assessment and alternative design solutions for ... sr design bending moment (kn.m) msy yielding...

J. Civil Eng. Architect. Res. Vol. 2, No. 12, 2015, pp. 1181-1191 Received: May 27, 2015; Published: December 25, 2015

Journal of Civil Engineering

and Architecture Research

Assessment and Alternative Design Solutions for Strengthening of RC Structure—A Case Study

Tanya Chardakova and Marina Traykova

Department of RC Structures, University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria

Corresponding author: Tanya Chardakova ([email protected])

Abstract: The rehabilitation and strengthening of an existing reinforced concrete structure of a technical room, part of a fountain in a public garden are presented. The lack of maintenance during long years of use and the unfavorable climatic conditions have led to many damages in the structural elements. The paper addresses a study for two alternative design solutions for strengthening—with reinforced concrete and with fiber reinforced polymer (FRP). The case presented some interesting design challenges that are discussed in the paper: the geometry of the structure, the concept of the design, the technical limitations and requirements of the stakeholder, etc. The site investigation and the general conclusions for the actual state of the structure are presented in the paper first. Then numerical assessment of the structure is done, using the results of the site investigation. Finite element analysis is used for this purpose. A detailed analysis of the two design solutions is presented. Due to technical requirements of the stakeholder, some redistribution of bending moments is allowed after the strengthening. Both design solutions are based on this fact. Original design procedure for the design of the strengthening with reinforced concrete, taking into account the initial loading of the structure before the strengthening is presented. The reasons for the final choice of design solution are discussed. Finally, some general conclusions and recommendations in such cases are given. Key words: RC Structures, rehabilitation, strengthening, FRP, shotcrete, moment redistribution, initial loading.

Nomenclature:

As,e Existing reinforcement (mm2) As,r Strengthening reinforcement (mm2) Asw Transverse reinforcement (mm2) Mp1 Bending moment from initial loading p1 (kN.m)

Mp2 Bending moment from loading, applied after strengthening (kN.m)

MEd Design bending moment (kN.m) Msy Yielding bending moment (kN.m) VEd Design shear force (kN) VRd,e Shear force resistance of the existing element (kN) VRd,r Added shear force resistance after the strengthening (kN)b Width of the section (mm) de Design height of the existing section (mm) dr Design height of the strengthened section (mm)

fcd Design compressive cylinder strength of the concrete (MPa)

fyd,e Design yield stress of the existing steel reinforcement (MPa)

fyd,r Design yield stress of the strengthening steel reinforcement (MPa)

x Height of the compression zone (mm) z Moment arm of the inner forces (mm)

εce,p1Maximal strain of the existing concrete under initial loading (dimensionless)

εce,p2Maximal strain of the existing concrete under loading, applied after the strengthening (dimensionless)

εse,p1Strain of the existing reinforcement steel under initial loading (dimensionless)

εse,p2Strain of the existing reinforcement steel under loading, applied after the strengthening (dimensionless)

εsr Strain of the strengthening reinforcement steel (dimensionless)

σce,p1Maximal stress of the existing concrete under initial loading (MPa)

σce,p2Maximal stress of the existing concrete under loading, applied after the strengthening (MPa)

σse,p1Stress of the existing reinforcement steel under initial loading (MPa)

σse,p2Stress of the existing reinforcement steel under loading, applied after the strengthening (MPa)

σsr Stress of the strengthening reinforcement steel (MPa) θ Angle between the crack and beam axis

1. Introduction

The National Palace of Culture in Sofia, Bulgaria, is

an emblematic building in the center of the city. The


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building and the garden in front of the Palace are

executed in the 80s of the 20th century. The fountain

and the water cascade are the “heart” of the whole

complex and a very attractive place for rest and walk.

During a very long period of time the unfavorable

climatic conditions and the lack of maintenance have

led to serious damages and to the decreasing of the

bearing capacity of the main structural elements. In

the same time, many inappropriate interventions are

executed. All these circumstances determined the

actual state of the structure.

The existing structure is executed from cast in situ

reinforced concrete and consists of slabs, beams and

columns. The structure forms a cascade, each level

being a beam slab and the bottom of the fountain—a

flat slab. For the shifting of the levels beams are

designed, so each level is encircled by series of beams

(Figs.1 and 2). During the major part of the year the

structure is under water.

