Technical Note
Various Schemes for Strengthening Concrete Structures
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guin, Ph.D., F.ASCE.1
Gilbert H. Be
Abstract: Increased traffic loads and the creation of passages and openings in buildings by cutting a piece of slab or a portion of a wall require
the strengthening of the weak or impaired member. Means are various: addition of a supporting beam, prestressing the section with external
tendons, attaching steel plates or carbon-fiber-reinforced plastic (CFRP) strips to the weak face of a slab or wall. Adding a steel beam with the
purpose of creating a composite action between the beam and slab was critically examined. Strength as well as rigidities of the modified structure were affected. DOI: 10.1061/(ASCE)SC.1943-5576.0000377. © 2018 American Society of Civil Engineers.
Author keywords: Structural upgrading; Slabs; Arch bridge; Extra-supporting members; Postcomposite action; Posttensioning; Glued
reinforcement.
Strengthening a Bridge Deck
Introduction
Increased traffic loads demand the assessment of the load capacity
of urban structures, and in the case of deficiencies, a strengthening
of the deficient elements is required. In buildings, the cutting of
openings in slabs and in walls often requires a strengthening of the
regions adjacent to the opening.
Strengthening by Adding Concrete
This is the first solution that comes to mind. This method has to
cope with two basic problems: (1) the bond between new and older
concrete, and (2) the effect of shrinkage and creep in the new concrete on this bond. In Europe, where the concrete of roadways is often protected by an impervious membrane topped by a thickness of
bituminous material, the removal and replacement of such cover
prevents the application of this method.
Nevertheless, in a large exhibit hall, some limited areas were
strengthened in this manner to allow for the passage of trucks. As a
first step, the bituminous layer and the concrete that covers the reinforcing steel were removed; the slab was supported and slightly
jacked up. Then, additional steel bars were placed and bound to the
existing ones. Later, a layer of microbeton (concrete with smaller
aggregates) was poured and carefully cured. The additional concrete and reinforcement at the upper face and the steel plates, seen
in Fig. 1, glued to the underside of the slab, provided the required
increase of strength. A load test was carried out with loaded trucks.
Stresses were measured in the steel plate, in the adjacent concrete,
and in a reinforcing bar nearby as shown in (Fig. 2). The various
measured strains were quasi-identical.
Strengthening by Adding Supporting Members
To add some support to the weaker elements to relieve them seems
a straightforward solution, but it is less simple than it may appear
and has pitfalls.
1
Consultant, Ch. Au Revelin 32, CH-1422 Grandson, Switzerland.
E-mail: ghbeguin@gmail.com
Note. This manuscript was submitted on August 24, 2017; approved
on December 20, 2017; published online on May 3, 2018. Discussion period open until October 3, 2018; separate discussions must be submitted
for individual papers. This technical note is part of the Practice Periodical
on Structural Design and Construction, © ASCE, ISSN 1084-0680.
© ASCE
A deck-stiffened arch bridge and its approaching spans built of reinforced concrete between 1953 and 1954 needed assessment because
of the increased traffic. It was found analytically that the deck slab
could not support the new loads without damage; a strengthening of
the deck (Fig. 3) and of the arch was planned.
The deck is made of two main girders and two edge beams, each
of constant height (110 cm); they support a slab with a thickness of
25 cm. The main girders are 6.5 m apart, and the edge beam is
3.05 m away from the adjacent main one. The edge beams carry
cantilevered sidewalks.
Cross-beams are found at intervals varying from 4.8 to 7.0 m,
and are supported by slender concrete walls resting on twin arches.
Between the main girders, the concrete slab is a two-way continuous plate spanning fields ranging from 6.5 4.8 to 6.5 6.85 m,
which are bonded to the narrower slabs connecting the edge beam
and main girder.
To strengthen this central part of the deck slab, the engineer in
charge placed a longitudinal wide flange (WF) 800 steel girder
(height 80 cm) half-way between the existing reinforced-concrete
main girders. This steel beam should act in a composite manner
with the existing deck slab. For this purpose, small segments of steel
bars (diameter 16 mm, 26 cm long) were welded every 20 cm on the
upper flange of the steel girder, and holes, each 20 cm apart, were
later drilled in two staggered rows on the entire length of the flange.
