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This article presents a concise overview on condition monitoring and retrofitting/ strengthening of structures including a practical case study of strengthening for an existing historical building. Condition assessment of an existing structure is required mainly to check serviceability and safety requirements of the structure after short term events like earthquake or long term degradation of the structure with time. It is carried out to assess the ability of a structure to perform its intended operations under changed loading conditions with time or modification in its structural system as per newly imposed requirements. The condition assessment and strengthening may also be required for integrated extension of an existing structure. After assessing the condition of the structure, either it is retrofitted (or strengthened) or it is demolished according to the severity of the damage. In this article, such a critical condition assessment for an existing historical masonry building is presented and appropriate strengthening schemes are suggested by following two separate measures (concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative advantages and disadvantages of the strengthening measures are discussed from a practical engineering perspective. Aim of this article is not to propose any new method for condition assessment and strengthening of structures, rather we take a systematic approach to demonstrate our experience. Critical case studies on condition assessment and strengthening of historical buildings with adequate technical insights are very scarce to find in scientific literature. This article would serve as a valuable reference for the practicing engineers and the concerned scientific community.
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Condition assessment and strengthening of aged
structures: Perspectives based on a critical case study
T. Mukhopadhyaya
*
, S. Naskarb, S. Deyc, A. Chakrabartid
aDepartment of Engineering Science, University of Oxford, Oxford, UK
bWhiting School of Engineering, Johns Hopkins University, Baltimore, USA
cMechanical Engineering Department, National Institute of Technology Silchar, Silchar, India
dDepartment of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee , India
Abstract
This article presents a concise overview on condition monitoring and retrofitting/
strengthening of structures including a practical case study of strengthening for an existing
historical building. Condition assessment of an existing structure is required mainly to check
serviceability and safety requirements of the structure after short term events like earthquake
or long term degradation of the structure with time. It is carried out to assess the ability of a
structure to perform its intended operations under changed loading conditions with time or
modification in its structural system as per newly imposed requirements. The condition
assessment and strengthening may also be required for integrated extension of an existing
structure. After assessing the condition of the structure, either it is retrofitted (or
strengthened) or it is demolished according to the severity of the damage. In this article, such
a critical condition assessment for an existing historical masonry building is presented and
appropriate strengthening schemes are suggested by following two separate measures
(concrete jacketing and fiber reinforced polymer strengthening). Subsequently, the relative
advantages and disadvantages of the strengthening measures are discussed from a practical
engineering perspective. Aim of this article is not to propose any new method for condition
assessment and strengthening of structures, rather we take a systematic approach to
demonstrate our experience. Critical case studies on condition assessment and strengthening
of historical buildings with adequate technical insights are very scarce to find in scientific
literature. This article would serve as a valuable reference for the practicing engineers and the
concerned scientific community.
Keywords: structural health monitoring; condition assessment; FRP strengthening;
retrofitting; concrete jacketing
*
Corresponding author: Tanmoy Mukhopadhyay
E-mail address: tanmoy.mukhopadhyay@eng.ox.ac.uk
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Introduction
Civil engineering structures are always subjected to considerable amount of risk factor
due to their continuous depreciation under time-driven operating and service environments.
The condition assessment of an existing structure is required mainly to check serviceability
and safety requirements of the structure after short term events like earthquake and fire or
long term degradation of the structure with time. Civil engineering structures are constantly
subjected to geophysical and human-induced loads during their service life. Such structures
are likely to be damaged when loads exceed the capacity of the structures. As construction of
a new structure in place of the damaged structures is not often possible due to economic
reasons (three-fold economic criteria involved with demolition of the damaged structure,
construction of new structure and loss of revenue for the interruption in important functions/
operations of the structures), a decision to repair and strengthen the existing structure can be
made at appropriate level. These situations may warrant retrofitting of the structure to
continue its intended operations. The decision for strengthening/ retrofitting is taken on the
basis of condition assessment. Condition assessment and subsequent strengthening may also
be required for integrated extension of an existing structure to investigate its capability to
bear additional loads. The purpose is to assess the ability of a structure to perform its
intended operations under changed loading conditions with time or modification in its
structural system. After assessing the condition of the structure, either it is retrofitted
(/strengthened) or it is demolished according to the severity of the damage. Plenty of studies
have been reported in the scientific literature on damage modelling (Skrzypek et al. 1998;
Nichols and Murphy 2016; Naskar et al. 2017) and damage identification (Mukhopadhyay
2018; Naskar and Bhalla 2015; Mukhopadhyay et al. 2015, 2016a) in structures.
The local strengthening of reinforced concrete members by concrete jacketing is a
common mode of retrofitting/ strengthening (Hamid et al. 1994; Bracci et al. 1997;
Lakshamanan 2006; Lee et al. 2006). The jacket generally consists of added concrete and
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longitudinal cum transverse reinforcement around the existing structural member. Such type
of strengthening improves the axial and shear strength for a column while
the flexural strength of the column and the strength of beam-column joint remain mostly
unchanged. Chipping away of concrete cover of original member and roughening its surface
is required in this method to improve the bond between the old and new concrete. Fibre
reinforced composites have attracted wide attention in the last two decades for an alternative
and efficient way of strengthening/retrofitting structural elements (JBDPA 1999; ACI 440,
2000; TCSUK 2000). Application of fibre reinforced polymers (FRP) as reinforcement for
structures has gained rapid popularity and appeal due to several advantages like affordability
of such materials compared to conventional steel reinforcement or concrete encasements,
light weightiness, high strength-to-weight ratio and better quality control (Dey et al. 2017,
2018a, 2018b; Naskar et al. 2018, 2019; Karsh et al. 2018). Moreover, the ease of handling,
lack of requirement for heavy lifting and handling equipment and corrosion resistance are
some other factors which are advantageous in the repair, retrofitting and rehabilitation of civil
engineering structures. Due to continuous research and development on new composite
materials (Dey et al. 2015, 2016a, 2016b, 2016c, 2016d, 2016e, 2016f; Mukhopadhyay et al.
