# Design Guidelines

Based on the findings of this research program a series of design guidelines have been developed which can be used by practitioners to design HM CFRP strengthening for steel-concrete composite beams (Schnerch et al., 2005). This section presents a summary of the proposed flexural design procedure including a discussion of the determination of the allowable increase of the live-load level for a strengthened beam.

The flexural analysis and design of a steel-concrete composite beam strengthened with HM CFRP materials are based on a non-linear moment-curvature analysis. The analysis satisfies the requirements of equilibrium and compatibility and neglects the effect of shear-lag between the steel and the CFRP. A non-linear material characteristic is used to represent the stress-strain behavior of the concrete and the steel while the CFRP is assumed to remain linear and elastic to failure.

The moment-curvature behavior of a given cross-section is determined based on the strain at the top level of the compression flange together with an assumed neutral axis depth. The cross-section is broken down into levels corresponding to the concrete deck, the longitudinal steel reinforcement of the concrete deck, the flanges and web of the steel beam, and the HM CFRP strips at the bottom of the cross-section. The strain, £x, at any distance, x, from the neutral axis of the section can be calculated using Equation (1) as,

£

£x = —x Equation (1)

c

where £c is the strain at the top surface of the concrete deck and c is the assumed neutral axis depth. From the strain profile and the constitutive relationships of the materials, the corresponding stress profile for the beam can be established. The corresponding resultant forces for the different elements of the cross section can be calculated by integration of the stress profile using Equation (2),

F = b J f (x )dx Equation (2)

where F is the calculated resultant force, b is the width of the element under consideration and f(x) is the constitutive relationship of the material. The assumed neutral axis depth is iterated until horizontal force equilibrium is satisfied. The corresponding moment can then be calculated by replacing the term f(x) in Equation (2) by the term x f(x) and re-evaluating the integrals. The curvature of the section can then be calculated from the strain at the top surface of the concrete deck, ec, and the appropriate neutral axis depth, c. This strain is subsequently increased to determine the next increment of curvature and the procedure is repeated. This procedure can be easily extended to predict the load deflection behavior of a beam with a given loading and support configuration by integration of the curvature profile using any commonly accepted method.

 Figure 7: Load levels and moment-curvature behavior for a strengthened beam

While the nominal behavior of the member can be used to predict the behavior under service loading conditions, the design ultimate capacity should incorporate suitable reduction factors to ensure that the member remains safe. These reduction factors should account for the uncertainty of the HM CFRP material properties and should take into consideration the sudden, brittle failure which is typical of most HM CFRP strengthened steel-concrete composite beams. This guideline has adopted the approach outlined in ACI 440.2R-02 for the calculation of the ultimate capacity of concrete beams strengthened with externally bonded FRP materials. However, the approach has been modified to account for the inherent difference between the behavior of steel beams and concrete beams.

To account for the statistical uncertainty of the measured ultimate capacity of the HM CFRP materials, the mean strength of the CFRP reported by the manufacturer, fFRP u, should not be used directly in calculating the ultimate capacity of the strengthened section. Rather, the average ultimate strength of the FRP should be reduced by 3 times the standard deviation, O, as in Equation (3) (ACI 440.2R, 2002).

fFRP, u = fFRP, u – 30 Equation (3)

To account for possible environmental degradation of the CFRP materials throughout the

lifetime of the strengthening, ACI 440.2R-02 recommends the use of an environmental reduction

factor, CE. For carbon fiber materials subjected to exterior exposure, which is typical for most bridge structures, a value of CE of 0.85 should be used. Therefore, the design strength of the HM CFRP material can be calculated as

fFRP, u = CEfFRP, u Equation (4)

The design ultimate strain of the CFRP material, eFRP, u can be calculated by dividing the calculated design strength of the CFRP by the average elastic modulus, EFRP, reported by the manufacturer.

The nominal moment capacity of the strengthened member, Mn, S, should be calculated using the proposed moment-curvature procedure and the design strength and ultimate strain of the CFRP. The nominal capacity of a steel-concrete composite beam strengthened with high modulus CFRP materials is typically governed by rupture of the CFRP materials. This type of failure occurs in a sudden, brittle manner without significant warning. To account for the brittle nature of failure, a strength reduction factor, ф, of 0.75 is recommended. This reduction factor is consistent with the reduction used in the AISC LRFD Specification (2001) for rupture type limit states. The design ultimate capacity of the strengthened beam, MUS should be calculated as фMn, S.

Conclusions

This paper presents the details of an experimental program which was conducted in three phases to investigate the fundamental behavior of steel-concrete composite beams strengthened using high modulus CFRP materials. Based on the findings of the first phase of the experimental program, it is evident that HM CFRP materials can be used to increase the elastic stiffness, yield load and ultimate capacity of steel-concrete composite beams which are typical of most highway bridge structures. Additionally, the presence of the CFRP helps to reduce the residual deflection due to overloading conditions which can help reduce or eliminate the need for future repair or replacement of the structure. The fatigue durability of the strengthening system was demonstrated in the second phase of the experimental program. Two beams were strengthened with a reinforcement ratio of CFRP of

4.3 percent and subjected to three million fatigue loading cycles with an increase of the simulated allowable live-load level of 20 percent as compared to an unstrengthened control beam. Both strengthened beams exhibited superior fatigue performance to the unstrengthened control beam with regards to the fatigue-creep behavior of the concrete deck. Further, the bonding technique did not appear to affect the fatigue behavior of the strengthening system. Based on the measured strain profile of the five strengthened beams which were investigated in the shear-lag study, the effect of shear-lag between the steel beam and the CFRP materials is minimal.

This paper also presents a proposed flexural design procedure, which is based on a non-linear moment-curvature analysis, which can be used to design the required HM CFRP strengthening for a steel-concrete composite beam. Based on the proposed guidelines, the allowable live load increase for a strengthened beam should satisfy three conditions. Particularly,

(i) Md + Ml ^ 0.6 Mys

(ii) ав Md + aL Ml < Mu, s

(iii) Md + Ml < Mn, us

The findings of this research demonstrate that new externally bonded HM CFRP materials provide an effective, cost-efficient repair alternative for conventional steel-concrete highway bridge girders.