This scheme is seen in Fig. 4. The required holes (9 cm deep) were
drilled first in the slab from its underside with the same pattern.
Because holes cannot be drilled in a reinforced-concrete member
with sufficient accuracy, a template of the holes as drilled was made
on the spot at the underside of the slab. Later, this 6-m-long template was transferred to the workshop and placed on the flange to
locate the holes in the upper flange of the steel beam.
The flange of the steel girders was fastened by means of set
screws to the underside of the slab, and mortar was pressed in the
space remaining between concrete and steel.
The critical question is: does a composite action effectively take
place?
The effective width (we) of the concrete slab participating in the
composite action must first be determined. For a wide-flange T-beam,
a span of 2l (Timoshenko and Goodier 1970) indicates we 0.16 (2l).
In this derivation, web and flanges are made of the same material.
A reduced effective width of 0.12 (2l) is probably a good guess
in this special case. It follows that, instead of considering the inertia
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of the sole steel profile (35.91 dm4), a greater inertia (73.14 dm4)
must be taken into account, the geometrical parameters of the concrete section being reduced by a factor 10. The designer intended
the reinforcing beam to act as a continuous member; the extremities
of adjacent beams were tied with two high-stress bolted ties
26.5 mm in diameter placed in the upper part of the end plate of
each WF 800 profile. In the area where negative moment acts in the
WF 800, the concrete layer adjoining steel was stressed in tension;
positive bending moment in the longitudinal direction was found in
only approximately 27% of the span on each side of the midspan.
Fig. 1. Steel plates at the underside of slab (Image by author)
The condition of equal deflection of slab and beam, say at midspan, under two loads of 100 kN some 1.2 m apart in a 6-m
clamped square slab yielded a force of 127.2 kN acting between
slab and WF 800. The compressive stress at midspan at the upper
face of the steel section was 398 N/cm2 (i.e., 40 N/cm2 in the
adjacent concrete). These computations postulated a perfect bond
between steel flange and adjoining concrete. But between concrete and steel, there was a 2–3-cm layer of mortar with a modulus
of elasticity close to 2 106 N/cm2.
The maximum strain at the base of the layer of mortar was equal
to « max = 40/2 106 = 0.2 10−4, but the drying shrinkage of a
mortar, which can hardly be properly cured, was approximately
0.4 10−4; this reduced the postulated composite action. Moreover,
the shear deformation of the layer of mortar—examined in the appendix—further limited a perfect binding of steel beam and concrete slab.
Thus, it appears that there was a lower limit to the ratio
span=height of girder, under which one cannot expect a composite
action between steel and concrete. In composite bridges, this ratio is
close to 20, whereas in the case at hand, it was equal to 7.5.
This manner of strengthening the deck with a stiff beam has a
drawback: it causes negative bending moment in the slab at the top of
the WF 800 girder in the transverse direction, at midspan, where
most steel lies near the bottom of the slab. To stiffen the weak part of
the deck, one could place three or more longitudinal steel beams
instead of one. The spacing and rigidities of these beams would be
chosen to minimize the negative transverse bending in the deck at the
top of the beams. To reduce the stressing of the main longitudinal
reinforcing steel, one could attach a few steel plates or carbon-fiberreinforced plastic (CFRP) strips to the underside of the concrete slab.
In short, a few well-distributed stiffening beams are better than one.
Strengthening Arches of a Deck-Stiffened Arch Bridge
Fig. 2. Measurement of strains (Image by author)
The engineer in charge of the rehabilitation of this bridge (Fig. 5)
found by analysis that the twin arches were too weak to carry the
increased traffic loads; the engineer planned a strengthening scheme
in which the first two bays, on each side of the arch bridge, were
stiffened with a pair of hollow steel profiles (diameter 245 mm)
placed diagonally in each bay. The connection of the additional
members at the junctions of arch and cross wall is shown in Fig. 6.
Concrete blocks were poured at the joints and were anchored by
means of four longs bolts provided with a large square head. The
bolts were set in holes previously drilled in the arch. A plastic sleeve
drawn over the length of the bolt allowed the later stressing of the
long bolts. At the opposite side, two large U-bolts, later embedded
in the block, fastened the end plate welded at the extremities of the
tubular members. After the six bolts were in place, the concreting of
the blocks began.