2016b), the use of such materials is found to be advantageous in terms of weight-sensitivity
and cost-effectiveness. The confinement of reinforced cement concrete (RCC) columns by
FRP jackets enhances their strength and ductility. Several researches have been carried out
around the world on this issue concerning the enhancement of structural performance by
means of FRP (Teng et al. 2000; Antonopoulos and Triantafillou 2003; Bacque et al. 2003;
Choi and Xiao 2010; Minicelli and Tegola 2007; Sundarraja and Rajamohan 2009; Smith
and Kim 2009; Bank 2006; Kezmane et al. 2016) and it is expected that the design criteria
will continue to enhance as the results of these research and development become known in
the coming years based on optimal utilization of available resources.
In general, long-term field data are required to accurately predict the life of FRP
strengthening systems. The respective design guidelines can be benchmarked to account for
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environmental degradation and long-term durability by suggesting reduction factors for
various working environments. The load-carrying capacity of the existing structure is
required to be assessed based on the information gathered in the field investigation, the
review of design calculations and drawings, and as determined by analytical or other suitable
methods. Load tests or other methods can be incorporated into the overall evaluation process
if deemed appropriate. However, due to variety of structural conditions during the
construction and operational phase, it is not easy to develop general rules for retrofitting.
Every strengthening/ retrofitting process for building needs to adopt specific approaches
depending upon the structural deficiencies. In the detail retrofitting scheme, it must comply
with the latest building codes. The results generated by adopting retrofitting techniques
should fulfil the minimum requirements prescribed by the building design codes such as
deformation, detailing strength etc. Practical case studies on condition assessment and
strengthening of civil engineering structures (particularly buildings) are very scarce to find in
literature (Teworte et al. 2015; Bergamo et al. 2014; Livina and Perry 2017; Hadianfard et al.
2017; Alessandri and Turrioni 2017; Cosenzo and Ivervolino 2007; Valluzzi et al. 2005;
Verma et al. 2016), even though such studies can be valuable references for practicing
engineers and the concerned scientific community. The present article provides a case study
on structural condition assessment of an existing building including comprehensive technical
discussions. Thereby detail strengthening schemes based on two different approaches are
presented for the deficient structural members. Aim of this article is not to propose any novel
methodology for structural retrofitting; rather we focus on rendering a practical perspective
on this subject. The paper hereafter is organized as: I. brief overview on the technical details
of strengthening structural members; II. description of the problem considered for practical
case study; III. details of computer modelling of the building; IV. results of structural
condition assessment and subsequent strengthening schemes; V. conclusion and outlook.
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Fig. 1 FRP strengthening applications
Strengthening of structural elements
The strengthening through repair, retrofitting and rehabilitation of civil engineering
structures is of paramount significance to reduce the risk and ensure the reliability during
service life. Based on assessment of the present condition of an existing building, prudent
strengthening schemes can be suggested. Two widely used approaches of structural
strengthening are: concrete jacketing and FRP confinement. In both the methods, the space
optimization and cost component are needed to be taken into account based on the structure
under consideration. Schematic diagrams corresponding to strengthening schemes for
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deficiencies in different types of load carrying capacities for the common structural elements
are explained in figure 1. The figures clearly indicate the position of FRP placement for three
different types of load carrying deficiencies.
The strategy followed for concrete jacketing to strengthen a structural element is straight
forward. First structural analysis is carried out for a structural member to find out its load
carrying capacity. Thereby computer simulation is performed to calculate the loads that
different members of a building experience. Comparing the imposed loads on a particular
member and its capacity, the deficiency in load carrying capacity is calculated. Based on the
deficiency, extra reinforcement (Ø) is provided (refer to figure 2(a)) to satisfy the design
requirements (Pillai and Menon 2009; Punmia et al. 2006; IS 456 2000; IS 875 1987; IS 1893
2002; IS 13920 1993; ACI 318-05; ACI 440.2R-08). However, for FRP strengthening, a
relatively more complex design procedure is needed to be followed (Kezmane 2016, ACI
440.2R-08). As it is found that most of the columns are deficient in load carrying capacity
(detailed results are provided later in this paper) in the present problem of strengthening an
existing building, a representative strengthening scheme for a column based on FRP
confinement is briefly discussed here. The FRP confinement mechanism for a column section
is depicted in figure 2(b). For the purpose of demonstration, it is assumed that design forces
on a particular column are: Pu (axial force), Mux (moment with respect to x-direction) and Muy
(moment with respect to y-direction), while the corresponding load carrying capacity of the
column are: Puc, Muxc and Muyc, respectively. If the load carrying capacity is less than the
design forces, the column needs to be strengthened to carry the additional loads. For this
purpose FRP wraps can be utilized (ACI 440.2R-08). A bilinear interaction curve is
considered for the case of combined axial force and bending to optimize the number of layers
for FRP wraps as shown in figure 3. The values of
n
P
and
n
M
are calculated
corresponding to the three different points A, B and C as (ACI 440.2R-08)
 
'
() 0.8 0.85
n A cc g st y st
P f A A f A


 

(1)
7
(a)
(b)
Fig. 2 Strengthening of column sections using (a) Concrete jacketing for strengthening of
column sections (b) Strengthening mechanism of FRP confined concrete columns
32
( , ) ( ) ( ) ( )
n B C t t t si si
P A y B y C y D A f


 

(2)
4 3 2
( , ) ( ) ( ) ( ) ( )
n B C t t t t si si i
M E y F y G y H y I A f d


 

(3)
Here the Points A, B and C correspond to three zones of a column section with pure
compression caused by a uniform axial compressive strain of unconfined concrete (εccu),
8
Fig. 3 Typical representation of bilinear interaction curve
Fig. 4 Strain distributions corresponding to the three points of bilinear interaction curve
shown in figure 3
strain distribution corresponding to zero strain at the layer of longitudinal steel reinforcement
nearest to the tensile face and compressive strain εccu on the compression face and strain
distribution corresponding to balanced failure, respectively (refer to figure 4) (ACI 440.2R-
08). A, B, C…H in equation (1) - (3) are the constant coefficients depending on the properties
of FRP materials used and can be obtained from expressions provided in ACI 440.2R-08. If
the condition of design force and moment interaction point lies in the zone between the
bilinear interaction curves corresponding to the unconfined and confined columns, the
9
column is designated as safe. A case study of condition assessment and subsequent
strengthening for a building is presented in the following sections.
