Flexural Analysis of Axially Restrained Ferro cement Slab ... 2/Issue 6/IJESIT201306_13.pdf ·...

ISSN: 2319-5967

ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT)

Volume 2, Issue 6, November 2013

115

Abstract— Ferro cement slabs having end restraints may achieve a load capacity different from those which are axially

unrestrained. Consequently, analytical models proposed for flexural analysis of Ferro cement slabs may fail to predict the

load capacity of slabs that are axially restrained against movement. In this paper a classical method for the analysis axially

restrained slabs is modified and assessed as to its ability to predict the behavior of axially restrained Ferro cement slabs.

The ultimate load based on this method grossly over predicted the slab strength mainly due to neglecting the role of

important parameters such as elastic curvature and large deformation. A new approach based on the elastic and

elastic-plastic behaviors of materials, large deflection and stability of the thin section slab strip was proposed for analysis.

Both the ultimate load and the load-deflection response calculated using the proposed large deflection elastic- plastic

method was found to be quite accurate and the obtained test / calculated ultimate load was found to be 1.05. Accordingly,

the proposed analytical method can be used for calculating accurately the load capacity of axially restrained one way Ferro

cement slabs having span / depth ratios up to 58.

Index Terms— Curvature, Deflection, Ferro cement Slab, Stability.

I. INTRODUCTION

It is experimentally evident that in the case of fully axially restrained slabs, the ultimate load capacity is

considerably higher than that obtained using yield line theory. This enhancement in load has been attributed to the

effect of the induced compressive membrane action and the corresponding modification of the yield criterion [1].

Many analytical approaches have been proposed for calculating the ultimate load capacity of axially restrained RC

slabs [2]-[6]. Such methods were found to give accurate ultimate load capacity for thick slabs. Eyre [7, 8], in two

papers, presented the general concept of the maximum membrane force (MMF). The method was proposed in

order to take into consideration the effect of geometric imperfections due to instability and large deformations.

According to the MMF method, the maximum safe load occurs at the plastic deflection at which the maximum

membrane force occurs. This load is usually smaller than the peak load associated with the load-deflection

relationship. Welch [9] utilized Park and Gamble's modified rigid-plastic method [3] to develop a more general

solution for axially restrained reinforced concrete slabs. The peak thrust according to compressive membrane

theory occurs when the axial shortening of the slab and outward support movement (if the end supports are partially

restrained) are at a maximum. It is demonstrated that estimating the peak thrust using a modification of Park and

Gamble's theory gives an improved correlation with experimental data for a range of span to depth ratios (L/h)

between 2.7 and 28.3[9].

Since Ferro cement members are characterized as thin sections with large values of L/h, the methods proposed for

analyzing axially restrained slabs may not be accurate for calculating the ultimate load capacity. This is due to the

fact that thin sections usually suffer from large elastic deformation and instability due to flexural buckling.

In this paper, simply supported ferrocement strips are analyzed as thin slabs. These strips are fully reinforced with

wire mesh without skeletal reinforcement. The span / depth ratio of the slabs was larger than 22 which Welch [9]

considers to be the limiting ratio for a thin slab. The proposed method for calculating the load-deflection

relationship is essentially based on consideration of the elastic and plastic responses of the slab materials and its

geometrical flexural instability.

This paper presents a method for determining the capacity of thin, axially restrained, ferrocement slabs. Prior to

presenting the final method of analysis, the possibility of using a modified form of rigid plastic analysis is

considered. This approach is presented in section II. The more appropriate large deflection elastic-plastic method

is presented in section III and is found to correlate well with the experimental results.

Flexural Analysis of Axially Restrained Ferro

cement Slab Strip Azad A. Mohammed, Yaman S. Shareef

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II. MODIFIED RIGID- PLASTIC ANALYSIS

Since the width / thickness ratio of one-way slabs is large, the lateral buckling is not an issue and shear stress and

shear deformation are relatively small. Therefore, developing analytical methods are easier for one way slab or slab

strips as compared with the other types of slabs. The rigid plastic analysis approach was proposed basically for RC

slabs of relatively thick sections and here it will be tested for its accuracy when applied to ferrocement slabs which

are usually thin. The modified rigid-plastic approach proposed by Park and Gamble [3] in its basic form has been

used for deriving the geometrical compatibility relationship. The yield criterion adopted is that proposed by

Mansur [10] for ultimate stress distribution of ferrocement slabs.

