Al Ain University (AAU)
College of Engineering (CoE)
Mechanics (0111211)
Final Takehome Exam
(Term paper)
Student ID
Student Name
Spring Semester
2019–2020
Sunday/Monday
April 26/27, 2020
Class time
2
0
1
7
1
0
8
Abdulrahman Ibrahim Elshinawy
Component
Course Learning
Outcomes (CLO)
Total
Mark
Organization
1, 5
5
Language
1, 5
2.5
Ideas
1, 5
2.5
Analysis
1, 5
5
Presentation
1, 5
5
8
6
Student
Mark
Instructions:
1. The objective of the term paper is to teach you how to write and present professional
technical paper relevant to the knowledge you acquired in this course.
2. Each student will choose a subject related to the course and find two online papers about
the subject you select and write a technical paper summarizing those two papers as
explained in the next page.
3. The term paper must be 6 pages (single line spacing, 12-point font, Time New Roman).
4. The term paper is expected to be professional in terms of formatting, presentation of the
technical information and data, and citation of the references.
5. The term paper is due on Sunday April 26 for AD students and Monday April 27 for AA.
6. Each student will have about 5 minutes to present the term paper.
7. Use this page as the cover page and write your name and your student id above.
1
Beam bending behavior
By Abd ulrahman Ibrahim Elshinawy
Abstract
Today's, rather than steel reinforcements, Fiber strengthened compound (FRP) rebars are
exploitation within the ferroconcrete structures. Moreover, by comparison FRP and steel rebars,
exploitation the FRP rebars reduced stiffness and enhanced the load capability. Six of the beams
performed as T-shape during which 3 of them strengthened with FRP rebars and 3 others were
strengthened with steel rebars. In this analysis, a twelve ferroconcrete T-shape beams were
shapely exploitation ABAQUS finite component software package. Because the same as initial
six beams property, alternative six beams outlined by rectangular performance. The results
showed that, the stiffness of T-shape beam is far over the beams with rectangular performance.
Because of skinny skins and soft core, it's apt to native indentation inducement the concurrence
of geometrical and material non one-dimensionality in a sandwich structures. Additionally, it's
found that no native indentation arises at the start, whereas later that will increase step by step
with loading displacement increasing. The peak of the mid-span section additionally as loadcarrying capability decreases considerably with native indentation depth increasing. A changed
formulation for the instant at mid-span section of sandwich beams below massive deflection is
bestowed, and energy absorption performance is assessed supported energy absorption potency.
Within the paper, finite component simulation is employed to research the bending behavior of
light-weight sandwich beams below massive deflection.
Introduction
Lightweight sandwich constructions area unit usually manufactured from 2 skins warranted with
a light-weight Core that has high specific rigidity and strength. Because of skinny skins and
weak core, sandwich Constructions area unit apt to native indentation, which might lower loadcarrying capability of the structures. Yu etc.al. Found that the quasi-static response of sandwich
beams can be well foreseen by a changed Gibson’s model, and therefore, the force-displacement
relationship below impact loading is incredibly from that below quasi-static loading [1].
Additionally, another investigation showed that sandwich beams had a better impact resistance
than a monolithic beam, and honeycomb cores sandwich beams reveal primarily giant
international deformation, whereas the froth core sandwich beams tend to native deformation and
failure [2]. Recently, Hao etc. al. developed a theoretical model to predict the bending response
of sandwich beams below giant deflection considering native indentation result that agrees well
with numerical and experimental results [3]. According to elastic-plastic response of fabric,
many analytical models were developed to examine native indention behavior of sandwich
constructions, as well as elastic beams [4-5], elastic membrane [6] and plastic membrane [7-9],
all placed on rigid-perfectly plastic foundation wherever elastic deformation of core material
were neglected. With respect to bending behavior of sandwich beams, two analytical ways were
utilized. In one way, native indentation was neglected, and therefore, the height of cross section
2
of sandwich beams was thought-about to be constant. Within the alternative approach, the
influence of native indentation on the world bending behavior was thought-about [10-11].
