10th International Conference on Short and Medium Span Bridges

Quebec City, Quebec, Canada,

July 31 – August 3, 2018

BEHAVRIOR OF BOLTED SIDE PLATES STRENGTHENED CONCRETE GIRDERS

Su, R.K.L.1,3 and Li L.Z.2

1 Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China

2 College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, P.R. China

3 klsu@hku.hk

Abstract: Reinforced concrete bridges often need strengthening due to prolonged use together with material deterioration, defective construction, having higher loads than those foreseen in the initial design of the structure, or as a result of accidental damage. Previous experimental and numerical studies conducted by the authors have demonstrated that the use of bolted side plates (BSP) can effectively enhance the flexural and shear capacities of RC beams and girders. In this paper, the structural behavior of short-span BSP girders is presented. Some design recommendations for BSP girders are summarized.

1. INTRODUCTION

Many reinforced concrete (RC) bridges require repairs, upgrades or strengthening due to various reasons, such as material deterioration, defective design or construction, structural damage, new and more stringent codified requirements, etc. RC girders, as one of the key load-bearing structural components, may need to be strengthened over time.

Since 2003, the authors have been studying the use of bolted side plates (BSP) for strengthening RC beams and girders. The typical configuration of a BSP girder is shown in Fig.1 (the typical dimensions and material properties of BSP girder will be mentioned in next section). In this strengthening method, steel plates are fixed to the side faces of girders using anchor bolts to increase girder’s shear and flexural capacities. The practical advantages of BSP girders are briefly described herein. First, mechanical anchors instead of adhesive are used; pre-mature debonding and peeling failures of plate can be avoided. Second, unlike bolted soffit plate, the congested bottom rebars would not be disturbed; drilling bolt hole on the side face of girder is easier. Third, props may be provided under the girder soffit if the effects of preloaded gravity loads need to be compensated.

One special feature of BSP girders is that as mechanical shear connectors are used, relative movements between the steel plates and concrete girder, which are known as bolt slip, are unavoidable. Such slips would increase the deformation of girder and reduce the interaction between the steel plates and concrete counterpart and should be minimized as practical as possible. If bolt slips are ignored in the strength design of BSP girder, the flexural capacity of the girder will be overestimated and result in an unsafe design. In our study, special washers developed by HILTI Coporation which allow injection adhesive to be dispensed into the clearance holes (as shown in Fig.1) are adopted to minimize the slips. Such washers can also ensure a uniform distribution of forces among different bolts under static and cyclic loads.

Dc

Dp

RC girder

Steel plate

Anchor bolt

HILTI Dynamic set washer

Beam section

Figure 1: A typical BSP girder

The structural behavior of BSP girder is also controlled by the depth of the steel plates. For shallow plate case, the depth of steel plate (Dp) is less than or equal to one-third of the depth of girder (Dc). For deep plate case, the depth of steel plate is larger than or equal to half of the girder depth. When shallow plates are put to the tension side of the girder, the longitudinal interaction between the plate and girder is more significant. The plate is subjected to a large net tension together with a small bending. For deep plate case, the transverse interaction between the plate and girder is more significant. The plate is subjected to a large moment with a small net tension. Shallow steel plates can be used to effectively strengthen lightly reinforced girders. In contrast, deep steel plates can be used for both lightly and moderately reinforced girders. The behavior of the BSP girders with these two plate depth cases will be discussed in the following section.

1. BEHAVIOR OF BSP GIRDERS

This strengthening method can be used to retrofit short-to-medium span old concrete girders with a span of not more than 30 m. Those old girders were usually lightly or moderately reinforced and made of normal strength concrete with cube compressive strength fcu ≤ 40 MPa. To ensure ductile failure mode of the BSP girders, mild steel plates are used so that plate yields prior to bolt fracture. The structural behavior of BSP girders will be briefly discussed herein.