A. Geometrical Compatibility Condition

A consideration of the compatibility of deformation of a rigid portion of slab strip leads to the following equation

based on the depths of compression zone as derived below.

cL

bLhc

2

4

2

2

(1)

The above value of cwas derived by Park and Gamble [3] and can be used for ferrocement slab analysis because

it is based on compatibility of deformations and independent on cross-section properties.

B. Stress Distribution for Yield Criterion

The method proposed by Mansur [10] (Method B) for calculating the moment capacity of a ferrocement section

uses the familiar rigid-plastic concept. The ferrocement wires are uniformly distributed throughout the

cross-section of the element. The plastic compressive stress is taken as 0.85f c. Fig. 1 shows the stress distribution

at ultimate stage for the ferrocement section.

C. Yield Criterion

For a simply supported axially restrained one-way ferrocement slab, equilibrium of forces acting on the section

shown in Fig. (2) leads to:

fTsTCC

(2) Where:

sT is the tensile forces in the skeletal steel reinforcement )( yfsAsT .

fT is the tensile force due to the ferrocement wire mesh )]([ chtuf

fT , and

C' and C is the compressive force acting at the ends of the strip given by the following two equations

cc

fC 85.0 (3)

ccfC 85.0 (4)

Substituting Eq. (3) and Eq. (4) into Eq. (2) and rearranging, gives

cc (5)

In which and are stress parameters having the following values:

cf

tufcf

85.0

85.0 , and

cf

htufyfsA

85.0

Solving Eq. (1) and (5) simultaneously provides

1

2

4

2

2

L

bLh

c (6)

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The axial shortening and support movement (b

) in Eq. (6), are related to the axial force uN as follows

chE

uN ,

S

uN

b and cES 1.005.0

in which S is the stiffness of the end restrained.

Fig. 1 Stress distribution across the ferrocement section Fig. 2 Rigid portion of slab strip of axial deformation

at collapse ( Mansur[10]) (Park and Gamble[3])

cE is the composite modulus of elasticity. According to Shah and Balaguru [11], cE can be calculated as follows

nRL

VmEcE 1

For the welded wire mesh, both directions are considered as a main direction (i.e. RTVRLV ) and RLV can be

calculated according to the equation proposed by Walraven and Spiereburg [12] as follows:

hLs

iNsfA

RLV 7.1

n is the modular ratio given by

mE

REn

where

RLV is the volume fraction of reinforcement in the longitudinal direction

sfA is the cross-sectional area of one wire (

2mm ).

iN is the number of layers of wires.

sL is the spacing of wires ( mm).

h is the thickness of the cross-section ( mm).

n is the modular ratio.

RE is the modulus of elasticity of reinforcement.

mE is the modulus of elasticity of mortar.

When

L

b2

is a maximum, the thrust is a maximum and this indicates the peak capacity.

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uNLSchEL

b

S

uN

LchE

uN

L

b

21222

Therefore, Eq.( 6 ) becomes

uNLSchE

Lh

c14

212

1

2

( 7 )

But

cc , on substituting

uNLSchE

L

hc14

212

21

( 8 )

Let

21

1

h , and

14

212

LSchEL

Both Eqs. (7) and ( 8 ) can be simplified to

uNc (9)

uNc (10)

The concrete compressive force C at a negative moment zone at the end [Fig. 2] for a strip of unit width is

statically equal to the compressive membrane force uN , or

ccfuN 85.0 (11)

Substituting Eq. (10) into Eq. (11) leads to calculating the membrane force uN per unit width of the slab as

follows:

LSchE

Lcf

cfhcf

uN

21

4

285.0

1

85.02

85.0

(12)

The moment per unit width in the center of the slab is:

c

hchchtuf

chccf

hdyfsAuM

222285.0

2

Or

22285.0

2

cchtuf

chccf

hdyfsAuM

On substituting Eq.( 9 ) and simplifying,

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2

2

2

85.02

85.0

85.022

NutufcfNuh

tufcf

htufcfh

dyfsAuM

(13)

The moment per unit width of the slab at the supports is given by:

2285.0

chccfuM

On substituting Eq. (10) and simplifying, the following equation is obtained

22

22

22

425.0

Nu

uNhhh

cfuM

(14)

For the end portion of the rigid – plastic slab strip, the sum of the moment for calculating the internal work is taken

as

uNuMuM .