Topping, etc. al. investigated the bending behavior of sandwich beams considering the influence
of flexural rigidity of core material [12-13]. Additionally, Associate in nursing analytical model
was developed for bending behavior of clamped sandwich beams below a focused load,
considering the influence of native indention on international bending. The results indicated that
the structural response can be divided into 3 stages: difficult elastic-plastic Response, yielding
below the action of moment and axial force, and tensile dominated by membrane force [14].
Within the paper, finite component simulation was wont to study the bending behavior of
simply-supported sandwich beams below giant deflection. A changed formulation for the instant
at mid-span section of sandwich beams below giant deflection is given, and therefore, the
development of characteristic of native indentation with loading displacement is disclosed
supported numerical results. Generally, strengthening by Fiber strengthened chemical compound
(FRP) has been victimization to extend to load capability and plasticity of ferroconcrete
structures. Gregoria et al. (2018) used the failure criteria to predict the shear capability of
ferroconcrete beam. He tested one management beam and 9, retrofitted beams that the results
showed that the wrapping up the tensile faces of beam had super performance in increasing
flexural capability. Their results showed that the plasticity of beams retrofitted in shear and
flexural space reduced and deflection of retrofitted beams compared with beams while not
retrofitting was similar. Naseri et al. (2009) evaluated the shear and flexural criteria of RC beams
retrofitted by GFRP sheets. Tang et al. (2006) studied on the flexural behavior of RC beams
retrofitted by FRP bars victimization NSMR methodology. Nayak et al. (2018) had experimental
take a look at on RC beam outwardly retrofitted by GFRP. Soleimani et al. (2015) and Roudsari
et al.
Methodology
In one way, native indentation was neglected, and also the height of cross section of sandwich
beams was thought-about to be constant. Additionally, associate degree analytical model was
developed for bending behavior of clamped sandwich beams underneath a focused load,
considering the influence of native indention on world bending. Within the paper, finite component
simulation was wont to study the bending behavior of simply-supported sandwich beams
underneath massive deflection. In his experimental analysis, the result indicated that victimisation
this methodology increased the load capability and also the tensile behavior of beam. Naseri et
al.evaluated the shear and flexural criteria of RC beams retrofitted by GFRP sheets. Tang et al
studied on the flexural behavior of RC beams retrofitted by FRP bars victimisation NSMR
methodology. Due to thin skins and weak core of sandwich beams, the load especially concentrated
load tends to result in local indentation. Cal indentation depth and global bending deflection, i.e.
moreover, the height of the mid-span section would decrease gradually under a concentrated load,
which leads to a plastic hinge at mid-span section. Due to weak core, sandwich beams are apt to
local indentation under concentrated loads, which makes the height of cross section decrease
3
gradually. In this research the behavior of two different groups of RC beams have been
investigated. The first group includes GFRP bars and the second group contains steel bars which
in each group the beams have been designed as rectangular and T-shape performance. In the term
of geometry, the total length of the beams is considered 4 meters with simple support at both ends.
Results and Analysis
A sketch of sandwich beams loaded underneath three-point bending was shown in Figure one,
wherever the thickness of the skins which of the core area unit h and c severally.
Figure 1. A sketch of sandwich beams under three-point bending
Finite Element Models
The mechanical properties of skin material was derived from the stainless-steel Cr18Ni8 within
the paper [15]. The modulus and also the Poisson magnitude relation of that area unit 200GPa and
zero.3 severally. The core material was thought-about as auriferous foam. Auriferous foams area
unit typical light-weight materials, wide wont to fabricate sandwich constructions. Mechanical
property of auriferous foam was typically thought-about in reference to denseness, and also the
property of its matrix material. Elaborated mechanical properties of auriferous foam can be
documented to the literature [8]. The same basic setup of finite component models as that within
the paper [8] was established, including component sort, contact condition, etc. aside from
boundary conditions. The radius of the loading head and bearings were each set 5 mm, and
different parameters elect within the models were listed in Table one, wherever ρc and ρs area unit
density of froth which of its matrix material, severally. The means of the signal SH1M1 was
outlined as follows. As an example, H1indicated the thickness of the skins was 1 mm, and money
supply meant the primary sort cores material, and so on.
