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The basic concept of using the finite element method of analysis in constructing analytical models for the study of behavior of reinforced concrete members is discussed. The finite elements method chosen to represent the concrete, the steel reinforcement, and the bond links between the concrete and steel reinforcement are described, modeling with a proper finite element program in idealization the considered structure is greatly needed. In this paper demonstrates that the behavior of reinforced concrete cracked slabs (350x80x20) were tested under fatigue loading with 3.3 Hz 

mahran, usama mostafa

 International Journal of Sciences: Basic and 
Applied Research (IJSBAR) 
 
ISSN 2307-4531 
 
http://gssrr.org/index.php?journal=JournalOfBasicAndApplied 
 
New Numerical Study for Strengthening Slabs Behavior 
 under Repeated Loads 
 
U. M. MAHRAN 
Associate Prof., Civil Eng. Dept., Assiut University, Assiut 71516, Egypt 
 
Abstract 
The basic concept of using the finite element method of analysis in constructing analytical models for the study 
of behavior of reinforced concrete members is discussed. The finite elements method chosen to represent the 
concrete, the steel reinforcement, and the bond links between the concrete and steel reinforcement are 
described, modeling with a proper finite element program in idealization the considered structure is greatly 
needed. In this paper demonstrates that the behavior of reinforced concrete cracked slabs (350x80x20) were 
tested under fatigue loading with 3.3 Hz ( 200 r.p.m ) and had the same cross section of dimensions and main 
longitudinal reinforcement distribution and cross sections for all slabs. These slabs had four deformed 
longitudinal steel with 10 mm diameter as main steel at depth 17.5 cm, the total length of each slab was 3.5 m 
and the span length was 3.0 m, the width was 80 cm, and the total depth was 20 cm. The slabs were loaded 
under fatigue loads in two point loads [2]. Many variables have been investigated in regard to stress and 
deformation. However, due to the complex nature of the phenomenon and due to great difficulties in measuring 
the relevant properties in the vicinity of a steel bar in concrete there is still a lack of know-how and the general 
applicability of results is still insufficient. It was thought worthwhile to treat repeated load in a nonlinear 
numerical analysis by taking into account cracking and larger local deformations. If the method of material 
modeling and numerical procedure should be successful, it would be possible to treat numerous external and 
internal variables only by varying the material properties. External variables could be loading rate and 
strengthening methods, whereas internal variables could be concrete composition, strength, bar surface, and 
dimensions. In all cases, the calculation would be the same, only the input parameters would be different. The 
template is used to format your paper and style the text. All margins, column widths, line spaces, and text 
fonts are prescribed; please do not alter them. 
In this study, a special smeared crack model is adopted. The constitutive matrix used in this analysis has been 
derived in detail by reference [5]. Within this model the initiation of a cracking process at any location happens 
when a principal stress component exceeds a prescribed tensile limit [1]. 
Keywords: repairing; gluing, CFRP, shotcrete, fibershotcrete. 
------------------------------------------------------------------------ 
* Usama MAHRAN. Tel: +20-1062489624; fax. +02-0862364636 
Email address: usamhrn1@yahoo.com 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
. 
1-Introduction 
An important characteristic of concrete is its cracking behavior at low tensile stresses. The cracking of concrete 
is a major factor contributing to the nonlinear behavior of reinforced concrete structures. Realistic theoretical 
analyses taken into consideration, the cracking in concrete even under service loads. The cracking in concrete 
structures have widely been modeled in finite element analyses and some fumes program like ABAQUS. As 
discussed in reference [3], the authors are of opinion that the steel strain εs is so far not yet considered in any 
other formulation. 
2- Material response characteristics of the elements (CPE4) 
In this study, we have used solid continuum elements 4- node blinear elements for concrete elements. These 
elements have two degree of freedom 1, 2 and four faces for plane stresses. The description of the interface 
element was adopted in ABAQUS program which developed by reference [6] and for steel truss elements were 
used, The Lagrange multiplier method is usual approach for contact constraints in this type of element. The 
friction forces acting on the contact area follow Coulomb's law.   
3- Concrete 
As the loading changes from uniaxial to triaxial stress states, a unified approach is advantageous when selecting 
a constitutive model for concrete. Such as model was proposed recently by Ottosen [4] and is adopted herein. 
The model is quite simple to work with, as it is based on nonlinear elasticity, in which the secant values of 
Young's modulus and Poisson's ratio are changed appropriately. This alternation is obtained through use of a 
nonlinearity index that relates the actual stress state to the failure surface. This model has a number of desirable 
features:- 
-It includes the effect of all three stress invariants. 
-Dilatation is considered. 
-Completely smooth stress-strain curves are predicted. 
-Realistic failure stresses are predicted. 
-Different post-failure behavior can be easily simulated. 
The model applies to all stress states including those where tensile stress occurs. In addition, calibration of the 
model requires only simple data. These data are obtained usually by standard uniaxial tests of the concrete in 
question. The construction of the model can be conveniently divided into steps:-  
(1)- Failure and cracking criteria. 
(2)- Nonlinearity index. 
(3)- Change of the secant value of Young's modulus. 
(4)- Change of the secant value of Poisson's ratio. 
4- Results  
4.1Slabs strengthening with Carbon Fibers 
The stress and displacements curves for beams are shown in Fig. 1 to Fig 3. Fig 1 shows total displacements 
and other curves observed(u1)and (u2). Fig. 4 to 5 observed the stresses σ1,  σ2 for slabs strengthening with 
Carbon Fibers. Fig. 6 the vertical displacement with time but  Fig. 7 discusses support reaction Rft reflects the 
influence of external load with time for slabs strengthening with Carbon Fibers. 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
Fig. 1 The vertical displacement(u1) of the Slabs Strengthened with Carbon Fibers 
 