For a slab strip under two central line load ( 2/uP ), the external virtual work is:

auP

WE2

..

while the internal virtual work is given by:

uNuMuMWI ..

On substituting the expressions for each of the force and moment terms, the I.W. becomes

22185.0

2

2

212

122

85.0

2

22

21

21

2

85.0

22..

uNcftuf

uNhcfh

tuf

hhcf

htufh

df

fsAWI

(15)

Equating the internal and external virtual work leads to

uNuMuMauP

2

Or

uNuMuMauP

2

The value of Pu then becomes

uNuMuMa

uP 2

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The final load-deflection equation can be written as follows

22185.0

2

2

212

122

85.0

2

22

21

21

2

85.0

22

2

uNcftuf

uNhcfh

tuf

hhcf

htufh

dyfsA

auP

(16)

Where

uP is the ultimate load (N/mm).

a is the shear span ( mm).

sA is the cross sectional area of steel (2

mm /mm).

d is the effective depth of steel ( mm).

h is the slab thickness ( mm).

tuf is the ultimate tensile strength (2

N/mm ).

,,, are stress parameters for modified rigid-plastic analysis.

cf is the concrete cylinder strength (2

N/mm ).

uN is the membrane force acting at mid-span (N/mm).

Hence the load-deflection relationship of ferrocement slab strip can be obtained using Eq. (16) and Eq. (12).

It should be noted that for the case of reinforced concrete slab strips the derived load-deflection relationship has

been suggested as being likely to accurately predict behavior when sufficient deformation occurs (i.e. is

sufficiently large) to allow full plasticity to develop at the critical section. Moreover, the load-deflection

relationship is only valid when the membrane force is compressive (Nu is positive) and when Nu become zero the

analysis is stopped.

III. LARGE DEFLECTION ELASTIC- PLASTIC METHOD

The most important shortcoming of modified rigid-plastic analysis when applied to axially-restrained thin slabs is

that it neglects elastic curvature and the significant deformations due to flexural instability. There is no doubt that

the rigid-plastic approach was proposed for analysis of thicker reinforced concrete slabs and it is expected to be not

accurate when compared with the test results for axially restrained ferrocement slab strips. This will be

demonstrated later. In this section of the paper, an alternative model is developed based on plate theory taking into

account the effect of in-plane compressive membrane forces on deformation. To simplify the derivation, the

ferrocement section is considered to be fully reinforced with wire mesh only and to have no skeletal reinforcement.

First, the moment-curvature relationship is derived taking into account the successive cracking stages that occur as

the curvature changes as well as the material characteristics in both tension and compression.

A. Idealized Stress- Strain Relationship

The idealized stress-strain relationship for ferrocement in compression is shown in Fig. (3-a). The role of wire

meshes in compressive stress is not included because it was found to be insignificant as demonstrated by many

researchers. Fig. (3-b) shows the idealized stress-strain relationship of ferrocement in tension, which is based on

three stages: elastic, elastic-plastic and plastic stages.

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Fig.3 Idealized stress- strain relationship of ferrocement: (a) in compression (b) in tension

B. Moment- Curvature Relationship for Elastic Stage

Figg. 4 illustrate the stress and strain distributions associated with the elastic and elastic-plastic stages at the critical

section at mid-span of a slab strip. The depth of the neutral axis, c, can be obtained using equilibrium of forces

acting on the section. The summation of forces acting on the section is equal to the vcompressive membrane

force N .