4
Symbol
SH1M1
SH1M2
SH2M1
SH2M2
Table 1. The parameters selected in the FE models
span
Width Thickness Thickness Properties of metallic foam
L/mm
b/mm
of core
of skins
ρc/ρs
Ec/
σc
c/mm
h/mm
GPa /MPa
200
30
20
1
1
2
2
0.05
0.1
0.05
0.1
0.235
0.941
0.235
0.941
1.245
3.523
1.245
3.523
Load-carrying capability of sandwich beams below giant deflection
Below the loading mode of three-point bending, the load-carrying capability originates from
bending resistance at mid-span cross section. Once the loading displacement is little, the instant
at mid-span section can be calculated by.
M0 =PL/4
Due to skinny skins and weak core of sandwich beams, the load particularly focused load tends
to end in the native indentation. Thus, total displacement of the loading head U would be
composed of native indentation depth δ and world bending deflection △, i.e.U = +∆ δ. Moreover,
the peak of the mid-span section would decrease bit by bit beneath a focused load that ends up in
a plastic hinge at mid-span section. With the displacement increasing, the reaction force between
sandwich beams, and also the bearings not erected upward, which might vary with the beams
rotating.
The development, and influence of native indentation
Due to weak core, sandwich beams are apt to native indentation underneath targeted masses
that makes the peak of cross section decrease bit by bit. Figure five, offers the displacement of
the highest and bottom skin at mid-span section, whose distinction is native indentation depth,
i.e. δ=Utop-Ubottom. It may be seen that the event of native indentation may well be roughly
divided into 2 stages. Initially, the displacement of the highest and bottom skin is a close to
identical, and no native indentation arises. With loading displacement increasing bit by bit,
native indentation depth in addition because the sectional height unceasingly will increase.
5
Modeling in ABAQUS
By considering 3D modeling in this research, the concrete damage plasticity model is used to
define the concrete behavior. Moreover, the beam is defined as solid part with C3D8R meshing
family which R indicates the reduce integration method of analyzing. He did numerical study
using MATLAB toolbox in order to find out the compressive and tensile parameters of concrete
and the corresponding damages. The Fig. 1 showed the type of element. Also, in order to model
of longitudinal and transvers bars, the truss element is used because of the capability of having
axial load.
T-Shape Result
In the Fig .5 the result of T-shape beam models as the load-displacement diagram is shown by
comparing the S1 (low steel), S2 (intermediate steel) and S3 (high steel).As it is clear, the more
bar diameter caused more load capacity in which S3 with 2 longitudinal 36 mm bars had the
most load capacity as 108.83 KN. In addition, S1 model by having the low steel rate has the
maximum ductility.G3 model with two 36 mm diameter of GFRP bars had the maximum load
capacity in comparison of two other models.is shown the load displacement diagram of beams
with FRP bars. In Fig.6.
6
Conclusions
Based on the findings of this study, it can be concluded that:
1- Under giant deflection, world bending deformation of sandwich beams develops
related to native indentation. No native indentation arises at first, whereas later that will
increase bit by bit with loading displacement increasing.
2- In this analysis, the flexural behavior of RC beams victimization steel and GFRP
bars has been assessed:
• Victimization GFRP bars will increase load capability from eleven.19% to 48.15%
• GFRP bars improve the stiffness of RC beam
• Beams with steel bars have a higher malleability Compared with GFRP
• T-shape beam has higher performance as compared With rectangular-shape beam.
References
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beams with closed-cell aluminum-foam core in three-point bending. International Journal of
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[2] ZH Wang, L Jing, JG Ning, Zhao LM. The structural response of clamped sandwich beams
subjected to impact loading. Composite Structures, 2011; 93(4): 1300-1308.
[3] WQ Hao, JM Xie, FH Wang. Theoretical prediction for large deflection with local indentation
of sandwich beam under quasi-static lateral loading. Composite Structures, 2018, 192:
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[4] RJ Green. Penetration of Beam on Plastic Foundation. Journal of the Engineering Mechanics
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[5] PD Soden. Indentation of composite sandwich beams. Journal of Strain Analysis for
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[6] Turk MH and Fatt MSH. Localized damage response of composite sandwich plates.
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