Problem description
Assessment of the present condition and accordingly strengthening measures were
required to be taken for an existing historical library building situated at Uttarakhand, India.
The unique G+1 storey building with historical significance was designed and constructed in
early 1900s and subsequently one more storey was required to be added due to requirement
of expansion of the library building. The building was constructed as RCC framed structure
with load bearing brick masonry walls in the periphery. For condition assessment and
strengthening of the building, supplied structural drawings of the building have been studied
in detail and a separate analysis/design of the building was carried out using ETABS (ETABS
2012) and SAFE (SAFE 2012). To ascertain different parameters used in the aforementioned
analysis and design, a site visit was also conducted. This report aims to assess the present
condition of the existing library building and to suggest necessary measures of strengthening
according to the requirement.
Computer modelling
The entire building except the foundation has been modelled in ETABS, wherein the
beam and columns are modelled using line element as frame (refer to figure 5). Beams and
columns provided in the building have different dimensions and orientations. Dimension of
the beams and columns are shown in Table 1. The modelling of slabs has been done using
shell elements. Shell element is used because the purpose of modelling slab was to transfer
loads as well as to provide stiffness to the floor. Shell element helps in analysing the bending
behaviour of slabs under various loads. The outer walls of the building are load bearing walls
and they have been modelled using shell element for normal elastic analysis. Thickness of
slabs, ramps and walls are 75 mm, 150 mm and 250 mm, respectively. Material properties
10
Fig. 5 Typical three dimensional view of the building model
used in the analysis are shown in Table 2. Reinforcements (Ø) have been modelled as per
existing drawings. The support conditions at the base have been assigned as no translation
and no rotation in any direction, which resembles a fixed support.
Column locations at base level are shown in figure 6. Figure 7 presents the location of
beams at the first and second floor level including position of slabs and load bearing walls.
To access the requirement of strengthening in the existing structural components of first and
second floor level for adding one more storey to the building, the third storey has been
modelled in this study as a replica of the second story. Thus beam locations for the roof level
are same as figure 7(b). The only difference adopted in computer modelling of the third
storey is that no load bearing wall is designed following present construction practices. It
should be noted that the existing building was designed and constructed in early 1980s, when
framed building structures were not very common. Thus it is expected that the columns in the
third storey will need extra reinforcement compared to second storey to balance the effect of
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Table 1 Dimension of beams and column sections (refer to figure 6 and 7)
Structural
element
Type
dimension
Colour code
Beam
Rectangular
200x750(mm)
Beam Type I
Rectangular
200x500(mm)
Beam Type II
Rectangular
120x300(mm)
Beam Type III
Column
Rectangular
500x200 (mm)
Column Type I
Rectangular
230x230 (mm)
Column Type II
Circular
230 Ø (mm)
Column Type III
Table 2 Material Properties
Material
Concrete
Masonry
Compressive Strength
20000 KN/m2
-
Mass/Volume
2.4007 g/m3
-
Weight/Volume
24KN/m3
16 KN/m3
Modulus of Elasticity
22360679.8 KN/m2
4200000 KN/m2
Reinforcement Yield Stress
415000 KN/m2
-
Poisson’s Ratio
0.2
0.2
Shear Modulus
9316949.9 KN/m2
1750000 KN/m2
removing load bearing walls. The requirement of extra reinforcement can be taken care of
effectively while designing the new storey.
Results and discussion
The dead load and live load considered as per codal provisions (IS 875 1987) in this
study are shown in Table 3. For considering earthquake loading as per IS 1893 2002 (Part 1),
different parameters used are as follows: zone factor: 0.24 (seismic zone IV), response
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Table 3 Static loads considered in the design
Super Imposed
Dead Load
Roof
0.22 KN/m2
2nd Floor
0.20 KN/m2
1st Floor
0.20 KN/m2
Live Load
Roof
1.5 KN/m2
2nd Floor
3 KN/m2
1st Floor
6 KN/m2
Ramps and landing of staircase
4 KN/m2
Table 4 Different loading combinations considered in the analysis with appropriate factor of
safety (DL: Dead load; SD: Super imposed dead load; LL: Live load; EQX and EQY:
Earthquake loadings in two perpendicular directions)
Sl. No.
Design combinations
1.
1.5(DL+SD)
2.
1.5(DL+SD+LL)
3.
1.2(DD+SD+LL+EQX)
4.
1.2(DD+SD+LL-EQX)
5.
1.2(DD+SD+LL+EQY)
6.
1.2(DD+SD+LL-EQY)
7.
1.5(DL+SD+EQX)
8.
1.5(DL+SD-EQX)
9.
1.5(DL+SD+EQY)
10.
1.5(DL+SD-EQY)
11.
0.9(DL+SD)+1.5EQX
12.
0.9(DL+SD)-1.5EQX
13.
0.9(DL+SD)+1.5EQY
14.
0.9(DL+SD)-1.5EQY
13
Fig. 6 Plan View of building including column positions (refer Table 1 for colour codes)
reduction factor: 3 (OMRF), importance factor: 1.5 (important service and community
building), damping factor: 0.05 (RCC structures), soil type: medium. As the problem under
consideration is not of high rise building, effect of wind loading has not been accounted in
the analysis. Different loading combinations that have been analysed to access performance
of the structural components are shown in Table 4 including the factor of safety values as per
codal provisions. A particular structural component is considered as ‘failed’ if it fails in any
one of the loading case. For analysing the foundations, allowable bearing pressure considered
at a depth of 2 m below the ground surface is 8 t/m2, as per soil testing report.