0

0c

chNydycEydycE

Solving and simplifying the above equation lead to the following equation:

hcE

Nhc

2 (17)

in which:

h is the slab thickness. N is the compressive membrane force per unit width of the slab. cE is the composite

modulus of elasticity, calculated as for modified rigid-plastic analysis and is the curvature. The limiting or

critical value of curvature is related to the first cracking strain and for the linear strain distribution is as follows

ch

crcr

In which

Ec

rfcr

and

cr is the cracking strain and rf is the modulus of rupture.

According to ACI 318M-05 Code [13]

cfrf 62.0

The flexural moment curvature relationship for this stage is given by

0

0

22

c

chdyycEdyycEeM

Upon integration, the above equations becomes:

hcchhcE

eM2

32

33

3

(18)

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Fig.4 Stress and strain distribution acting on ferrocement section for different cracking stage

C. Moment- Curvature Relationship for Elastic- Plastic Stage

Fig. 4 shows the stress-strain distribution for this stage. Once again, the depth of the neutral axis can be obtained

from equilibrium of forces:

ch

hc

Ndycry

crtu

rftufhcydycE

c

ydycE

0

0 (19)

Let

crtu

rftuf

By integrating and then simplifying the above equation, the depth of neutral axis is given by the following quadratic

formula

cE

hcrhcEcr

NcEhcrcrh

c

2

2

12

2

222

(20)

and the flexural moment-curvature relationship is given by

dych

hcycrydyycE

hc

cdyycEepM

22

0

0 2

By integrating and simplifying the above equation, it becomes:

23

3

2

32

33

2

6

22

2

3

3

crEccrcrhh

chcrhccr

hccEepM

(21)

The elastic-plastic stage terminates when the tensile stress in the section reaches εtu (εtu = εsy) and accordingly the

curvature becomes

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ch

sy

εsy is the strain corresponding to the yield stress of wire mesh and is given by

cE

yff

sy

For thin sections this curvature is not expected to be reached because due to large elastic curvature the slab may be

unstable due to flexural buckling which limits the compressive membrane force.

D. Load- Deflection Equation for Ferrocement Slab Strip

The stresses and deflections associated with thin slabs subjected to transverse loads are directly proportional to the

applied loads. This statement is valid if the deflections are small such that the slight change in geometry produced

in the loaded slab has an insignificant effect on the loads themselves. This situation changes drastically when axial

loads act simultaneously with the transverse loads. The internal moments, shear forces, stresses and deflections

then become dependent upon the magnitude of the deflections as well as the magnitude of the external loads. They

are also sensitive to slab imperfections such as initial curvature and eccentricity of axial loads. For axially

restrained slab strip or beam subjected to two central point loads (each P/2) the deflection equation was derived by

Shareef[14] and found to have the following form:

2

16

2

4

2

2

8

2

7128

3

D

NL

D

NL

D

NL

D

LP

wo (22)

Where P and N are in mmN / and D is the flexural rigidity of the slab given by

12

3Eh

D measured in mmN.

For axially restrained slab strip the load- curvature is given by

wD

N

L

x

D

PL

dx

wd

sin

2

2

2

2

(23)

At the center of the slab strip the curvature then becomes

wD

N

D

PL

2

2

(24)

E. Calculation of Membrane Force

In order to determine the compressive membrane force (N) acting on a ferrocement slab section, it is helpful to

utilise assumptions and simplifications similar to those made for the rigid-plastic analysis. If it is assumed that the

slab strip is rigid in flexure but allowed to elastic shorten. Equilibrium of forces acting on the ends of slab portion

leads to the solution for compressive membrane force. Fig. (5) shows the rigid half strip of the ferrocement slab

between the center and one end. Equilibrium of forces is given by the following relationship:

NCf

TNC (25)

But f

TCN

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Fig. 5 Force acting on half slab strip

Therefore:

NC

or

c

NydycE0

(26)

The depth of compression zone at the end ( c ) then becomes

cE

Nc

2 (27)

From the previous equation associated with the rigid-plastic analysis, the value of c was found to be

cwchE

NLwhc

2

2 (28)

Combining the two above equations leads to the following relationship 2

2

22

cwchE

LNwh

cEN

(29)

According to the above relationship, the solution for N must be obtained by trial and error. A direct solution for

N based on equation (29) is not possible since , w and c are dependent on membrane force N . The calculation

undertaken and presented in this paper have been based on accepting an error between the left and right side of this

equation of up to 10% as this was found to result in very small change in N..