Fig. 1 View of the fountain.

Fig. 2 Partial section of the structure.

The assessment of the actual state of the structure is

performed in two steps: Site investigation and

numerical assessment. Based on the results, two

alternative design solutions for rehabilitation and

strengthening are developed.

Based on a real case study, the paper deals with the

design process of the strengthening of existing

structures. Many factors: technical, financial,

architectural, specific requirements etc., can play a

decisive role for the final solution. The correct

engineering approach sometimes needs a complex

analysis of the structure: site investigation with

detailed description of the actual state of the structure,

numerical assessment for identification of the

problematic details, design of the appropriate

strengthening. It’s possible to choose a variant

different from the traditional approaches or to propose

alternative solutions. Finally the retrofit solution

should focus mainly on developing safe, simple and

cost effective technique which satisfies the

requirements of the acting standards.

2. Site Investigation

The site investigation is focused on the

determination of the grade of the concrete and the

diameter and the type of the reinforcement steel. A

visual inspection of the structural elements is done.

According to the results of the instrumental

assessment the following results for the materials are

found:

The grade of the concrete is C40/50 for the slabs

and the beams at level -0.15, +0.65 and +1.05 and

C45/55 for the slab and the beams at level +0.25 (the

grade notification is in accordance with BDS EN 1992

[1]);

The grade of the concrete for the columns is

C28/35;

The diameter of the reinforcement is: for the

slabs 14 mm, for the beams 16 mm and for the

columns 18 mm.

The following conclusions after the site

investigation are made:


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Serious cracks (Fig. 3);

Very high level of carbonization of the concrete

(Fig. 4);

Loss of concrete cover;

Corrosion of the reinforcement;

Serious damages in the insulation on the top side

of the slab.

3. Numerical Assessment

The existing structure is assessed for gravity loads

only, as it is underground and its surrounding thick

walls act as a stiff box, so seismic action is not an

issue. A static analysis of the existing structure is

performed, as follows:

Fig. 3 Wide cracks at the bottom side of the slab.

Fig. 4 Effects of carbonization.

the slabs at level +1.05, +0.65 and +0.25

are solved separately as simply supported one-way

slabs;

the slab at level -0.15 is solved by finite element

analysis; the model is partial of the slab itself, the

surrounding beams and the relevant supports (modeled

as simple)—the columns under this slab and the wall

on axis 8 (Fig. 5); the latter is necessary due to the

lack of direct support of beams 28 and 29 (numbers of

the beams in accordance with Fig. 6);

the beams are solved by finite element analysis of

a model of the whole structure (Fig. 7), as the load

path is not quite clear, due to the fact, that beams 28

and 29 are not supported directly; again, the columns

and the walls are modeled as simple supports;

the axial forces in the columns are obtained by

the finite element model of the beams; incidental and

second order eccentricity are calculated in accordance

with [1].

The numerical assessment of the capacity of the

existing structural elements is based on the site

investigation results. The capacity is compared to the

design effects, obtained by the static analysis. The

following conclusions are made, based on this

comparison and the actual state of the structure:

Fig. 5 Finite element model of the slab at level -0.15.


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Fig. 6 Numbering of the beams.

Fig. 7 Finite element model of the beams.

the calculated capacity of the slabs for bending

and shear is adequate and the deflections are within

acceptable limits, so design of their strengthening is

not needed; however, due to their poor actual state,

rehabilitation is necessary and minimal strengthening

is recommended;

the capacity of some of the beams for bending in

the mid span, bending over the support and/or shear is

not adequate; for these beams strengthening shall be

designed; for the other beams rehabilitation is

necessary and minimal strengthening is recommended;

the capacity of all the columns for axial force

with and without bending is quite adequate, indeed by

a large margin; their actual state is very good, too -

much better than the state of the slabs and beams;

therefore, no strengthening is needed and only

rehabilitation is recommended.

4. Alternative Design Solutions for the Strengthening of the Structure

Two alternative design solutions for strengthening

are presented: by reinforced concrete and by fiber

reinforced polymer (FRP). Regardless of the choice of

strengthening solution, rehabilitation of the structure is

required, including:

filling of cracks with low viscosity epoxy resin;

treatment of the exposed reinforcement by

corrosion inhibitor;

removal of loose concrete until the substrate is

solid;

cleaning of the concrete and reinforcement steel

until free of dust, rust, grease, oils, etc; additional

roughening of the concrete surface if needed;

treatment of the deteriorated concrete surfaces by

thixotropic low-shrinkage fiber reinforced cement

mortar after proper preparation of the substrate.

