Flexural Behavior of Two-Span Continuous Prestressed Concrete Girders with Highly Eccentric External Tendons. Paper by Thiru Aravinthan, Eakarat Witchukreangkrai, and Hiroshi Mutsuyoshi/AUTHORS' CLOSURE

Discussion by Jinsheng Du and Xuejun Wang

Associate Professor, School of Civil Engineering, Beijing Jiaotong University, Beijing, China; Senior Bridge Engineer, First Highway Survey and Design Institute of China, Xi An, China.

The discussers thank the authors for writing an interesting paper on the behavior of prestressed concrete girders with highly eccentric external tendons. The following points are offered for discussion to hopefully complement the paper.

The discussers partially agree with the authors' point of view that by making the external tendons highly eccentric, flexural strength of the beam can be improved. In essence, the enhanced flexural moment as well as service moment is due to the greater increase of stress in the external tendons as opposed to in normally eccentric tendons. Because there are many factors affecting the change of stress in external tendons, simply saying the external tendons are highly eccentric does not always guarantee the flexural strength of the member to be enhanced. One of the main parameters influencing the increase of external tendon stress is the reinforcement index or ratio. If one uses the following combined reinforcement ratio q^sub 0^ to evaluate the reinforcement ratio of the present nine specimens, it will be found that all the q^sub 0^ at critical section of nine beams are extremely low (listed in Table A).

... (4)

where A^sub p^ is the cross-sectional area of external tendons, f^sub pe^ is the effective prestress in external tendons, b is the compressive width of the section, d^sub p^ is the distance of centroid of external tendons to the extreme compression fiber of the section, and f'^sub c^ is the compressive strength of concrete.

For a rectangular section, and neglecting the contribution from compression reinforcement, q^sub 0^ somewhat reflects the force equilibrium of the section and it is approximately proportional to c/d^sub p^, where c is the depth of neutral axis at critical section. The tests of unbonded partially prestressed concrete beams20,21 have indicated that the stress increment in unbonded or external tendons increases with the decrease of c/d^sub p^. Regarding the authors' test beam, it is the extremely low value of q^sub 0^ (q^sub 0^ less than 0.002 and 0.006 at midspan and center support section, respectively, as shown in Table A) that leads to the larger stress increment in external tendons, correspondingly, resulting in the improvement of flexural strength. That is to say, with the high eccentricity of external tendons (namely, larger value of d^sub p^), if any other parameters in Eq. (4) are also changed and result in the greater value of q^sub 0^, the final flexural strength of the member will not be improved.

The authors' investigation on the increase in external tendon stress supports some other researchers' conclusions that the increment of unbonded or external tendon stress is directly related to the midspan deflection of the beam. So the discussers believe that deformation-based equation, such as recently proposed by Roberts-Wollmann et al.22 on the prediction of stress increment in external tendons is still applicable to the present highly eccentric external tendons.

REFERENCES

21. Campbell, T. I., and Chouinard, K. L., "Influence of Nonprestressed Reinforcement on the Strength of Unbonded Partially Prestressed Concrete Members," ACI Structural Journal, V. 88, No. 5, Sept.-Oct. 1991, pp. 546-551.

20. Du, G., and Tao, X., "Ultimate Stress of Unbonded Tendons in Partially Prestressed Concrete Beams," PCI Journal, V. 30, No. 6, Nov.-Dec. 1985, pp. 72-91.

22. Roberts-Wollmann, C. L.; Kreger, M. E.; Rogowsky, D. M.; and Breen, J. E., "Stresses in External Tendons at Ultimate," ACI Structural Journal, V. 102, No. 2, Mar.-Apr. 2005, pp. 206-213.

AUTHORS' CLOSURE

The authors would like to thank the discussers for expressing interest in the research work and for their valuable comments and discussion.

The discussers stated that placing the external tendons at high eccentricity does not always enhance the flexural strength of the member because there are several factors affecting the change of stress in external tendons. They argued that, in a member with highly eccentric external tendons, if other parameters are changed so that the reinforcement index q^sub 0^ becomes larger, the final flexural strength of the member will not be improved.

The authors agree with the discussers that the stress increase in unbonded or external tendons at ultimate Δf^sub ps^ is dependent on many factors. It is generally known that the behavior of stress increase in unbonded or external tendons is member-dependent instead of section-dependent.23 The member-dependent effects are generally incorporated by the span-depth ratio L/d^sub p^, type of loading (or length of plastic hinge), and loading pattern (in the case of continuous beams). Hence, it is evident that the tendon depth d^sub p^ does not only take into account the sectional-dependent effect (reinforcement index q^sub 0^), but also the impact of memberdependent characteristic (L/d^sub p^). Previous researchers24,25 have shown that Δf^sub ps^ becomes larger with decreasing L/d^sub p^, that is, increasing d^sub p^. As a consequence, the authors believe that the tendon depth can be regarded as the most important parameter affecting the stress increase in externally unbonded tendon. It is, therefore, the authors' view that placing the external tendons at high eccentricity will significantly enhance the flexural strength of the member. In addition, the authors would like to take this opportunity to clarify that the flexural strength of a continuous girder with external tendons does not simply depend on the tendon eccentricity of the midspan or the center support, but a combination of both, due to the effects of moment redistribution and secondary moments due to prestress. This has been the main thrust for conducting the experimental investigations, which yielded such interesting results.