F. Procedure for Calculation Load- Deflection Relationship

The simply supported ferrocement slab strips (without the skeletal reinforcement) allowing for compressive

membrane action can now be analyzed using the above theory. In this analysis, the effects of elastic curvature, large

deflection and instability are considered. The following stepwise approach has been used to obtain the deflection,

curvature, depth of compression zone as well as the flexural rigidity for any load increment for the whole loading

history.

1- Calculate the initial flexural rigidity (D) for the uncracked ferrocement slab section.

2- Specify the first small value of load P .

3- Specify the first small value of membrane force N .

4- Calculate the deflection from Eq. ( 22 ).

5- Calculate the curvature from Eq. ( 24 ).

6- Having the values of and N , calculate the depth of neutral axis ( c ) and check the limit of for testing that

the elastic-plastic stage is reached or not.

7- Calculate the moment corresponding to the curvature and then calculate the flexural rigidity by dividing the

moment by the curvature.

8- Calculate the correct value of membrane force N using Eq. (29) and repeat steps 3 to 7.

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9- Calculate the ratio of flexural rigidity (present to initial flexural rigidity) and check that is not smaller than 10 %.

If it smaller than 10 %, the analysis is stopped indicating the end of compressive membrane action ( 0c and w=

∞) and here the section is nearly fully cracked at the center of slab strip, accepting a 10% error.

10- Repeat steps 2 to 9 for another value of load to calculate deflection, curvature, membrane force and flexural

rigidity.

IV. VALIDATION OF THE PROPOSED METHODS

Based on the above calculation steps, a computer program was developed and all necessary data were obtained.

The theoretical predictions including those of the modified rigid-plastic analysis are compared with the test results

in Table ( 1 ).

As shown from the results of the Table ( 1 ), the modified rigid-plastic predictions is not safe and not accurate for

all slabs since the mean value for the ultimate load (Test / Theory) is 0.56. The reason for this is that the method was

proposed basically for reinforced concrete slabs of thick sections and not applicable to thin slabs like ferrocement

slabs. In contrast the predictions of the proposed large deflection elastic-plastic analysis are accurate and close to

test data. The mean value for the ultimate load (Test / Theory) is 1.05 which means the predictions are safe and very

accurate.

Fig. 6 shows the load-deflection relationship for group (1) and group (3) slab strips tested by Mohammed and

Shareef [15]. For each figure there are two identical experimental curves: one curve is based on the modified

rigid-plastic analysis and the other on the large deflection elastic-plastic analysis. It can be generally seen that there

is a difference between the two theoretical predictions and the experimental curves with the elastic-plastic analysis

predictions being much closer to the experimental plots. On the other hand, the considerable difference between the

test results and modified rigid-plastic analysis results illustrate that the method is not accurate.

It should be noted that the elastic-plastic predicted maximum deflection is lower than the test one for all slabs as

shown from Fig. 6. Such results are expected because only the compressive membrane force analysis was done

( N is compressive) and the analysis was stopped when the slab was fully cracked at the center. It is well known that

this stage is not the final point of failure and the slab can carry further load as a result of tensile membrane action.

the ferrocement slab fails at a deflection value larger than that obtained from the proposed elastic-plastic analysis

due to the additional effects of tensile membrane action which is not addressed in the present paper. It is clear that

for slabs there are two stages of cracking - elastic and elastic-plastic. For very thin sections, such as slabs S1-1 and

S1-11 (h= 25 mm and span / depth ratio is 58), only very low deflections can be tolerated in the elastic- plastic stage

(not shown in the figure) before the occurrence of instability. Table( 1 ) Test and calculated load and deflection of ferrocement slab strips

Sla

b s

ym

bo

l

Tes

t δcr

,mm

Tes

t P

cr,k

N

Tes

t δp

,mm

Tes

t P

u,k

N

Car

cula

ted

δp

,mm

( R

igid

-P

last

ic)