4.1 Concept of the Design

There is a thick, high-strength stucco, fountain

equipment and decorations at the upper side of the

slabs, as well as boards at the upper side of the beams.

The stakeholder requires these to be left intact.

Therefore, the strengthening at the upper side of the

structure would be technically challenging. The

concept of the design is based on that fact. Regardless

of the choice of strengthening solution, all

interventions are to be at the bottom side of the

structure. As the clear height of the technical room

under the fountain is limited, significant increase of


1185

the height of the elements is not appropriate. Thus, the

concept of the design is to add strengthening tensile

reinforcement—either steel rods with subsequent

shotcreting, or FRP.

This approach is very suitable for increasing the

capacity for bending in the mid span of the beams.

Concerning the capacity for bending over the supports,

however, this would not be of much help. One

possible solution is to allow the forming of plastic

hinges in the beams near the supports, and to

redistribute the moments from these sections towards

the mid span (Fig. 8). This approach is very common

for the reinforced concrete structures, and recent

studies show that it is applicable for continuous RC

beams strengthened with FRP, too [2-4].

Thus, the design moment in the mid span is

determined by Eq. (1):

, , 2I J

i pl i elM MМ M

(1)

where the notifications are according to Fig. 8.

To increase the capacity of the beams for shear,

transverse reinforcement should be added. Given the

cross-section of the beams and the fact that

interventions are only to be undertaken from the side

of the technical room, the shear additional transverse

reinforcement is L-shaped, anchored at the bottom

side of the beam.

4.2 Strengthening with Reinforced Concrete

The following assumptions are adopted for the

design of the strengthening:

Bernoulli's hypothesis is valid;

tension stresses in the concrete are neglected;

the deformation of the reinforcing rods is equal to

the deformation of the adjacent concrete;

slipping between strengthening and existing

material is neglected;

the stress-strain relationship of the materials is

according to Fig. 9;

the superposition principal is adopted to account

for the initial loading of the structure, along the lines

of FRP strengthening [5, 6] (Fig. 10).

Fig. 8 Redistribution of the moments in the beams.

Fig. 9 Stress-strain relationship of the a) concrete; b) reinforcement steel.

,, ,

, ,

,,

3

. ..

2

.

.

c eyd e s e

c e yd ee

c ec e cd

c

x bf A

xd x

f

(3)

First the stress and strain state of the sections under

initial loading is determined in accordance with

Chardakova et al. [7]. For this purpose the yielding

moment of the section is calculated by Eq. (2), which

is a moment equilibrium equation in accordance with

Fig. 11:


1186

, ,. .3sy yd e s e exM f A d

(2)

where x is determined using the equations of the

physics and the geometry (Eq. 3).

The stress and strain of the concrete and the

reinforcement are determined by the same system of

equations. It is verified that the maximal concrete

strain is lower than εc3 (εc3 according to Fig. 9a). If this

is not so, the obtained results are not valid and

recalculation is needed [7].

As the moment from the initial loading (just before

strengthening) Mp1 is lower than the yielding moment,

the stress and strain state of the section under initial

loading (Fig. 12) can now be determined:

1, 1 ,

1, 1 ,

1, 1 ,

, 1, 1 ,

3

.

.

.

.

pse p yd e

sy

pse p yd e

sy

pce p ce sy

sy

ce pce p cd e

c

MMM

fMMM

f

(4)

For the design of the strengthening it is assumed

that both the existing and the new materials are fully

used, i.e. their stress and strain are:

,

, 2 , , 1

, 2 3 , 1

, 2 , 1

sr yd r

se p yd e se p

ce p cu ce p

ce p cd ce p

ff

f

(5)

Here the design compressive strength of the new

concrete is not relevant, as the strengthening is in

tension zone. Nevertheless, it is the common practice

to recommend the grade of the new concrete to be at

least one above the grade of the existing concrete, due

to contact slip issues. In this case however this is not

possible, as the grade of some the slabs is as high as

C45/55, and the grade of the shotcrete is limited by the

specifics of the technique (water-cement ration,

chemical additives, etc.). Thus the highest locally

available grade of shotcrete is recommended and the

new-old concrete connection is verified.