1. Strengthening Effectiveness and Failure Modes

Extensive experimental studies (Su et al. 2010; Siu and Su 2010; and Li et al. 2013) have been conducted to investigate the effectiveness of BSP strengthening method. More than 40 BSP beams have been tested to examine their flexural and shear behavior as well as their modes of failure. Su et al. (2010) and Siu and Su (2010) studied the bolt-plate arrangement for lightly-reinforced concrete beam (with the longitudinal steel ratio of 0.76%) with a span of 3.6 m strengthened with shallow steel plates. HAS-E anchor rods of 12 mm diameter by HILTI Corporation were used as the mechanical connectors of all specimens. The bolt-plate arrangements of various specimens are summarized in Table 1. Their study revealed that for weak-bolt arrangements fracture of bolts can limit the ductility and deformability of the strengthened beams. For strong-bolt and strong-plate arrangements, concrete often fails in brittle crushing due to over-reinforcement problem (with the equivalent longitudinal steel ratio of 2.3%). For strong-bolt and weak-plate arrangement, over-reinforcement can be avoided and the beam fails in a relatively ductile manner. The flexural capacity of lightly-reinforced beams with shallow plates can be increased up to 40%. Furthermore, for four-point loaded simply supported BSP beams, anchor bolts should also be provided in the pure flexural region to avoid crushing of concrete in the post-peak stage due to enormous transverse slips occurred after the formation of plastic hinges (see Fig. 2). The serious reduction of the effective lever arms of the plate tension can decrease the stiffness and load-carrying capacity of BSP beam.

Table 1: Summary of bolt-plate arrangements of BSP specimens.

Specimen SBSP

Specimen WBSP

Specimen WBWP

Specimen SBWP

No. of bolts on shear span

8

3

3

5

Strength of bolts on shear span

608 kN

228 kN

228 kN

380 kN

Plate size

6 mm × 150 mm

6 mm × 150 mm

6 mm × 75 mm

6 mm × 75 mm

Plate strength

605 kN

605 kN

302 kN

302 kN

Li et al. (2013) tested moderately reinforced RC beams with a longitudinal steel ratio of 1.8% strengthened with shallow and deep plate cases. The flexural strengths of the control specimen and the specimen strengthened with deep plates were found to be 268 kN and 382 kN respectively. The flexural capacity was found to be increased by around 40% for deep plate cases. The strength and response of BSP beams are controlled by plate buckling at the compressive side (see Fig. 3). Adding stiffeners or closely spaced bolts to the plate's compressive side can remarkably improve the flexural strength and deformability of the strengthened beams.

Pure bending zone

Concrete crushing

Shift up of the steel plate causing the reduction of moment arm

Steel plate

Figure 2: Failure mode of BSP beam without anchor bolts in pure bending region

Figure 3: Failure mode associated with plate buckling

Longitudinal slip

Transverse slip

Figure 4: Typical slip profiles of a four-point loaded beam

1. Longitudinal and Transverse Slips

The longitudinal and transverse slips are attributed to the looseness of the axial strain or the curvature of the steel plates. Such slip can significantly reduce the coupling action between the steel plates and concrete beam. The slip behavior has been extensively studied experimentally and numerically (Li et al. 2013; Siu and Su 2011; Su et al. 2013; Su et al. 2014 and Li et al. 2017). The typical longitudinal and transverse slip profiles of a four-point loaded BSP beam is illustrated in Fig. 4. It can be seen that the maximum longitudinal slips occur at the supports and the extreme values of the transverse slips happen at the supports and loading points. In general the transverse slip at the loading points is more critical. The experimental results obtained by Li et al. (2013) further indicate that the magnitudes of the longitudinal and transverse slips are proportional to the bolt spacing. Larger bolt spacing will cause higher bolt slips. Furthermore, increasing the plate depth will decrease the longitudinal slips but increase the transverse slips. Thus, transverse slips for deep plates play a more important role in the flexural design of BSP beam than the longitudinal slips. A simplified piecewise linear model was developed by Li et al. (2017) to simulate the transverse shear transfer for BSP beam subjected to general vertical loads as illustrated in Fig. 5.

For the shallow plate case, the effect of longitudinal slip is significant. Base on the assumptions of (i) linear shear force-slip relationship of anchor bolts, (ii) the same curvatures for steel plates and concrete beam, and (iii) elastic response of beam under service condition, Su et al. (2014) analytically derived the longitudinal slip profile of BSP beam. The predicted longitudinal slips have been verified against the results from the finite element analysis through a wide range of loading cases.

F3

Negative shear transfer block

Positive shear transfer block

Superposition

Figure 5: Piecewise linear transverse shear transfer

1. Strain and Curvature Factors

As mentioned, the slips of anchor bolts can significantly influence the response of BSP beam. To quantify the effects of slip, the strain and curvature factors as expressed in [1] and [2], respectively, are introduced by Su et al. (2010).