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Fig. 7 Location of beams with different dimensions (refer Table 1) in (a) first floor level and (b) second floor level. The rectangular areas in sky blue
colour show position of the landing slabs of staircase and double lines in red colour at the periphery indicate location of load bearing brick masonry
walls. Filling in grey colour indicates location of slab.
15
Fig. 8 Location of failed columns at (a) third storey (b) second storey. Failed columns are indicated in red colour (these columns are strengthened).
Other colours indicate different levels of safety as per design requirements (green being the safest, followed by blue, yellow and pink). The grey colour
indicates the position of slabs in a particular floor.
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Fig. 9 Location of failed columns at (a) first storey (b) base level (Ground). Failed columns are indicated in red colour (these columns are strengthened).
Other colours indicate different levels of safety as per design requirements (green being the safest, followed by blue, yellow and pink). The grey colour
indicates the position of slabs in a particular floor.
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Fig. 10 Location of failed foundations (indicated in red colour)
Condition assessment
In the present analysis, it is observed that beams and slabs remain safe after the addition
of extra storey. This is quite expected as the extra static loads are supposed to be transferred
through the columns of first and second floor to the foundations. Several columns at different
levels (refer to figure 8 and 9) and foundations (refer to figure 10) are found to be unsafe after
the proposed expansion. The foundations failed due to gross bearing pressure of soil.
Strengthening schemes
For the strengthening of the columns, two different schemes (concrete jacketing and FRP
strengthening) have been explored in this project. The adopted strengthening measures using
concrete jacketing (increase in dimension and reinforcement, as required; refer to figure 2(a))
for the failed columns at different sections are presented in Table 5 (detailed results are
shown in APPENDIX: Table A1- A4). It should be noted here that the requirement for
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Table 5 Proposed strengthening schemes for the failed columns of first storey (detailed
results are shown in APPENDIX: Table A1- A4)
Column
number
Existing
Size
(mm2)
Proposed
Size
(mm2)
Existing
Reinforcement
(mm2)
Rebar
Percentage
Reinforcement
Required
(mm2)
Additional
Reinforcement
Required (mm2)
Extra
Bars
C12
230 Ø
330 Ø
1205.76
0.95
812.1
0
C17
230 Ø
330 Ø
1205.76
1.94
1658.4
452.6
4-12 Ø
C20
230 Ø
330 Ø
1205.76
1.92
1641.3
435.5
4- 12Ø
C24
230 Ø
330 Ø
1205.76
0.8
683.8
0
C25
230 Ø
330 Ø
1205.76
1.18
1008.7
0
C26
230 Ø
330 Ø
1205.76
2.01
1718.2
512.5
4- 16Ø
.
.
.
C43
500x200
600x300
1440
0.8
1440
0
Table 6 Manufacturer’s reported FRP system properties
Thickness of ply (tf)
0.33 mm
Ultimate tensile strength (ffu)
3792 MPa
Rupture strain (εfu)
0.017
Modulus of elasticity (Ef)
227.523 MPa
Table 7 Capacity of the column before (n = 0 plies) and after (n = 6 plies) FRP strengthening
Points
n = 0 (plies)
n = 6 (plies)
ΦPn (kN)
ΦMn(kN-m)
ΦPn(kN)
ΦMn(kN-m)
A
9133.54
0
10331
0
B
6998
196
7856
359
C
3127
378
5639
489
increased dimension and reinforcement for third storey (new addition) can be taken care of
during new construction.
Representative results for FRP strengthening is presented for column C41 as per the
guidelines of ACI 440.2R-08. From the structural analysis results, the design forces
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Table 8 Proposed strengthening schemes for foundations (detailed results are shown in
APPENDIX: Table A5)
Column
Existing Size
Remarks
Proposed
size
Depth
existing
Proposed
C1
2500x980
Valid Design
C2
2500x980
Fails on GBP
2500x1065
450
450
C3
2500x980
Fails on GBP
2500x1255
450
450
C4
2500x980
Fails on GBP
2500x1270
450
450
C5
2500x980
Fails on GBP
2500x1170
450
450
.
.
.
C44
2500x980
Fails on GBP
2500x1135
450
450
obtained for the column are: Pu = 7321.55 kN ; Mux = 170.25kN-m and Muy = 2.295kN-m
(negligible). However, capacity of the column is: Puc = 6000 kN and Muxc = 156 kN-m. So it
is required to increase the load demand by 22% at constant eccentricity. The properties of
FRP used in this study are given in Table 6. A wrapping system composed of 6 plies has been
used for the strengthening by constructing the bilinear curve (refer to figure 3). Typical
results for 6 plies are shown in Table 7, wherein it is clear that if six plies are used for the
purpose of strengthening, the column becomes safe under the applied loading conditions.
However, the design can be optimized further by trying lesser number of plies. Due to
addition of the extra storey, several footings are found to be unsafe as indicated in figure 10.
As the foundations fail due to gross bearing pressure (GBP), it has been recommended to
increase dimension of the foundations as per requirements (refer to Table 8 and Table A5).