Fig. 3. Bridge cross section; WF = Wide Flange
© ASCE
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Fig. 4. Connection of steel flange to concrete slab; WF = wide flange
to a central part acting as a stiffened arch. Axial forces appeared in
the deck, and the cross walls suffered increased stressing. At the
junction of the truss to the remains of the original structure, unexpected bending moment appeared in the arch and in the deck, too.
This alteration of the original system was said to increase the
buckling load of the twin arches, although the buckling length and
the rigidity of the members of the arch were left unchanged.
Aesthetically, this solution is hardly satisfactory (Fig. 8).
Originally, the vertical loads transmitted by the cross walls were
taken up almost entirely by the arch, whose axial rigidity was
approximately 10 times that of the added steel diagonals.
Observations (deflections, stress measurements) were never made
either before rehabilitation or afterward. This absolute reliance on
computations is miles away from Maillart’s thinking, for he
designed a first version of this project (Bill 1949).
Fig. 5. Original arch bridge (Reprinted from Bill 1949)
Strengthening with the Help of Unbonded
Prestressed Tendons
For traffic load, the behavior of the deck-stiffened arch was
altered; the static scheme was a hybrid: two end quarters of the
bridge were transformed in a truss (Fig. 7) of variable height joined
© ASCE
This method has already been applied successfully in several cases.
Two specific applications for reinforcing concrete slabs are indicated here.
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Fig. 6. Diagonal attached to the arch
Fig. 7. Arch bridge strengthened with diagonals
© ASCE
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Fig. 9. Ribbed slab to strengthen (Image by author)
Fig. 8. Strengthened bridge (Image by author)
Ribbed Slab
The underside of the slab seen in Fig. 9 allows the easy placing of a
steel tendon between the ribs. In this building, the floor made of a
ribbed slab with a span of 5.5 m was designed for a load of 1,500 N/m2;
the owner wanted to increase the allowable live load to 2,800 N/m2. An
unbonded steel tendon set at the proper height between the ribs
(Fig. 10) and running from the end beam, which closed the profile
to the opposite one, was stressed with an appropriate jack
(Fig. 11); this provided the required strength increase.
Buried Service Gallery
At a large airport, the increased traffic load required the strengthening, over some 250 m, of the roof of a buried service gallery subjected to heavier wheel loads. This rectangular box structure, 4.0 m
wide and 2.6 m high with an upper slab 28 cm thick, was crowded
with a number of ducts and electrical lines; little space was left for
additional supporting members. A solution was adopted in which
unbonded steel tendons were placed in the transverse direction every meter over the entire 250-m-long gallery, near the bottom of the
roof slab. The tendons were stressed at 250 kN each.
Strengthening of Slabs with Steel Plates or CFRP Strips
This method has been known since the work of L'Hermite and
Bresson (1967) in France. It requires a concrete of good quality
because the critical parameters are the adhesion of the additional
member to the concrete and the shear strength of the outer layer of
concrete. The tests by Bresson (1971) showed that for a concrete of
standard quality, a steel plate with a thickness up to 3 mm may
reach its elastic limit. For thicker plates, adhesion and shear strength
of concrete are critical (Beguin 1991, 1992). Steel plates require
temporary support during the hardening of the adhesive. Steel plates
have been superseded by CFRP. These strips are much lighter and
thus easier to apply; however, in both systems, the weak link lies in
the anchorage area.
Various schemes of anchoring the ends of the strips have been
tested (Zhang and Yan 2017). The quality of the anchorage dictates
the allowable stress in the reinforcing strip.
In the strengthening of members by means of steel plates or by
CFRP laminates glued to the concrete, uninformed engineers often
consider the steel plate or the CFRP strip as an additional reinforcing bar comparable to those embedded in the concrete, which is not
the case.
© ASCE
Fig. 10. Cross section of slab
In a mathematical study, Pflüger (1947) considered a 2-dimensional. half-plane subjected to a uniform tension and strengthened
at its upper edge by a strip firmly attached to its support. The strip
had a length b, a thickness t, and a modulus of elasticity EL; the material of the half-plane had an elastic modulus E. The condition of
equilibrium and the boundary condition led to an integral equation.