[1]

[2]

where and are the longitudinal strains of the steel plates and the RC beam respectively at the centroidal level ypc of steel plate; p and c are the curvatures of the steel plates and RC beam respectively. Once the strain profile of concrete beam has been defined, based on the strain and curvature factors, the strain distribution of steel plates will be defined, see Fig. 6. The internal stresses and forces in the BSP beam can then be evaluated by the conventional sectional analysis by invoking the material stress-strain relationships.

Figure 6: Strain distributions

(a)

(b)

Figure 7: Typical strain and curvature profiles along a BSP beam (a) strain factor and (b) curvature factor

1.0

0.8

0.6

0.4

0.2

0.0

Strain factor

Curvature factor

Shallow plate cases

Deep plate cases

Shallow plate cases

Deep plate cases

Mid-span deflection

Mid-span deflection

0.0

0.0

(a)

(b)

Figure 8: Strain and curvature factors against mid-span deflection (a) strain factor and (b) curvature factor

The typical strain and curvature factor profiles of a 4-point loaded BSP beam are illustrated in Fig. 7(a) and 7(b) respectively. These two factors are controlled by the flexural and axial stiffnesses (EI and EA values) of steel plates and concrete beam as well as the shear stiffness of bolts. Increasing the bolt stiffness or the number of bolts can increase these two factors. For the idealized full interaction case where there is no bolt slip, these two factors are equal to one.

Li et al. (2013) experimentally studied the variations of strain and curvature factors at the mid-span of four-point loaded moderately reinforced BSP beams against the mid-span deflection with various plate depths and bolt spacings. As shown in the Fig. 8, the measured strain factors of BSP beams with shallow plate case are approximate 0.7 and decrease to 0.4 as the increase of mid-span deflection due to the softening effects of anchor bolts as the load increases. The strain factors for deep plate cases are very small as the centroidal levels of deep plate and concrete beam are close together resulting in negligible axial strain in steel plates. On the other hand, the curvature factors of BSP beams for shallow and deep plate cases are generally higher than 0.8. This means that the curvatures of steel plates and concrete beams are quite similar and are not sensitive to the plate deep.

Lo et al. (2014) conducted a numerical parametric study to investigate the effects of strain and curvature factors on the degree of flexural strengthening. Their study found that as the strain or the curvature factor increases from 0.1 to 0.5, the strengthening effect increases significantly. However, further increases of these factors do not result in a considerable increase in strength. Therefore, excessive connection between the steel plates and the RC beam is neither necessary nor economic. Furthermore, a strain or curvature factor of 0.6 can achieve a relative strength increase of 0.9 with a reasonable number of anchor bolts, which is an optimal choice between the strengthening effect and the strengthening efficiency. Consequently, a value of 0.6 is recommended for both the strain and the curvature factors in the design of BSP beams with various combinations of beam types and plate depths as shown in Table 2.

In the flexural strengthening of BSP beams, there can be too many unknowns if both the plate size and bolt arrangements need to be determined at the same time based on the required bending moment capacity. By introducing a value of 0.6 for both the strain and curvature factors, the plate size can be determined directly without considering the bolt arrangement. The number of bolts can then be determined using the conditions of αε,min ≥ 0.6 and αφ,min ≥ 0.6. Based on that, Li et al. (2016b) developed a simplified three-step flexural design procedure for BSP beams.

Table 2: Recommended strain and curvature factors for design

Beam type

Strengthened by

Shallow plates

(Dp≤1/3Dc)

Deep plates

(Dp≥1/2Dc)

Lightly-reinforced

αε = 0.6

αε = 0.6

αφ = 0.6

Moderately-reinforced

Not recommended

αφ = 0.6

1. Buckling of Deep Steel Plates

As mentioned, undesirable plate buckling may occur when the RC beam is strengthened by deep steel plates. Li et al. (2016a) conducted local buckling push tests of bolted steel plates under concentric and eccentric loading. The effects of plate thickness, bolt spacing and buckling restraints on the plate buckling strength were investigated. Their study found that the increase of the plate thickness can increase the buckling strength. However, such method is less economical and is not recommended for general use. On the other hand, reduction of bolt spacing in the compression zone of steel plate and adding buckling restraints in the form of longitudinal stiffeners can both significantly improve the plate buckling strength. The latter method is recommended for practical use due to the ease of construction. Furthermore, Li et al. (2016a) carried out nonlinear finite element analysis for optimum design of the stiffeners of bolted steel plates. Their study reveals that for optimal design of stiffeners, the following conditions should be satisfied: (1) the ratio of the breadth of stiffener to the plate thickness b/t = 6, (2) the ratio of breath to thickness of stiffener b/a ≥ 5 and (3) the area ratio (ab)/(Dpt) = 0.1.

