2 0 L

su p p o rt= .2 5 L

su p p o rt= .3 0 L



Fig.44: Load Deflection Relationships of Steel Deck Plate with One Way-Open Ribs Stiffened by Floor I-

Beams and Varying Lengths of Thickening Plate under Central Point Load


0

5

10

15

20

25

30

35

cent

ral p

oint

load

(to

n)

th ick = 0 .0 0 L

th ick = 0 .0 5 L

th ick = 0 .1 0 L

th ick = 0 .1 5 L

th ick = 0 .2 0 L

th ick = 0 .2 5 L

th ick = 0 .3 0 L

Fig.45: Load Deflection Relationships of Steel Deck Plate with One Way-Open Ribs Stiffened by Floor I-

Beams and Varying Lengths of Thickening Plate under Uniformly Distributed Load

-400-350-300-250-200-150-100-500cen tra l d e flec tio n (m m )

0

50

100

150

200

250

300

350

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick = 0 .0 0 L

th ick = 0 .0 5 L

th ick = 0 .1 0 L

th ick = 0 .1 5 L

th ick = 0 .2 0 L

th ick = 0 .2 5 L

th ick = 0 .3 0 L

-80-60-40-200


0

5

10

15

20

25

30

cent

ral p

oint

load

(to

n)

su p o r t= 0 .0 0 L

su p o rt= 0 .0 5 L

su p o rt= 0 .1 0 L

su p o rt= 0 .1 5 L

su p o rt= 0 .2 0 L

su p o rt= 0 .2 5 L

su p o rt= 0 .3 0 L

Fig.46: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Varying Lengths of

Thickening Plate under Central Point Load

Fig.47: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Varying Lengths of

Thickening Plate under Uniformly Distributed Load

-700-600-500-400-300-200-1000cen t ra l d e flec tio n (m m )

0

100

200

300

400

500

600

700

800

900

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick = 0 .0 0 L

th ick = 0 .0 5 L

th ick = 0 .1 0 L

th ick = 0 .1 5 L

th ick = 0 .2 0 L

th ick = 0 .2 5 L

th ick = 0 .3 0 L

3. Effect of Changing the Aspect Ratio of the Steel Rectangular Plate

4. Effect of Changing the Spacing between Ribs with Keeping the Same Total Weighta. Steel deck plate with one-way open ribs

Fig.48: Load Deflection Relationships of Steel Rectangular Plate with Varying Aspect Ratios under

Central Point Load

-50-40-30-20-100

cen tra l d eflc tio n (m m )

0

1

2

3

4

5

cent

ral p

oint

load

(to

n)

a s= 1

a s= 1 .1 3 7

a s= 1 .3 0 6

a s= 1 .5 1 7

a s= 1 .7 7 7

a s= 2 .1 1 5 7

a s= 2 .5 6

a s= 3 .1 6

a s= 4

Fig.49: Load Deflection Relationships of Steel Rectangular Plate with Varying Aspect Ratios under

Uniformly Distributed Load

-20-16-12-8-40


0

200

400

600

800

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

a s= 1

a s= 1 .1 3 7

a s= 1 .3 0 6

a s= 1 .5 1 7

a s= 1 .7 7 7

a s= 2 .1 1 5 7

a s= 2 .5 6

a s= 3 .1 6

a s= 4


0

20

40

60

80

100

cent

ral p

oint

load

(to

n)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

Fig.50: Load Deflection Relationship of Steel Deck Plate with One-Way Open Ribs, Changing the

Spacing between Ribs and Keeping the Total Weight under Central Point Load

Fig.51: Load Deflection Relationship of Steel Deck Plate with One-Way Open Ribs, Changing the

Spacing between Ribs and Keeping the Total Weight under Uniformly Distributed Load


0

50

100

150

200

250

300

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

b. Steel deck plate with open ribs and stiffened by transverse floor I-beams

c. Steel deck plate with closed ribs


0

20

40

60

80

cent

ral p

oint

load

(to

n)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

Fig.45: Load Deflection Relationship of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-

Beams, Changing the Spacing between Ribs and Keeping the Total Weight under Central Point Load


Beams, Changing the Spacing between Ribs and Keeping the Total Weight under Uniformly