Discussion
In this paper we have discussed a critical study concerning the strengthening of an aged
building. It can be noted that the intension of this article is not to propose any new
methodology; rather we have adopted some of the well-established techniques here. The
building was actually designed for G+1 storey and it was mentioned in the structural
drawings that no further storey should be constructed over the existing building. However,
20
due to requirement of vertical expansion owing to the purpose of capacity enhancement, one
extra storey is proposed to be added leading to a requirement of strengthening the existing
structure. The library building being a monumental structure with historical significance,
demolition and subsequent reconstruction of a new building is not an option in this case. In
general, such masonry buildings share a large percentage of the current building stock in
most parts of the world. The use of unreinforced masonry (URM) for load bearing walls in
these buildings is a common practice. The URM walls are normally prone to failure under
seismic in-plane and out-of-plane deformations. The in-plane behaviour of URM walls is
crucial, as it provides the primary load path for transfer of seismic loads. However, URM has
also very low tensile strength and hence, the URM walls are highly vulnerable to out-of-plane
flexure. The contemporary design guidelines, which were followed during construction of the
buildings, were not very sophisticated to account for the effect of earthquake loading. Thus to
ensure the modern safety and serviceability requirements, these buildings are often needed to
be strengthened as per the latest codal provisions. Due to sustained policies of several
governments worldwide, old structures are encouraged to be strengthened/ retrofitted
according to modern design guidelines for economic benefits and to preserve monumental
structures of historical significance (Power 2010; Fernandez 2017). Computer modelling of
the present G+2 storey library building reveals that several columns and footings fail to
satisfy the design requirement as per latest codal provisions. In most of the cases, the size of
the columns are increased with minor or no change in the area of longitudinal reinforcements
for concrete jacketing (Pillai and Menon 2009, IS 15988 2013). Most of the footings fail due
to soil bearing pressure. Mostly the depth and size of the column footings are suggested to be
increased without significantly changing the area of the reinforcements so as to make the
strengthening work feasible (refer to figure 11) (Thermou and Elnashai 2006; Website 2019).
No major action of strengthening is required to be taken for beams and slabs. Though here
the columns are strengthened by following two different schemes: concrete jacketing and
FRP strengthening, future investigations can be carried out to investigate other potential
21
Fig. 11 Strengthening scheme for column footings
methods of strengthening such as steel-jacketing (Campione et al. 2017; Ferrotto et al. 2018).
In view of the above discussion, it is observed that most of the columns and footings are
required to be strengthened for the safety of the library building. From a construction point of
view, though the columns can be easily strengthened either by using FRP or by concrete
jacketing, but strengthening the footings by increasing their size is difficult due to
involvement of excavation. FRP strengthening may be a superior choice than concrete
jacketing for strengthening of columns form the viewpoint of space optimization. A direct
comparative economic assessment on the basis of the cost of materials can be carried out
22
based on the detailed strengthening scheme presented in this article considering the concrete
jacketing and FRP strengthening. The issue of cost effectiveness of the two prospective
methods should be accounted before choosing the most suitable option for strengthening of a
particular structural element. The execution of such strengthening works should be decided at
appropriate level based on economical and constructional feasibility.
Conclusion
A brief overview of condition assessment and strengthening for existing structures has
been presented in this article. To illustrate the topic further a practical problem has been
considered concerning strengthening the structural elements of a historical library building,
which is examined for the purpose of prospective vertical expansion. Even though the beams
and slabs do not need any major strengthening measure due to addition of an extra storey,
several columns and footings are found to fail as per the existing structural configuration. For
strengthening the columns, two different schemes (concrete jacketing and FRP strengthening)
have been explored and detail results are presented. The footings are found to fail due to
gross bearing pressure of soil and therefore, to strengthen the footings, their dimensions have
been increased in most of the cases. Monumental structures with historical significance are
often required to be strengthened or retrofitted, instead of a complete demolition and
subsequent reconstruction. Moreover, due to sustained policies of several governments
worldwide, old structures are encouraged to be strengthened/ retrofitted according to modern
codal provisions ensuring various safety and serviceability criteria, after appropriate
condition assessment instead of constructing a new structure in place of the old one. As
practical case studies on condition assessment and strengthening of civil engineering
structures with adequate technical insights are very scarce to find in published literature, this
article on the critical aspects of structural health monitoring of historical old buildings is
expected to serve as a valuable reference for practicing engineers and the concerned scientific
community.
23
Acknowledgement
The authors would like to acknowledge the financial support received from MHRD, India
during the period of this work.
References
1. ACI (American Concrete Institute) 318-05, Building Code Requirements for
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27
APPENDIX
Table A1 Proposed strengthening schemes for the failed columns of third storey
Column
number
Existing
Size
(mm2)
Proposed
Size
(mm2)
Existing
Reinforcement
(mm2)
Rebar
Percentage
Reinforcement
Required
(mm2)
Additional
Reinforcement
Required (mm2)
Extra
Bars
C8
230x230
330x330
803.84
0.8
871.2
68
4-12 Ø
C9
230x230
330x330
803.84
0.8
871.2
68
4-12 Ø
C12
230 Ø
330 Ø
1205.76
0.8
683.8
0
C13
230 Ø
330 Ø
1205.76
0.8
683.8
0
C16
230 Ø
330 Ø
1205.76
0.8
683.8
0
C17
230 Ø
330 Ø
1205.76
0.8
683.8
0
C18
230 Ø
330 Ø
1205.76
0.8
683.8
0
C19
230 Ø
330 Ø
1205.76
0.8
683.8
0
C20
230 Ø
330 Ø
1205.76
0.8
683.8
0
C21
230 Ø
330 Ø
1205.76
0.8
683.8
0
C24
230 Ø
330 Ø
1205.76
0.8
683.8
0
C25
230 Ø
330 Ø
1205.76
0.8
683.8
0
C26
230 Ø
330 Ø
1205.76
0.9
769.3
0
C27
230 Ø
330 Ø
1205.76
0.9
769.3
0
C28
230 Ø
330 Ø
1205.76
0.8
683.8
0
C29
230 Ø
330 Ø
1205.76
0.8
683.8
0
C32
230 Ø
330 Ø
1205.76
0.8
683.8
0
C33
230 Ø
330 Ø
1205.76
0.8
683.