The author examined more precisely the condition at the end of the
strip: there, a linear transition over a length equal to a few times the
thickness (t) reduced the shear stress to a finite value. However,
with such a linear transition, the stress (s x ) perpendicular to the
strip still grew to infinity at its end. The author showed that a transition zone in which the strip thickness has at its end a tangent parallel
to the edge of the half-plane leads to a finite shear stress (t ) and to a
finite value for s x only when the shear stress is t ¼ 0 at this point.
Forming the end of a strengthening strip in such a shape is not
practical. However, the CFRP laminates can be shaped to form an
anchorage, as shown by Orton et al. (2008). By designing a specified geometrical anchorage, described by Kim et al. (2014), the
weakness appearing at the end of the laminate was obviated. In the
practice, this has not yet found a large application.
Discussion
The various solutions adopted for strengthening reinforced-concrete
urban structures reflect the designer’s understanding of the play of
forces in the structure.
By modifying the path of forces within the structure, one runs
the risk of causing some deficiencies elsewhere. Therefore, the
engineer should attempt to retain the original system; if some rigidities must be modified, the rigidities of the connected members
should also be modified in a proportionate manner. Unfortunately,
the advent of limit design (Wood 1961) has blurred the intimate
relationship between strength and deformation.
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Fig. 12. Layer of mortar between steel and concrete
Fig. 11. Jack for stressing the tendon (Image by author)
Two examples are given here. In a large office building, part of
the wall of the underground bank safe deposit had to be removed
over a length of approximately 4 m; this wall supported a
reinforced-concrete slab with a thickness of 45 cm. Fearing some
deflections, the engineer in charge requested steel plates to be glued
to the underside of the thick slab. To take up any stress, the steel
plates have to undergo some stretching through a curvature of the
slab. Given the thickness of the slab and the limited span, it is doubtful that the steel plates will serve their intended purpose.
In an underground structure, a wall had to be cut between two
rooms, leaving an opening 5 m wide. Above the planned opening,
the portion of reinforced-concrete wall left in place had a height of
120 cm and a thickness of 60 cm. The engineer in charge planned
the setting of three steel columns to support the open span, columns
simply fitted in the opening. A simple computation showed that the
deflection of the wall portion left in place was, at the location of the
columns, a small fraction of the shortening of the steel columns
under loads. Of course, in the thinking of limit design, the columns
take up large loads.
Regarding the reinforcing of slabs, it must be recalled that many
slabs have a reserve in strength (Bakht and Jaeger 1990; Das and
Sen 1979) that does not appear in the usual design computations.
Fig. 13. Infinite strip under shear stress
respect to the lower one is given by E u ¼ t o fð4 sh2 a tÞ=½a ð2 a t sh 2 a tÞg cos a x, with a ¼ p =l.
(t) is a small fraction of l, one can write Eu ¼
When the height
t 0 ð3l2 Þ=ðp 2 tÞ cos ax, where E is the modulus of elasticity of the
mortar. In the case examined here, with l = 300 cm and
2 t ¼ 3 cm,
umax = 0.06 cm, and an average strain of 0:06 2=ðp 300Þ ¼
1:26 104 .
Notation
Conclusion
The solutions shown—two of which did not originate in the
author’s office—reflect the variety of approaches to the problem of
strengthening an existing structure, or part of a structure. The engineer should strive to modify as little as possible the original static
system, for in this type of work, one often finds oneself in a dilemma: what is best? An estimate of the corresponding rigidities of
support and supported member, of reinforcement, and member to
be reinforced is necessary to judge the efficiency of the planned
measures.
Appendix: Analysis of Composite Action
The layer of mortar is inserted between steel flange and the underside of the slab. It is subjected mainly to a shear stress (Fig. 12).
Consider an infinite strip of rectangular section with thickness 2t
subjected to a distributed shear force (t o cos Ax) acting on the two
opposite faces of the strip seen in Fig. 13. In the plane stress theory
of elasticity, the displacement [u ða xÞ] of the upper face with
© ASCE
The following symbols are used in this paper:
E ¼ modulus of elasticity;
l ¼ span;
t ¼ thickness;
u ¼ displacement;
s ¼ normal stress; and
t ¼ shear stress.
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© ASCE
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