Distributed Load


0

50

100

150

200

250

300

350

400

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

-200-160-120-80-400


0

20

40

60

80

100

cent

ral p

oint

load

(to

n)

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

sp a ce= 6 0 0

sp a ce= 6 5 0

Fig.47: Load Deflection Relationship of Steel Deck Plate with Closed ribs, Changing the Spacing

between Ribs and Keeping the Total Weight under Central Point Load


Fig.48: Load Deflection Relationship of Steel Deck Plate with Closed ribs, Changing the Spacing

between Ribs and Keeping the Total Weight under Uniformly Distributed Load

-700-600-500-400-300-200-1000


0

100

200

300

400

500

600

700

800

900

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

sp a ce= 6 0 0

sp a ce= 6 5 0


5. Effect of Changing the Spacing between Ribs a. Steel deck plate with one-way open ribs

b. Steel deck plate with open ribs and stiffened by transverse floor I-beams

-400-300-200-1000


0

20

40

60

80

cent

ral p

oint

load

(to

n)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

Fig.52: Load Deflection Relationship of Steel Deck Plate with One-Way Open Ribs and Changing the Spacing between Ribs under Central Point Load


Fig.53: Load Deflection Relationship of Steel Deck Plate with One-Way Open Ribs and Changing the

Spacing between Ribs under Uniformly Distributed Load

-120-80-400


0

20

40

60

80

100

120

140

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0



Beams and Changing the Spacing between Ribs under Central Point Load

-250-200-150-100-500


0

10

20

30

40

50

60

70

cent

ral p

oint

load

(to

n)

s= 1 5 0

s= 2 0 0

s= 2 5 0

s= 3 0 0

s= 3 5 0

s= 4 0 0

s= 4 5 0

s= 5 0 0


Beams and Changing the Spacing between Ribs under Uniformly Distributed Load

-350-300-250-200-150-100-500cen tra l d e flec tio n (m m )

0

50

100

150

200

250

300

350

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 1 5 0

sp a ce= 2 0 0

sp a ce= 2 5 0

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

c. Steel deck plate with closed ribs


0

20

40

60

80

cent

ral p

oint

load

(to

n)

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

sp a ce= 6 0 0

sp a ce= 6 5 0

sp a ce= 7 0 0

Fig.56: Load Deflection Relationship of Steel Deck Plate with Closed Ribs and Changing the Spacing

between Ribs under Central Point Load

Fig.57: Load Deflection Relationship of Steel Deck Plate with Closed Ribs and Changing the Spacing between Ribs under Uniformly Distributed Load

-800-700-600-500-400-300-200-1000cen tra l d e flec tio n (m m )

0

100

200

300

400

500

600

700

800

900

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sp a ce= 3 0 0

sp a ce= 3 5 0

sp a ce= 4 0 0

sp a ce= 4 5 0

sp a ce= 5 0 0

sp a ce= 5 5 0

sp a ce= 6 0 0

sp a ce= 6 5 0

sp a ce= 7 0 0

6. Effect of Changing the Support Conditions

-60-40-200cen tra l d e flc tio n (m m )

0

4

8

12

16

20

cent

ral p

oint

load

(to

n)

s .s a ll eg es

f-sh o r t s id e

f-lo n g s id e

f.f. a ll ed g es

Fig.58: Load Deflection Relationships of Steel Rectangular Plate with Different Edge Conditions


Fig.59: Load Deflection Relationships of Steel Rectangular Plate with Different Edge Conditions


-20-16-12-8-40cen tra l d eflc tio n (m m )

0

100

200

300

400

500

unfo

rmly

dis

trib

uted

load

(kN

/m^

2)s .s a ll eg es

f-sh o r t s id e

f-lo n g sid e

f.f. a ll ed g es

a. Steel rectangular plate

-400-300-200-1000cen tra l d e flec tio n (m m )

0

10

20

30

40

cent

ral p

oint

load

(to

n)

s .s

fx sy

sx fy

p la te free

r ib free

f.f.

Fig.60: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Different Edge

Conditions under Central Point Load

Fig.61: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Different Edge

Conditions under Uniformly Distributed Load

-160-140-120-100-80-60-40-200cen tra l d e flec tio n in (m m )

0

10

20

30

40

50

60

70

80

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

s .s

fx sy

sx fy

p la te free

r ib free

f.f.