0
C36
230 Ø
330 Ø
1205.76
0.8
683.8
0
C37
230 Ø
330 Ø
1205.76
0.8
683.8
0
Table A2 Proposed strengthening schemes for the failed columns of second storey
Column
number
Existing
Size
(mm2)
Proposed
Size
(mm2)
Existing
Reinforcement
(mm2)
Rebar
Percentage
Reinforcement
Required
(mm2)
Additional
Reinforcement
Required (mm2)
Extra
Bars
C12
230 Ø
330 Ø
1205.76
0.87
743.7
0
C13
230 Ø
330 Ø
1205.76
0.88
752.2
0
C17
230 Ø
330 Ø
1205.76
1.18
1008.7
0
C18
230 Ø
330 Ø
1205.76
0.8
683.8
0
C19
230 Ø
330 Ø
1205.76
0.8
683.8
0
C20
230 Ø
330 Ø
1205.76
1.17
1000.1
0
C26
230 Ø
330 Ø
1205.76
1.37
1171.1
0
C27
230 Ø
330 Ø
1205.76
1.37
1171.1
0
C32
230 Ø
330 Ø
1205.76
2.19
1872.1
666.3
4- 16 Ø
C33
230 Ø
330 Ø
1205.76
2.07
1769.5
563
4- 16 Ø
C41
500x200
600x300
1440
0.8
1440
0
C42
500x200
600x300
1440
0.8
1440
0
28
Table A3 Proposed strengthening schemes for the failed columns of first storey
Column
number
Existing
Size
(mm2)
Proposed
Size
(mm2)
Existing
Reinforcement
(mm2)
Rebar
Percentage
Reinforcement
Required
(mm2)
Additional
Reinforcement
Required (mm2)
Extra
Bars
C12
230 Ø
330 Ø
1205.76
0.95
812.1
0
C13
230 Ø
330 Ø
1205.76
0.96
820.6
0
C17
230 Ø
330 Ø
1205.76
1.94
1658.4
452.6
4-12 Ø
C18
230 Ø
330 Ø
1205.76
0.8
683.8
0
C19
230 Ø
330 Ø
1205.76
0.8
683.8
0
C20
230 Ø
330 Ø
1205.76
1.92
1641.3
435.5
4- 12Ø
C24
230 Ø
330 Ø
1205.76
0.8
683.8
0
C25
230 Ø
330 Ø
1205.76
1.18
1008.7
0
C26
230 Ø
330 Ø
1205.76
2.01
1718.2
512.5
4- 16Ø
C27
230 Ø
330 Ø
1205.76
2.04
1743.9
538.1
4-16 Ø
C28
230 Ø
330 Ø
1205.76
1.16
991.6
0
C29
230 Ø
330 Ø
1205.76
0.8
683.8
0
C32
230 Ø
330 Ø
1205.76
2.79
2385
1179
4-20 Ø
C33
230 Ø
330 Ø
1205.76
2.67
2282.4
1076
4-20 Ø
C36
230 Ø
330 Ø
1205.76
1.04
889
0
C37
230 Ø
330 Ø
1205.76
0.8
683.8
0
C40
500x200
600x300
1440
0.8
1440
0
C41
500x200
600x300
1440
0.8
1440
0
C42
500x200
600x300
1440
0.8
1440
0
C43
500x200
600x300
1440
0.8
1440
0
Table A4 Proposed strengthening schemes for the failed columns at base level (ground)
Column
number
Existing
Size
(mm2)
Proposed
Size
(mm2)
Existing
Reinforcement
(mm2)
Rebar
Percentage
Reinforcement
Required
(mm2)
Additional
Reinforcement
Required (mm2)
Extra
Bars
C12
230 Ø
330 Ø
1205.76
1.01
863.4
0
C13
230 Ø
330 Ø
1205.76
1.02
871.9
0
C17
230 Ø
330 Ø
1205.76
1.98
1692.6
486.8
4- 16Ø
C18
230 Ø
330 Ø
1205.76
0.8
683.8
0
C19
230 Ø
330 Ø
1205.76
0.8
683.8
0
C20
230 Ø
330 Ø
1205.76
1.97
1684
478.3
4- 16Ø
C24
230 Ø
330 Ø
1205.76
0.8
683.8
0
C25
230 Ø
330 Ø
1205.76
1.23
1051.4
0
C26
230 Ø
330 Ø
1205.76
3.49
2983.4
1777
4- 20Ø
C27
230 Ø
330 Ø
1205.76
3.6
3077.5
1871
4-20 Ø
C28
230 Ø
330 Ø
1205.76
1.21
1034.3
0
C29
230 Ø
330 Ø
1205.76
0.8
683.8
0
C32
230 Ø
330 Ø
1205.76
2.74
2342.3
1136
4-20 Ø
C33
230 Ø
330 Ø
1205.76
2.61
2231.1
1025
C36
230 Ø
330 Ø
1205.76
1.09
931.8
0
C37
230 Ø
330 Ø
1205.76
0.8
683.8
0
C40
500x200
600x300
1440
0.8
1440
0
C41
500x200
600x300
1440
0.8
1440
0
C42
500x200
600x300
1440
0.8
1440
0
C43
500x200
600x300
1440
0.8
1440
0
29
Table A5 Proposed strengthening schemes for foundations
Column
Existing Size
Remarks
Proposed
size
Depth
existing
Proposed
C1
2500x980
Valid Design
C2
2500x980
Fails on GBP
2500x1065
450
450
C3
2500x980
Fails on GBP
2500x1255
450
450
C4
2500x980
Fails on GBP
2500x1270
450
450
C5
2500x980
Fails on GBP
2500x1170
450
450
C6
2500x980
Valid Design
450
450
C7
2500x980
Valid Design
C8
1600x1600
Fails on GBP
1650x1650
450
450
C9
1600x1600
Fails on GBP
1660x1660
450
450
C10
2500x980
Valid Design
450
450
C11
2500x980
Fails on GBP
2500x1030
450
450
C12
1600x1600
Fails on GBP
1880x1880
450
450
C13
1600x1600
Fails on GBP
1880x1880
450
450
C14
2500x980
Fails on GBP
2500x1225
450
450
C15
2500x980
Valid Design
C16
1600x1600
Fails on GBP
1675x1675
450
450
C17
1600x1600
Fails on GBP
2175x2175
450
460
C18
1600x1600
Fails on GBP
1870x1870
450
450
C19
1600x1600
Fails on GBP
1870x1870
450
450
C20
1600x1600
Fails on GBP
2170x2170
450
450
C21
1600x1600
Fails on GBP
1715x1715
450
450
C22
2500x980
Fails on GBP
2500x1225
450
450
C23
2500x980
Valid Design
C24
1600x1600
Fails on GBP
1815x1815
450
450
C25
1600x1600
Fails on GBP
2225x2225
450
500
C26
1600x1600
Fails on GBP
2465x2465
450
600
C27
1600x1600
Fails on GBP
2475x2475
450
610
C28
1600x1600
Fails on GBP
2215x2215
450
500
C29
1600x1600
Fails on GBP
1845x1845
450
450
C30
2500x980
Fails on GBP
2500x1340
450
450
C31
2500x980
Fails on GBP
2500x1390
450
450
C32
1600x1600
Fails on GBP
2365x2365
450
570
C33
1600x1600
Fails on GBP
2325x2325
450
550
C34
2500x980
Fails on GBP
2500x1510
450
450
C35
2500x980
Fails on GBP
2500x1155
450
450
C36
1600x1600
Fails on GBP
2040x2040
450
450
C37
1600x1600
Fails on GBP
1925x1925
450
450
C38
2500x980
Fails on GBP
2500x1100
450
450
C39
2500x980
Fails on GBP
2500x1145
450
450
C40
2500x980
Fails on GBP
2500x1600
450
450
C41
2500x980
Fails on GBP
2500x2130
450
530
C42
2500x980
Fails on GBP
2500x2170
450
550
C43
2500x980
Fails on GBP
2500x1680
450
450
C44
2500x980
Fails on GBP
2500x1135
450
450
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... 5), then by glass specimen (BG1.5). This can be attributed to the effect of the modulus of Load-deflection relationship. ...
