Technical Note Various Schemes for Strengthening Concrete Structures Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. 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: [email protected] 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 06018004-1 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. Constr. Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. 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 06018004-2 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. Constr. Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. 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. 06018004-3 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. Constr. Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. Fig. 6. Diagonal attached to the arch Fig. 7. Arch bridge strengthened with diagonals © ASCE 06018004-4 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. Constr. Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. 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. 06018004-5 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. Constr. Downloaded from ascelibrary.org by Shri Govindram Seksaria Institute Of Technology And Science on 07/23/18. Copyright ASCE. For personal use only; all rights reserved. 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. References Bakht, B., and Jaeger, L. G. (1990). “Bridge testing—A surprise every time.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1990)116:5(1370), 1370–1383. Beguin, G. H. (1991). “Discussion of ‘Debonding of steel plate–strengthened concrete beams’ by S. A. Hamoush and S. H. Ahmad (February, 1990, Vol. 116, No. 2).” J. Struct. Eng., 10.1061/(ASCE)0733 -9445(1991)117:11(3549.3), 3549–3551. Beguin, G. H. (1992). “Discussion of ‘Premature failure of externally plated reinforced concrete beams’ by Deric John Oehlers and John Paul Moran (April, 1990, Vol. 116, No. 4).” J. Struct. Eng., 10.1061/(ASCE)0733 -9445(1992)118:3(862.2), 862–864. 06018004-6 Pract. Period. Struct. Des. Constr., 2018, 23(3): 06018004 Pract. Period. Struct. Des. 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