0

10

20

30

40

50

cent

ral p

oint

load

(to

n)

sx sy

p la te free

r ib free

fx fy

Fig.62: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-Beams and Different Edge Conditions under Central

Point Load

Fig.63: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-

Beams and Different Edge Conditions under Uniformly Distributed Load


0

40

80

120

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sx sy

p la te free

r ib free

fx fy



-300-200-1000

cern tra l d flec tio n (m m )

0

20

40

60

80

cent

ral p

oint

load

(to

n)

sx sy

fx sy

sx fy

p la te free

r ib fr ee

fx fy

Fig.64: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Different Edge



Fig.65: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Different Edge


-200-160-120-80-400


0

40

80

120

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

sxsy

fx sy

sx fy

p la te free

r ib free

fx fy


7. Effect of Changing of the Material Properties a. Steel rectangular plate


0

10

20

30

40

50

cent

ral p

oint

load

(to

n)

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

Fig.66: Load Deflection Relationships of Steel Rectangular Plate with Different Types of Steel

Property under Central Point Load

Fig.67: Load Deflection Relationships of Steel Rectangular Plate with Different Types of Steel

Property under Uniformly Distributed Load

-80-60-40-200cen tra l d eflec tio n (m m )

0

20

40

60

80

100

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

o n e q u a rter o f th e o th er p la tes


0

20

40

60

80

cent

ral p

oint

load

(to

n)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

Fig.68: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Different Types

of Steel Property under Central Point Load

Fig.69: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs and Different Types of Steel Property under Uniformly Distributed Load

-800-600-400-2000cen tra l d e flec tio n (m m )

0

200

400

600

800

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0


Fig.70: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-Beams and Different Types of Steel Property under

Central Point Load


0

40

80

120

cent

ral p

oint

load

(to

n)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

Fig.71: Load Deflection Relationships of Steel Deck Plate with One-Way Open Ribs Stiffened by Floor I-Beams and Different Types of Steel Property under



0

200

400

600

800

unif

orm

ly d

istr

ibut

ed lo

ad(k

N/m

^2)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0




0

40

80

120

cent

ral p

oint

load

(to

n)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

Fig.72: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Different Types of Steel

Property under Central Point Load

Fig.73: Load Deflection Relationships of Steel Deck Plate with Closed Ribs and Different Types of Steel

Property under Uniformly Distributed Load

-600-400-2000cen tra l d e flec tio n (m m )

0

200

400

600

800

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fy = 2 5 0

fy = 2 9 0

fy = 3 4 5

fy = 4 1 4

fy = 4 4 8 .5

fy = 4 8 3

fy = 6 2 1

fy = 6 9 0

8. The Effect of Initial Imperfection on the Steel Rectangular Plate

Fig.74: Load Deflection Relationships of Steel Rectangular Plate with Initial Imperfection under

Central Point Load

-50-40-30-20-100cern tra l d eflec tio n (m m )

0

4

8

12

16

20

cent

ral p

oint

load

(to

n)

d efl= 5

d efl= 7 .5

d efl= 1 0

d efl= 1 2 .5

d efl= 1 5

d efl= 1 7 .5

d efl= 2 0

d efl= 2 2 .5

d efl= 2 5

d efl= 2 7 .5

d efl= 3 0


Fig.75: Load Deflection Relationships of Steel Rectangular Plate with Initial Imperfection under


-20-16-12-8-40cern tra l d eflec tion (m m )

0

10

20

30

40

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

d efl= 5

d efl= 7 .5

d efl= 1 0

d efl= 1 2 .5

d efl= 1 5

d efl= 1 7 .5

d efl= 2 0

d efl= 2 2 .5

d efl= 2 5

d efl= 2 7 .5

d efl= 3 0


SENSITIVITY ANALYSIS OF SOME PARAMETERS AFFECTING FIBROUS CONCRETE SLABS

The dimensions of the slab are 4.5 m by 4.5 m and 150 mm thick.The steel fiber volume fraction (Vf) is 1.0 percent with aspect ratio (lf/df) of 30. For fibrous

reinforced concrete slabs, it is assumed that top and bottom reinforcements in two directions are used of the following values: the reinforcements in x-direction are 0.076 mm2/m (x=0.33%) and 0.108 mm2/m ('x=0.49%) at positive and negative moment, respectively. Conversely at y-direction an amount of 0.036 mm2/m (y=0.17%) and 0.051 mm2/m ('y=0.23%) at positive and negative moment, respectively. The compressive strength is assumed equal to 30.49 MPa and the other material properties are calculated by using the equations listed previously.