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Several approaches were used to explore the characteristics of reinforced concrete (RC) structural elements. Experimental work in the lab was extensively used as a means to examine the structural response and influence of different parameters under shear loads. Also, using numerical analysis to look into these components has been proven effective. This paper focuses on the shear conduct and response of circular beams reinforced with steel bars using the finite element (FE) model by considering the effect of reinforcement type and ratio, shear span-depth ratio (a/d), and member's size. The FE model results were confirmed with the experimental outcomes of full-scale circular RC specimens tested earlier by scientists. The outcomes from the numerical study displayed that the proposed finite element replica was capable of simulating the characteristics of the beams, tested experimentally in the lab, with credible accuracy. From the FE model, it was found that the concrete shear contribution is best described as a formula that is inversely proportional to the member's depth and directly proportional to the square root of axial stiffness of the reinforcement. Keywords: circular beams; finite element (FE); flexural reinforcement ratio; ratio; shear span-depth ratio (a/d); shear strength; size effect; steel. INTRODUCTION Circular reinforced concrete (RC) members exist in many types of structures. Many of these members usually experience severe transversal/shear loads generated from earthquakes and/or wind stresses. As a consequence, a significant amount of shear load is applied to the member's cross section (Ali et al. 2020). Realizing and grasping the behavior of the RC members during loading is paramount to construct a completely safe and efficacious structure. In the last decade, the shear strength of fiber-reinforced polymer (FRP) RC members with rectangular cross sections received considerable attention. The experimental work focused mainly on beams without web reinforcement, but limited research has addressed beams with circular cross section. Yet, no finite element model or numerical equations have investigated circular concrete members reinforced with steel or FRP reinforcement under shear loads. In general, shear design provisions can be applied to circular members by using an equivalent rectangular cross section. The accuracy of such an approach should, however, be assessed because a circular section may not contribute to shear strength in the same way as a rectangular section. Circular members usually have longitudinal reinforcement uniformly distributed around the section's perimeter. This reinforcement reduces crack propagation above the neutral axis and limits crack width, which, in turn, increases the contributions of aggregate interlock. Moreover, these bars add to the dowel mechanism in resisting the relative transverse displacement between two
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
... 5), then by glass specimen (BG1.5). This can be attributed to the effect of the modulus of Load-deflection relationship. ...
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A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... Alam et al. [29] reinforced cracked wooden beams with steel and FRP, and found that these reinforcements were very effective; CFRP reinforcement provided the greatest bending strength, and the researchers concluded that that addition of FRP reinforcement to timber beams could improve strength and stiffness and possibly reduce the variability in the mechanical properties of the beams compared to non-reinforced elements. The methods of analyzing the strengthening with the use of FRP in the structures are given in the works [24,[30][31][32]. ...
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This article presents experimental results from the bending of technical-scale models of beams reinforced in the tension zone with CFRP (Carbon Fiber Reinforced Polymers) materials, with a focus on the benefits resulting from the increased ductility in the tension zone of these beams. In experimental tests, the mechanical properties of reinforced beams were compared with unreinforced beams in terms of the maximum load, deflection, images of damage, stiffness, and distribution of deformation. The results showed that the proposed reinforcement solution was advantageous due to its strength and stiffness, and the safety of the structure. Based on this analysis, it was concluded that the reinforcement of wood with CFRP materials has a positive effect on the behavior and safety of structures. Also, a method of analytical checking of strengthened beams with small cross-sections was presented in the article.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
Article
A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
Article
A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
... Mao et al. [15] determined the nonlinear impact responses of FGM shells subjected to impact loading in the thermal environment. Over the last decade, multiple deterministic and stochastic vibration and low-velocity impact analysis are reported for laminated composites, sandwich and FG structure [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. ...