Fig.2 The vertical displacement (u1) of the strengthening slabs with Carbon Fibers 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
 
 Fig.3 The horizontal displacement (u2) of the strengthening slabs with Carbon Fibers 
 
 Fig.4 The horizontal stresses (σ1) of the strengthening slabs with Carbon Fibers 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
Fig.5 The vertical stresses (σ2) of the strengthening slabs with Carbon Fibers 
 
Fig.6 Vertical displacement and time (u2) of the strengthening slabs with Carbon Fibers 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
 
Fig.7 Vertical support reaction and time (Rft) of the strengthening slabs with Carbon Fibers 
 
The figures show the strengthening slabs with Carbon Fibers increased fatigue strengths and also increased the 
resistance of the slabs with wider cracks compared with the other strengthening systems.  
This is due to the very high tensile strength, the modulus of elasticity and ductility of the Carbon sheets.  
4.1 Slabs strengthening with Shotcrete and Fibershotcrete 
The stress and displacements curves for beams are shown in Fig. 8 to Fig 10. Fig 8 shows total displacements and 
other curves observed (u1) and (u2). Fig. 11 to 12 observed the stresses σ1,  σ2 for slabs strengthening with 
Carbon Fibers. Fig. 13 the vertical displacement with time but Fig. 14 discusses support reaction Rft reflects the 
influence of external load with time. for slabs strengthening with shotcrete and Fibershotcrete.  
In the analyzing I take the half of the slabs for reduce the number of mesh elements, due to the symmetry of the 
slab under the vertical loads and in figures the support reaction instead of the vertical loads  
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
Fig. 8 The vertical displacement(u1) of the Slabs Strengthened with Shotcrete 
 
 
Fig.9 The horizontal displacement (u2) of the strengthening slabs with Shotcrete 
 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
Fig.10 The vertical displacement (u3) of the strengthening slabs with Shotcrete 
 
 Fig.11 The horizontal stresses (σ1) of the the strengthening slabs with shotcrete 
 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
Fig.12 The vertical stresses (σ2) of the strengthening slabs with shotcrete 
 
Fig.13 The vertical displacement and time (u2) of the strengthening slabs with shotcrete 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
  
Fig.14 The vertical support reaction and time (Rft) of the strengthening slabs with shotcrete 
The fatigue resistance. and due to big contact areas between the old concrete and both SpB and FSpB decrease 
of the induced shear stress in the contact layers between old concrete and both SpB and FSpB.and subsequently 
the slabs fatigue resistance big number of cycles. 
4-Comparison with the experimental results 
Fig. 7 and Fig. 14 show that the support reaction Rft reflects the influence of external load. The curves in this 
figures indicate that the numerical analysis is in good agreement with experimental results. Also, this figures 
clearly indicates that the reactions change with the time decreasing and increasing with time depending on the 
resistance of the slabs against the repeated loads. The mean load between the minimums am and maximums 
peak loads decrease with the time or after the big number of cycles.  
 
By the same manner the mean of total vertical displacement which take the same trend in the experimental 
results, that is attained, increases significantly with time or number of cycles. as shown in Fig. 15 to Fig. 17. 
Figures clear  that in the experimental test start statically and then release to zero and the fixed static 
displacement, after that the repeated loads start, so this gain static displacement  fixed all over the test slab 
process plus to the dynamic displacement which call total displacement or deflection.  
 