1. The Effect of Changing Thickness of Fibrous Concrete Slabs

a. Unrestrained fibrous concrete slab b. Restrained fibrous concrete slabc. Restrained fibrous reinforced concrete slab

-10-8-6-4-20


0

40

80

120

160

200

cent

ral p

oint

load

(kN

)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5

Fig.76: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Thickness under Central Point

Load


Fig.77: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Thickness under Uniformly

Distributed Load

-14-12-10-8-6-4-20


0

2

4

6

8

10

12

14

16

18

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5


Fig.78: Load Deflection Relationship of Restrained Fibrous

Concrete Slab with Varying Thickness under Central Point Load

-110-100-90-80-70-60-50-40-30-20-100


0

100

200

300

400

500

600

700

cent

ral p

oint

load

(kN

)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5

Fig.79: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Thickness under Uniformly

Distributed Load

-200-160-120-80-400


0

10

20

30

40

50

60

70

80

90

100

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5

-100-80-60-40-200

central deflction (mm)

0

100

200

300

400

500

600

cent

ral p

oint

load

(kN

)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5

Fig.80: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Thickness under

Central Point Load


Fig.81: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Thickness under


-200-180-160-140-120-100-80-60-40-200


0

20

40

60

80

100

120

140

160

180

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick 1 5

th ick 1 6

th ick 1 7

th ick 1 8

th ick 1 9

th ick 2 0

th ick 2 1

th ick 2 2

th ick 2 3

th ick 2 4

th ick 2 5


2. The Effect of Changing Length of the Edge Thickening Slabs


-20-15-10-50


0

20

40

60

80

100

120

140

160

cent

ral p

oint

load

(kN

)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L

Fig.82: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Length of Edges Thickening Slab



Fig.83: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Length of Edges Thickening Slab


-30-25-20-15-10-50


0

10

20

30

40

50

60

70

80

unif

orm

ly d

istr

ibut

ed lo

ad(k

N/m

^2)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L


-100-80-60-40-200

cen tra l d e flec tion (m m )

0

50

100

150

200

250

300

cent

eal p

oint

load

(kN

)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L

Fig.84: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Length of Edges Thickening

Slab under Central Point Load

Fig.85: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Length of Edges Thickening Slab


-80-60-40-200

cen tra l d eflec tio n (m m )

0

100

200

300

400

500

600

700

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L

-350-300-250-200-150-100-500


0

100

200

300

400

500

cent

ral p

oint

load

(kN

)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L

Fig. 86: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Length of Edges

Thickening Slab under Central Point Load


Fig.87: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Length of Edges

Thickening Slab under Uniformly Distributed Load

-600-500-400-300-200-1000


0

200

400

600

800

1000

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

th ick .0 0 L

th ick .0 5 L

th ick .1 0 L

th ick .1 5 L

th ick .2 0 L

th ick .2 5 L

th ick .3 0 L

central deflection (mm)central deflection (mm)

3. Effect of Changing Edge Support Conditions

a. fibrous concrete slab b. Fibrous reinforced concrete slab

Fig.88: Load Deflection Relationship of Fibrous Concrete Slab with Varying Edge Support


-50-40-30-20-100

cen tra l d eflec tion (m m )

0

50

100

150

200

250

300

cent

ral p

oint

load

(kN

)

ss-a ll ed ges

f-sh o r t e d g es

f-lo n g ed g es

ff-a ll ed g es

Fig.89: Load Deflection Relationship of Fibrous Concrete Slab with Varying Edge Support