1. CONCLUSIONS

The behavior of bolted side plates (BSP) strengthened girders has been concisely reviewed. The factors affecting the flexural strength design of short-span BSP girders, including bolt slip, plate depth and plate buckling, have been discussed. The design recommendations for BSP girders are summarized as follows:

Shallow steel plates (Dp≤1/3Dc) can be used to strengthen lightly reinforced girders but not moderately reinforced girders to avoid over-reinforcement problem.

Deep steel plates (Dp≥1/2Dc) can be used for both lightly and moderately reinforced girders.

For lightly-reinforced girders, strong-bolt and shallow weak plate arrangement should be used to maintain the desirable ductility capacity. Furthermore, for four-point loaded simply supported girders, anchor bolts should also be provided in the pure flexural region to avoid crushing of concrete in the post-peak stage.

Longitudinal and transverse slips control the degree of flexural strengthening for the shallow and deep plate cases respectively.

Anchor bolt with injection washer should be used to minimize bolt slips.

Strain and curvature factors are introduced to quantify the effects of slips and define the flexural strain distribution in steel plates. For optimal design of BSP girders, a value of 0.6 is recommended for both the strain and the curvature factors.

For the flexural strengthening employing deep steel plates, stiffeners should be added to the compression zone of the plate for suppressing plate buckling.

Using the BSP method, the flexural strength of RC girders can be increased by a maximum of 40%.

Acknowledgements

The research reported in this paper received financial support from the Research Grants Council of the Hong Kong SAR (Project No. HKU7151/10E), conference grant from The University of Hong Kong and technical support from the HILTI Corporation.

References

Li, L.Z., Lo, S.H. and Su R.K.L. 2013. Experimental Study of Moderately Reinforced Concrete Beams Strengthened with Bolted-Side Steel Plates. Advances in Structural Engineering, 16(3): 499-516.

Li, L.Z., Jiang, C.J., Jia, L.J. and Lu, Z.D. 2016a. Local Buckling of Bolted Steel Plates with Different Stiffener Configuration. Engineering Structures, 119: 186-197.

Li, L.Z., Jiang, C.J., Su, R.K.L. and Lo, S.H. 2016b. Design of Bolted Side-Plated Reinforced-Concrete Beams with Partial Interaction. Proceedings of the Institution of Civil Engineers - Structures & Buildings, 169(SB2): 81-95.

Li, L.Z., Jiang, C.J., Su, R.K.L. and Lo, S.H. 2017. A Piecewise Linear Transverse Shear Transfer Model for Bolted Side-Plated Beams. Structural Engineering and Mechanics, 62(4): 443-453.

Lo, S.H., Li, L.Z. and Su, R.K.L. 2014. Optimization of Partial Interaction in Bolted Side-Plated Reinforced Concrete Beams. Computers & Structures, 131: 70-80.

Siu, W.H. and Su, R.K.L. 2010. Effects of Plastic Hinges on Partial Interaction Behaviour of Bolted Side-Plated Beams. Journal of Constructional Steel Research, 66(5): 622-633.

Siu, W.H. and Su, R.K.L. 2011. Analysis of Side-Plated Reinforced Concrete Beams with Partial Interaction. Computers and Concrete, 8(1): 71-96.

Su, R.K.L., Siu, W.H. and Smith, S.T. 2010. Effects of Bolt-Plate Arrangements on Steel Plate Strengthened Reinforced Concrete Beams. Engineering Structures, 32(6): 1769-1778.

Su, R.K.L., Li, L.Z. and Lo, S.H. 2013. Shear Transfer in Bolted Side-Plated RC Beams. Engineering Structures, 56: 1372-1383.

Su, R.K.L., Li, L.Z. and Lo, S.H. 2014. Longitudinal Partial Interaction in Bolted Side-Plated Reinforced Concrete Beams. Advances in Structural Engineering, 17(7): 921-936.

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