 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
0
5
10
15
20
25
0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 1.00E+06 1.20E+06 1.40E+06 1.60E+06 1.80E+06 2.00E+06
No of cycles
D
ef
le
ct
io
n 
m
m
 
static
dynamic
total
 CW 
 theoretical def 
 
Fig.15 Deflections at middle point and Number of cycles for Slab Strengthening by CFRP 
. 
0
5
10
15
20
25
0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 1.00E+06 1.20E+06 1.40E+06 1.60E+06 1.80E+06 2.00E+06
No of cycles
De
fle
ct
io
n 
m
m
 
dynamic
static
total
theoretical
 def  mm
theoretical def 

 
Fig.16 Deflections at middle point and Number of cycles for Slab Strengthening by  SpB 
. 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
 
0
5
10
15
20
25
0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 1.00E+06 1.20E+06 1.40E+06 1.60E+06 1.80E+06 2.00E+06
No of cycles
D
ef
le
ct
io
n 
m
m
 
0.0
5.0
10.0
15.0
20.0
25.0
total
static
dynamic
theoretical
def. mm
theoretical def
 
Fig.17 Deflections at middle point and Number of cycles for Slab Strengthening by FSpB 
5- CONCLUSIONS 
The slab was strengthened with an insufficient area of Carbon sheets; had less fatigue strength and wider crack 
widths. For this reason good strengthening with systems must have sufficient areas of carbon sheets and these 
areas must be calculated to give the permissible defections for the reinforced concrete strengthening elements. 
Slabs were strengthened by externally bonded plates of carbon fiber reinforced plastics    ( CFRP ) is gaining 
ground due to its advantages over the strengthening with steel plates, slabs were strengthened by 4 deformed 
bars 10 mm diameter with 2.8 m length and fastened at the ends, then shotcrete applied or Fibershotcrete. 
From the above figures, the suggesting formula in the two dimensional for numerical modeling gives results 
closer to the experimental work in cracking loads, ultimate loads, displacements and the longitudinal and lateral 
strains are smaller[5]. 
REFERENCES 
[1] G. K. Schullerer. “A Numerical Investigation for the Analysis of  Fiber Reinforced Composites with 
Respect to Macromechanical and Micromechanical Modeling”. M.Sc. thesis, Innsbruck (Austria), Nov. 
(2000). 
[2] Usama M., “Study of Strengthening and Repairing of Reinforced Concrete Constructions by Using New 
Different Techniques, Methods and Materials”, PHD thesis, Innsburuk (Austria), Dec. (2000). 
 
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 International Journal of Sciences: Basic and Applied Research (IJSBAR) (2010) Volume 2, No  1, pp 9-21  
[3] CEB, "Concrete Structures under Impact and Impulsive Loading," Bulletind' Information No. 187. comito 
Euro-International du Beton. Lausann, 8/1988. 
[4] Ottosen, N. S., "Constitutive Model for Short-Time Loading of Concrete; ASCE Journal of  the 
Engineering Mechanics, V. 105, No. EM1, 1979, pp.127-141. 
[5] Schlüter, F H. "Dicke Stahlbetonplatten unter stoßartiger Belastung (Flugzeugabsturz),"  Massivbau und 
Baustofftechnologie Karlsruhe, Heft 2, Germany, 1987. 
[6] Hibbitt, Karlsson; and Sorensen, "ABAQUS User's Manual," Software Finite Element Program, V. 1 and V. 
2,  Version 4.9, 1992.   
 
 
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New Numerical Study for Strengthening Slabs Behavior  under Repeated Loads

Cold-formed structural members are being used more widely in routine structural design as the world steel industry moves from the production of hot-rolled section and plate to coil and strip, often with galvanised and/or painted coatings. Steel in this form is more easily delivered from the steel mill to the manufacturing plant where it is usually cold-rolled into open and closed section members. The present experimental study is on the effect of infilled Normal Concrete and Geopolymer concrete only at the joints in cold formed tubular sections and which may increase the load carrying capacity of the joints. In present study strength of the joint is increased by infilling different grades of concrete in the tubular specimens the joints with single number of bolts at the connection. This work presents number of experimental tests have been carried out on cold formed tubular tension members fastened with bolts, to calculate the failure capacity and increase in strength of the member and also to trace the entire load versus Strain/Elongation so that the behavior of the connection is examined and also MATLAB used for calculation of maximum loads for various thicknes

Deshamukh, Satalingappa

Experimental Study of Bolted Connections Using Light Gauge Rectangular Hallow Section, Normal Concrete and Geopolymer concrete Infilled only at the Joints

Not a member yet

New Numerical Study for Strengthening Slabs Behavior under Repeated Loads

Experimental Study of Bolted Connections Using Light Gauge Rectangular Hallow Section, Normal Concrete and Geopolymer concrete Infilled only at the Joints

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