Car

cula

ted

Pu

,kN

(Rig

id -

Pla

stic

)

Car

cula

ted

δcr

,mm

( E

last

ic-

Pla

stic

)

Car

cula

ted

Pcr

,kN

(Ela

stic

- P

last

ic)

Car

cula

ted

δp

,mm

( E

last

ic-

Pla

stic

)

Car

cula

ted

Pu

,kN

(Ela

stic

- P

last

ic)

Tes

t/C

alcu

late

d P

u

( R

igid

-pla

stic

)

Tes

t/C

alcu

late

d P

cr

( E

last

ic-p

last

ic

Tes

t/C

alcu

late

d P

u

( E

last

ic-p

last

ic)

S1-1

-

-

24

1.4

6.75

2.17

2.97

0.53

9.42

1.4

0.65

-

1.0

S1-2

-

-

24.5

1.4

6.75

2.29

2.84

0.53

8.93

1.4

0.61

-

1.0

S1-3

1.2

1.3

23

2.7

7.88

5.85

2.1

1.18

11.4

2.28

0.46

1.1

1.18

S1-4

1.3

1.38

23.4

2.9

7.88

6.36

2.05

1.24

9.5

2.33

0.46

1.11

1.25

S1-5

3.2

2.98

11.6

3.9

9.0

11.74

1.56

2.18

8.2

4.6

0.33

1.37

0.85

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0

1

2

3

4

5

6

7

0 5 10 15 20 25 30

Central deflection (mm)

Lo

ad

(k

N)

S1-3 , h=37mm , N=4 S1-4 , h=37mm , N=4 theo.(rigid-plastic)theo. (elastic-plastic)

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30


Lo

ad

(k

N)

S1-1 , h=25mm , N=3S1-2 , h=25mm , N=3 theo.(regid-plastic)theo. (elastic-plastic)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30


Lo

ad

(k

N)


0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 40 45


Lo

ad

(k

N)


S1-6

2.4 2.6 14.7 4.1 9.0 12.0 1.57 2.3 8.0 4.65 0.34 1.13 0.88

S1-11

4.2

1.46

35.4

2.1

6.75

2.54

2.97

0.52

15

2.09

0.83

2.8

1.0

S1-12

-

-

37.8

1.75

6.0

2.42

2.83

0.48

15.4

2.04

0.72

-

0.86

S1-13

-

-

34.1

4.4

7.87

7.0

1.58

2.37

13

3.98

0.63

-

1.1

S1-14

-

-

40.1

4.6

7.87

6.88

1.57

2.32

14.7

4.0

0.67

-

1.15

S1-15

4

3.65

33.9

7.7

9.0

15.56

1.56

2.52

15.8

6.62

0.50

1.45

1.16

S1-16

-

-

34.6

7.9

9.0

16.91

1.55

2.7

14.2

6.76

0.47

-

1.17

Mean

-

-

-

-

-

-

-

-

-

-

0.56

1.49

1.05

Fig. 6 shows the calculated load- deflection relationship for Groups (1) and (3) slabs obtained using elastic- plastic

method. It is obvious that both the slab thickness and wire mesh ratio considerably affects the ultimate load

capacity and the shape of load- deflection relationship. Theoretically, instability occurs momentarily. In practice,

however, failure is portended by increasing deflections with increasing load. The transition between the unstable

(flexural buckling) and the stable state (tensile membrane forces) is thus not a point but an interval. The choice of

an acceptable maximum design load is somewhat subjective.

Slab Strips S1-1 and S1-2 Slab Strips S1-3 and S1-4


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0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35 40 45


Lo

ad

(k

N)

S1-13 , h=37mm , N=8 S1-14 , h=37mm , N=8theo.(rigid-plastic)theo. (elastic-plastic)

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30 35 40


Lo

ad

(k

N)

S1-15 , h=50mm , N=10S1-16 , h=50mm , N=10theo.(rigid-plastic)theo. (elastic-plastic)


Fig. (6) Theoretical and Experimental Load-central deflection relationship of axially restrained ferrocement slab

strips

ACKNOWLEDGMENT

The material presented in this paper is a part of M.Sc. thesis undertaken by the second author to the Faculty of

Engineering, University of Duhok. Financial supports and efforts presented by the faculty are highly appreciated.