-70-60-50-40-30-20-100


0

10

20

30

40

50

60

70

80

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

ss-a ll ed g es

f-sh o r t ed ges

f-lo n g ed g es

ss- a ll ed g es

-100-90-80-70-60-50-40-30-20-100


0

50

100

150

200

250

300

350

cent

ral p

oint

load

(kN

)

ss-a ll ed ges

f-sh o r t ed g es

f-lo n g ed g es

ff-a ll ed g es

Fig.90: Load Deflection Relationship of Fibrous Concrete Reinforced Slab with Varying Edge Support Conditions under Central Point Load


Fig.91: Load Deflection Relationship of Fibrous Concrete Reinforced Slab with Varying Edge

Support Conditions under Uniformly Distributed Load

-200-180-160-140-120-100-80-60-40-200


0

20

40

60

80

100

120

140

160

180

200

220

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

ss-a ll ed g es

f-sh o r t ed g es

f-lo n g ed g es

ff-a ll ed g e s


4. Effect of Initial Imperfection


-6-5-4-3-2-10


0

10

20

30

40

50

60

70

cent

ral p

oint

load

(kN

)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0

Fig.92: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Initial Imperfection under Central

Point Load


Fig.93: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Initial Imperfection under


-10-9-8-7-6-5-4-3-2-10


0

1

2

3

4

5

6

7

8

9

10

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0


Fig. 94: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Initial Imperfection under Central

Point Load

-160-140-120-100-80-60-40-200


0

50

100

150

200

250

300

350

400

cent

ral p

oint

load

(kN

)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0

Fig.95: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Initial Imperfection under


-400-350-300-250-200-150-100-500

cen tra l d eflec tion (m m )

0

10

20

30

40

50

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0

-180-160-140-120-100-80-60-40-200


0

100

200

300

400

500

600

700

cent

ral p

oint

load

(kN

)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0

Fig.96: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Initial Imperfection



Fig.97: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Initial Imperfection


-250-200-150-100-500


0

100

200

300

400

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

d efl= 2 5

d efl= 5 0

d efl= 7 5

d efl= 1 0 0

d efl= 1 2 5

d efl= 1 5 0

d efl= 1 7 5

d efl= 2 0 0

d efl= 2 2 5

d efl= 2 5 0

d efl= 2 7 5

d efl= 3 0 0


5. Effect of Changing Strength of Concrete


Fig.98: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Ultimate Strength under Central

Point Load

-10-8-6-4-20


0

10

20

30

40

50

60

70

cent

ral p

oint

load

(kN

)

fc= 2 0

fc= 2 5

fc= 3 0

fc= 3 5

fc= 4 0


Fig.99: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Ultimate Strength under


-10-8-6-4-20


0

1

2

3

4

5

6

7

8

9

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fc= 2 0

fc= 2 5

fc= 3 0

fc= 3 5

fc= 4 0


Fig.100: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Ultimate Strength under Central

Point Load

-160-140-120-100-80-60-40-200


0

50

100

150

200

250

300

cent

ral p

oint

load

(kN

)

fc= 20

fc= 25

fc= 30

fc= 35

fc= 40

Fig.101: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Ultimate Strength under


-200-160-120-80-400


0

10

20

30

40

50

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fc= 20

fc= 25

fc= 30

fc= 35

fc= 40

-300-250-200-150-100-500


0

100

200

300

400

500

600

700

800

cent

ral p

oint

load

(kN

)

fc= 2 0

fc= 2 5

fc= 3 0

fc= 3 5

fc= 4 0

Fig.102: Load Deflection Relationship of Restrained Reinforced Fibrous Concrete Slab with Varying Ultimate

Strength under Central Point Load


Fig.103: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Ultimate Strength


-500-400-300-200-1000


0

100

200

300

400

500

600

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

fc= 2 0

fc= 2 5

fc= 3 0

fc= 3 5

fc= 4 0


6. Effect of Changing Aspect Ratio of the Steel Fibers


-12-10-8-6-4-20


0

10

20

30

40

50

60

70

cent

ral p

oint

load

(kN

)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 0 5

Fig.104: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Aspect Ratio under

Central Point Load


Fig.105: Load Deflection Relationship of Unrestrained Fibrous Concrete Slab with Varying Aspect Ratio under


-12-10-8-6-4-20


0

1

2

3

4

5

6

7

8

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 0 5


Fig.106: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Aspect Ratio under Central Point