The design height of the strengthened section dr is

predetermined by technical requirements.

The stress and strain state of the section under

loading after strengthening is shown at Fig. 13 [7].

The parameters α and β, defined at Fig. 13 are

calculated:

3 3

3 , 1

2 1

3. 1

cu c

cu ce p

(6)

Relative compression zone height ξ, relative arm of

the couple of the inner force ζ, and relative moment

mEd are calculated:

2 , 2 ,

2, 2

1 .

. ..

0,5. 1 . . .

r

p se p s e r eEd

r ce p

xd

M A d dm

b d

(7)

Then the required strengthening reinforcement is

calculated by Eq. (8):

2 , 2 ,,

. . . .

. .p se p s e e r

s rr yd

M A d dA

d f

(8)

The required transverse reinforcement is calculated

by Eq. (9):

, , ,. . .ctgswRd r Rd e ywd r

r

AV V z fs

(9)

It turns out that minimal transverse reinforcement is

sufficient for the strengthening of the beams.

The connection between the new and old concrete is

calculated in accordance with BDS EN 1992 [1]. The

stress in the contact surface is calculated for the most

unfavorable conditions possible:

, ,,

.0,5. .s r yd r

Ed surface cdsurface

A fv f

A (10)


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The contribution of the cohesion is neglected for the

calculation of the required dowel reinforcement, as the

intervention technique is shotcreting:

,,

,

.

.Ed surface surface

s dowelsyd dowels

v bA

f (11)

where μ is the friction coefficient.

Detail of the strengthening of one of the beams is

given at Fig. 14.

4.3 Strengthening with FRP

The design of the strengthening with FRP is in

accordance with CNR-DT 200 [6]. For the

strengthening for bending, FRP plates (laminates) are

suitable, and for shear-FRP strips. Only one layer of

FRP plates is used, as higher number of layers will

decrease the capacity of the beam for moment

redistribution [2, 3]. For the same reason special

consideration is given to the strengthening

configuration [4].

First, the ultimate design strength for intermediate

debonding is calculated:

,2 .fdd cr fddf k f (12)

where kcr can be taken equal to 3 and ffdd is the ultimate

design strength for laminate/sheet end debonding (this

failure mode can be avoided by proper anchoring).

Fig. 10 Superposition principal.

Fig. 11 Stress and strain state of the section under yielding moment.

Fig. 12 Stress and strain state of the section under initial loading.


1188

Fig. 13 Stress and strain state of the section under loading, applied after strengthening.

Fig. 14 Detail of the RC strengthening of the beam.


1189

The corresponding design strain is:

,2fddfdd

f

fE

(13)

where Ef is the elasticity modulus of the FRP.

Then the maximal tension strain of the FRP is:

max . ;fkfd a fdd

f

(14)

where εfk is the limit strain of the FRP, ηa is the

environmental conversion factor, and γf is partial

safety factor.

Again for the design of the strengthening for

bending, the initial loading is accounted for. The

design process is iterative: the quantity of the selected

FRP material is chosen, then the bending capacity is

calculated. For this purpose it is first assumed that the

FRP system reaches its limit strain before the concrete

(the assumption is checked in the end and if it is not

correct the moment is recalculated for crushing of the

concrete failure mode). Then the height of the

compressive zone is determined using the force

equilibrium equation. After that the bending capacity

can easily be calculated using the moment equilibrium

equation.

The strengthening for shear is somewhat unusual, as

it is not the typical U-wrapping, but L-wrapping, due to

the shape of the beam. However, given that proper

anchoring is ensured, the same approach as for

U-wrapping, proposed in CNR-DT 200 [6], can be used.

Again the design process is iterative: the quantity of the

selected FRP material is chosen, then the FRP

contribution to the share capacity is calculated:

, .0,9. . . .ctgfed fRd f f

Rd f

f wV d t

p

(15)

where γRd is partial factor, ffed is effective FRP design

strength, tf, wf and pf are the strip thickness, the strip

width and the axial distance between the strips.

Detail of the strengthening of one of the beams is

given at Fig. 15.

Fig. 15 Detail of the FRP strengthening of the beam.