REFERENCES

[1] Ockleston, A.J., "Arching Action in Reinforced Concrete slabs", The Structural Engineer , London, England, Vol.36,

June 1958, PP. 197-201.

[2] Park, R., "The Ultimate Strength and Long-Term Behavior of Uniformly Loaded Two-Way Concrete Slabs with Partial

Lateral Restraint at All Edges", Magazine of Concrete Research, London, England, Vol.16, No.48, September 1964, PP.

139-152.

[3] Park, R. and Gamble, W.L., "Reinforced Concrete Slabs", John Wiley and Sons, New York, 1980, PP. 562-609.

[4] Janas, M., "Large Plastic Deformation of Reinforced Concrete Slabs", International Journal of Solids and Structures,

Vol.4, 1968, PP. 61-74.

[5] Robert, E.H., "Load Carrying Capacity of Slab Strip Restrained Against Longitudinal Expansion", Concrete, Vol.3, No.9,

September 1969, PP. 369-378.

[6] Desayi, P. and Kulkarni, A.B., "Load-Deflection Behavior of Restrained Reinforced Concrete slabs", Journal of the

Structural Division, ASCE, Vol.103, No.ST2, February 1977,PP. 405-419.

[7] Eyre, J.R., "Direct assessment of Safe Strengths of RC Slabs under Membrane Action", Journal of Structural Engineering,

Vol.123, No.10, October 1997, PP. 1331-1338.

[8] Eyre, J.R., "Direct assessment of Safe Strengths of RC Slabs under Membrane Action", Journal of Structural Engineering,

Vol.123, No.10, October 1997, PP. 1331-1338.

[9] Welch, R.W., "Compressive Membrane and Capacity Estimates in Laterally Edge Restrained Concrete One-Way Slabs",

Ph.D, Thesis, University of Illinois at Urbana-Champaign, 1999.

[10] Mansur, M.A., "Ultimate Strength Design of Ferrocement in Flexural", Journal of Ferrocement, Vol.18, No.4, October

1988, PP. 385-395.

[11] Shah, S.P. and Balaguru, P.N., "Ferrocement", in New Reinforced Concretes by R.N. Swamy, Bishopbriggs, Glasgow,

Survey University Press, 1984.

[12] Walraven, J.C. and Spierenburg, S.E.J., "Behavior of Ferrocement with Chicken Wire Mesh Reinforcement", Journal of

Ferrocement, Vol.15, No.1, January 1985.

[13] ACI 318M-05, "Building Code Requirements for Reinforced concrete", American Concrete Institute, 2005.

[14] Shareef, Yaman S. "Flexural Behavior of Axially Restrained One-Way Ferrocement Slabs", M.Sc. Thesis, University of

Duhok, 2008, pp. 110. ( Unpublished )

ISSN: 2319-5967



128

[15] Mohammed, A.A and Shareef, Y.S.", Tests on Axially Restrained Ferrocement Slab Strips," Journal of Duhok University,

Vol.14 , No.1 ,2010, pp.138-155

AUTHOR BIOGRAPHY

Azad A. Mohammed is an Assistant Professor in Civil Engineering Department, Faculty of Engineering, University of

Sulaimani, Sulaimani, Iraq. He received B.Sc. degree in Civil Engineering, College of Engineering, University of Baghdad

in 1994, M.Sc. degree in Structural Engineering, Building Construction Department, University of Technology- Baghdad

in 1997 and Ph.D. in the same university in 2004. He published thirteen scientific papers. Dr. Mohammed’s research has

focused on strengthening concrete structures, ferrocement structures, membrane action in slabs and inelastic behavior of

concrete.

Yaman S. Shareef is a PhD candidate in the Faculty of Engineering & Industrial Sciences, Swinburne University of

Technology. He obtained B.Sc. degree in Civil Engineering, College of Engineering, University of Duhok in 2003 and

M.Sc. degree in Civil Engineering, College of Engineering, University of Duhok in 2008. His research has focused on

strengthening concrete structures and membrane action in slabs.

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