Load

-160-140-120-100-80-60-40-200


0

50

100

150

200

250

300

cent

ral p

oint

load

(kN

)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 05

Fig.107: Load Deflection Relationship of Restrained Fibrous Concrete Slab with Varying Aspect Ratio under Uniformly

Distributed Load

-200-160-120-80-400


0

10

20

30

40

50

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 0 5

-350-300-250-200-150-100-500


0

100

200

300

400

500

600

700

800

900

1000

cent

ral p

oint

load

(kN

)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 0 5

Fig.108: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Aspect Ratio under

Central Point Load


Fig.109: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Aspect Ratio under


-400-350-300-250-200-150-100-500


0

100

200

300

400

500

600

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

a s= 3 0

a s= 4 5

a s= 6 0

a s= 7 5

a s= 9 0

a s= 1 0 5


7. The Effect of Changing Reinforcement Steel Ratio in Restrained Fibrous Reinforced Concrete Slab

a. Changing bottom steel ratiob. Changing top steel ratio

-140-120-100-80-60-40-200


0

50

100

150

200

250

300

350

400

450

cent

ral p

oint

load

(kN

)

Fig.110: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Bottom Steel Ratio under Central Point

Load

Fig.111: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with

Varying Bottom Steel Ratio under Uniformly Distributed Load

-140-120-100-80-60-40-200


0

20

40

60

80

100

120

140

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

-100-80-60-40-200


0

50

100

150

200

250

300

350

400

cent

ral p

oint

load

(kN

)

Fig.112: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with Varying Top Steel Ratio under Central Point Load

Fig.113: Load Deflection Relationship of Restrained Fibrous Reinforced Concrete Slab with

Varying Top Steel Ratio under Uniformly Distributed Load

-220-200-180-160-140-120-100-80-60-40-200


0

20

40

60

80

100

120

140

160

180

unif

orm

ly d

istr

ibut

ed lo

ad (

kN/m

^2)

Conclusions

1.The results obtained using ANSYS software, in the analysis of steel deck plates adopting large deformation analysis (allowing for membrane action), are in agreement with the experimental tests.

7.Restraining the top plate of the steel deck plate and releasing the ribs give a structure having softening behavior at the beginning of loading but as the deformation become large the stiffening behavior appears, since the inducing of the membrane action. A reverse behavior could be gotten when releasing the top plate and restraining ribs against horizontal movement.

2.While very stiff solutions are obtained, when using ANSYS software in the analysis of fibrous reinforced concrete slabs, if compared with the experimental tests.

3.Conshell program gives very stiff solutions when Leonard's material parameters are used. But agreement with the experimental tests is obtained when the assumed material parameters are adopted.

4.For fibrous concrete slabs without reinforcement, an equivalent smeared layer for steel fibers shows good modification in the analysis results compared with other analysis results.

5.Small deformation analysis (membrane action is not allowing) could not give full load deflection curve. But it fails in a very small load compared with the experimental tests. So, conservative solution is obtained with small displacement analysis.

6.The stiffness of steel deck plate is affected by increasing the spacing between ribs for the same total weight. At the beginning of loading, the stiffness increases significantly. This is due to increasing the moment of inertia of the structure which makes the bending action be dominant. But as the deflection becomes large, the membrane action will be the dominant. So the changes in the stiffness of the steel deck plate has restricted values with increasing the spacing between ribs and keeping the same total weight.

9.In fibrous concrete slab, as the initial imperfection increases the strength of unrestrained fibrous concrete slab and restrained fibrous reinforced concrete slab increase. This is due to increasing the inclination of the induced membrane forces which increases the vertical components of them. But, when the initial imperfection increases the strength of restrained fibrous concrete slab reduces. This may attributed to formation more than one region having high tensile stresses which causes cracks in concrete slabs and reduce their strength.

8.When the initial imperfection increases the stiffness of the steel deck plate increases. This is attributed to increasing the inclination of the induced membrane forces which increase the resisting of these forces to the applied loads.

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FINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABSFINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABS

FINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABS.

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Transcript of FINITE ELEMENT ANALYSIS OF MEMBRANE ACTION IN STEEL DECK PLATES AND FIBROUS CONCRETE SLABS.