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This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) plates subjected to free vibration and low-velocity impact to identify the most influential parameters in the respective analyses. A hybrid moment-independent sensitivity analysis is proposed coupled with the least angle regression based adaptive sparse polynomial chaos expansion. Here the surrogate model is integrated in the sensitivity analysis framework to achieve computational efficiency. The current paper is concentrated on the relative sensitivity of material properties in the free vibration (first three natural frequencies) and low-velocity impact responses of FGM plates. Typical functionally graded materials are made of two different components, where a continuous and inhomogeneous mixture of these materials is distributed across the thickness of the plate based on certain distribution laws. Thus, besides the overall sensitivity analysis of the material properties, a unique spatial sensitivity analysis is also presented here along the thickness of the plate to provide a comprehensive view. The results presented in this paper would help to identify the most important material properties along with their depth-wise spatial sensitivity for low-frequency vibration and low-velocity impact analysis of FGM plates. This is the first attempt to carry out an efficient adaptive sparse PCE based moment-independent sensitivity analysis (depth-wise and collectively) of FGM plates under the simultaneous susceptibility of vibration and impact. Such simultaneous multi-objective sensitivity analysis can identify the important system parameters and their relative degree of importance in advanced multi-functional structural systems.
Research
The near-surface mounted (NSM) technique over the years has become the most popular retrofitting technique for obtaining enhanced strength and durability in reinforced concrete structural elements. It is mostly preferred for its easy application of composites in grooves cut on specimen concrete cover. The specimen surface is prepared with slits where polymer composite laminates are placed along with adhesives as filler to attain good bonding between laminates and the surface. The paper reviews the NSM carbon fiber reinforced polymer technique and its ascendancies over externally bonded composites retrofitting approach. Members strengthened with the NSM technique show enhanced shear strength, flexural capacity, and fatigue resistance. Motivated by the urge of gaining knowledge on various advantages of this emerging method, the paper reviews the load-carrying capacity, failure modes, durability, and bonding behavior along with the enhancement ascertained in shear, flexure, and fatigue resistance by the NSM technique. In addition to offering guidance on the experimental and computational investigations on the overall behavior of the technique, the present review also intends to encourage further development in the near-surface mounted carbon fiber polymer strengthening system of retrofit.
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The stochastic buckling behaviour of sandwich plates is presented considering uncertain system parameters (material and geometric uncertainty). The higher-order-zigzag theory (HOZT) coupled with stochastic finite element model is employed to evaluate the random first three buckling loads. A cubic in-plane displacement variation is considered for both face sheets and core while quadratic transverse displacement is considered within the core and assumed constant in the faces beyond the core. The global stiffness matrix is stored in a single array by using skyline technique and stochastic buckling equation is solved by simultaneous iteration technique. The individual as well as compound stochastic effect of ply-orientation angle, core thickness, face sheets thickness and material properties (both core and laminate) of sandwich plates are considered in this study. A significant level of computational efficiency is achieved by using artificial neural network (ANN) based surrogate model coupled with the finite element approach. Statistical analyses are carried out to illustrate the results of stochastic buckling behaviour. Normally in case of various engineering applications, the critical buckling load with the least Eigen value is deemed to be useful. However, the results presented in this paper demonstrate the importance of considering higher order buckling modes in case of a realistic stochastic analysis. Besides that, the probabilistic results for global stability behaviour of sandwich structures show that a significant level of variation with respect to the deterministic values could occur due to the presence of inevitable source-uncertainty in the input parameters demonstrating the requirement of an inclusive design paradigm considering stochastic effects.
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Over the last few decades, uncertainty quantification in composite materials and structures has gained a lot of attention from the research community as a result of industrial requirements. This book presents computationally efficient uncertainty quantification schemes following meta-model-based approaches for stochasticity in material and geometric parameters of laminated composite structures. Several metamodels have been studied and comparative results have been presented for different static and dynamic responses. Results for sensitivity analyses are provided for a comprehensive coverage of the relative importance of different material and geometric parameters in the global structural responses.
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This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framework for studying the dynamic and stability characteristics of composite laminates with spatially varying system properties. Most of the studies concerning the uncertainty quantification of composites rely on probabilistic analyses, where the prerequisite is to have the statistical distribution of stochastic input parameters. In many engineering problems, these statistical distributions remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based approach could be appropriate to characterize the effect of uncertainty. A novel concept of fuzzy representative volume element (FRVE) is developed here for accounting the spatially varying non-probabilistic source-uncertainties at the input level. Such approach of uncertainty modelling is physically more relevant than the prevalent way of modelling non-probabilistic uncertainty without considering the ply-level spatial variability. An efficient radial basis function based stochastic algorithm coupled with the fuzzy finite element model of composites is developed for the multi-scale uncertainty propagation involving multi-synchronous triggering parameters. The concept of a fuzzy factor of safety (FFoS) is discussed in this paper for evaluation of safety factor in the non-probabilistic regime. The results reveal that the present physically relevant approach of modelling fuzzy uncertainty considering ply-level spatial variability obtains significantly lower fuzzy bounds of the global responses compared to the conventional approach of non-probabilistic modelling neglecting the spatially varying attributes.
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The coupled effect of manufacturing uncertainty and a critical service-life damage condition (delamination) is investigated on the natural frequencies of laminated composite plates. In general, delamination is an unavoidable phenomenon in composite materials encountered often in real-life operating conditions. We have focused on the characterization of dynamic responses of composite plates considering source-uncertainty in the material and geometric properties along with various single and multiple delamination scenarios. A hybrid high dimensional model representation based uncertainty propagation algorithm coupled with layer-wise stochastic finite element model of composites is developed to achieve computational efficiency. The finite element formulation is based on Mindlin's theory considering transverse shear deformation. Numerical results are presented for the stochastic natural frequencies of delaminated composites along with a comprehensive deterministic analysis. Further, an inevitable effect of noise is induced in the surrogate based analysis to explore the effect of various errors and epistemic uncertainties involved with the system.
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This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loève expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/ system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.
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The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love’s and Donnell’s theory considering dynamic and shear deformable theory according to the Sander’s first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries.
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