4.4 Comparison of the Alternative Design Solutions and Final Decision for the Strengthening

The two alternatives are compared, so the

stakeholder can take informed decision for the best

solutions, given their priorities:

the capacity for bending of the elements after

strengthening is almost equal for the two alternatives;

the capacity for shear of the beams is higher even

with minimal strengthening with reinforced concrete

than that with FRP, because of the increase of the

cross-section dimensions;

the capacity for shear of the slabs is significantly

increased with reinforced concrete, but remains

practically the same as prior the strengthening with

FRP;

the stiffness of the elements, especially the slabs,

is significantly increased with reinforced concrete, but

remains practically the same as prior the strengthening

with FRP;


1190

the FRP strengthening technique is much quicker

and requires less wet processes;

the cost of the initial investment is much higher

for the FRP strengthening;

the FRP technique is much more sustainable,

because of the high effectiveness of the material.

Based on this information, given in detail, the

stakeholder made the decision that the strengthening

with reinforced concrete is undertaken. The main

reason for this decision was the cost of the FRP

interventions.

5. Conclusions

In this paper the site investigation, numerical

assessment and two alternative design solutions for the

strengthening of the structure of a fountain in Sofia,

Bulgaria is described. The case study is specific in

several ways: the concept of the design, the geometry

of the structure, the technical limitations, etc.

Based on this specific case study, the following

general conclusions can be made:

When there are technical limitations for the

strengthening, the redistribution of the bending

moments is a possible solution. However, the

redistributed moment should not be more than 30% of

the elastic moment, or else large rotation in the plastic

hinge can be expected.

When the load path or the static scheme of the

existing structure is not clear, full finite element model

of the structure may be the best solution for the

assessment.

The final decision whether or not a structural

elements should be strengthened should be made not

only based on the results from the numerical

assessment, but also based on the actual state of the

structure. In this case the numerical assessment shows

that many of the elements do not need to be

strengthened, but the site investigation proves

otherwise: the wide cracks suggest that these elements

have not responded well to the past and present loads

and actions.

The value of the initial loading of the existing

structure that is to be strengthened is crucial for the

effectiveness of the interventions. Therefore, it should

be clarified prior the design and taken into account in

the calculations.

The accompanying activities like the replacement

of insulation may proof to be as important as the

strengthening itself. In this case all the structural

problems were effects from the poor maintenance and

leaking. Without the execution of proper

waterproofing, all the undertaken interventions would

be just a temporary solution of the structural problems

and in a few years the state of the structure would be

as bad as it was before the strengthening.

In order to be able to use the remaining capacity

of the existing structure, rehabilitation should be

undertaken before any strengthening interventions.

Without this step, the adequacy of the design solution

is questionable.

The choice of strengthening materials is

dependent on the characteristics of the existing

materials. Sometimes, however, technical limitations

are the leading factor when choosing strengthening

materials. In such cases verification of the new-old

material connection is mandatory.

The decision-making for the most suitable

strengthening technique should be made on the basis

of certain technical, socio-economical and

architectural criteria that are predetermined. Weight

factors should be assigned to each criteria, depending

on the priorities of the decision-maker.

References [1] BDS EN 1992-1-1:2005/NA:2015 Design of reinforced

concrete structures, General rules and rules for buildings, Bulgarian Institute of Standardization, 2015. (in Bulgarian)

[2] A. Maghsoudi, H. Bengar, Moment redistribution and ductility of RHSC continuous beams strengthened with CFRP, Turkish J. Eng. Env. Sci. 33 (2009) 45-59.

[3] H. Akbarzadeh, A. Maghsoudi, Experimental and analytical investigation of reinforced high strength concrete continuous beams strengthened with fiber reinforced polymer, Materials & Design 31 (2010) 1130-1147.


1191

[4] M. Aiello, L. Valente, A. Rizzo, Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates, Mechanics of Composite Materials 43 (2007) 453-466.

[5] ACI 440.2R-08 Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, American Concrete Institute, 2008.

[6] CNR-DT 200/2004: Guide for the design and

construction of externally bonded FRP systems for strengthening existing structures-materials, RC and PC structures, masonry structures, National Research Council, Rome, 2004.

[7] T. Chardakova, K. Vazgechev, M. Traykova, Strengthening of structural elements from monolithic RC beam-column structures, New Campaign, Sofia, 2015. (in Bulgarian)

assessment and alternative design solutions for ... sr design bending moment (kn.m) msy yielding...

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