1. 1 ROAD & BRIDGE RESEARCH INSTITUTE WARSAW Juliusz Cieśla ASSESSSMENT OF PRESTRESSING FORCE IN PRESTRESSED CONCRETE BRIDGE SPANS BY THE PROOF LOAD

2. 2 ASSUMPTION It has been assumed, that proper level of prestressing is one of the most essential factor from the safety point of view of structure Evaluation of prestressing force should be the first step of safety appraisal of the structure. If the prestresssing force is below design value, in most of cases the reason of the lack of prestressing is the key to assessment of the safety of the structure. PROCEDURE General procedure of evaluation of prestressing force concerns the real structure and its structural model within such aspects, as: moment of crack formation in prestressed element, crack pattern in concrete of the span and map of stresses of its structural model, use of stiffness of prestressed element.

3. 3 ASSESSMENT OF SAFETY UNCRACKED STRUCTURECRACKED STRUCTURE USE OF STIFFNESS / CRACK MOMENT USE OF CRACK PATTERN ASSESSMENT OF PRESTRESSING FORCE DETERMINATION OF CAUSE OF PRESTRESSING SHORTAGE APPRAISAL OF CARRYING CAPACITY OF STRUCTURE Fig.1. Flow chart of assessment of safety of prestressed concrete structure

4. 4 USE OF CRACK FORMATION In case of absence of cracks under service load, the first observed crack under proof load is important resource of information about prestressing force. We can predict cracks in a beam element by calculation the value of cracking moment, using well known formula: (1) where: W-resistant modulus of element,  b -normal stress in concrete at the edge of element, according to the formula: e p – eccentricity characteristic value of unknown prestressing force P s, -coefficient, normally we assume it 1.7, f ctk -characteristic axial tensile strength of concrete. According to the results of tests made by author the value of 1.7 seems to be acceptable and quite close to EN 1992-1-1 assumption: (2)

5. 5 If we are able to establish bending moment in element, corresponding to the first crack, we can easily calculate value of prestressing force from the formula (1) or (2). If we assume in the formula (1) the value of f ctk =0, we have the value of so- called moment of decompression - M dec =W  b. We can conform the value of M dec during repeated load test of beam, because that value correspond to repeated opening crack, which has been formed before, during previous loading of the beam. Thanks to that we can asses the value of f ctk. After exceeding the moment of decompression, normally we obtain some reduction of stiffness of bending element. Otherwise, every unexpected reduction of stiffness may mean that we are closing to crack moment.

6. 6 USE OF STIFFNESS PHENOMENA Figure 2 Load-deflection curve of prestressed concrete girder

7. 7 where: F - value of load, z m - value of deflection in given cross-section of beam,  -value dependent on boundary conditions for the element, the length of span, geometrical characteristic of cross-section and the way of loading of the beam, e.g. for simply supported beam with single force in the midspan  = L 3 /48I, where I - cross-sectional moment of inertia. We can also introduce similar notion of E z ' according to the formula: where:  F and  z m - respectively are the finite differences of increments of force and deflection for beam element. (3) (4)

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12. 12 USE OF STIFFNESS The procedure is founded on the ground of functional dependence between value of load on the span and deflection of chosen point of structure. First step of procedure is creation of influence surface of deflection for given point of the structure. The influence surface for the point has been derived according with the Betti- Maxwell law mutuality of displacement, which may be described by formula: δ ij = δ ji, (5) using measured deflections of chosen points for all span under known load, placed in the point. Figure 7 Load for evaluation of influence surface of deflection

13. 13 In the Fig. 8 you can see examples of two influence surfaces, produced by single van. Figure 8. The influence surfaces IS for half-span point: a) on the span 4-5 of structure No 1, b) on the span 4-5 of structure No 2 a) b)

14. 14 Using influence surface, you can calculate deflection of the point for each load on the span, just multiplying each applied load, e.g.: weight of lorry, by the corresponding value of ordinate. In that way, it may be produced a functional dependence between total load on the span and deflection of the point, it means deflections of the web of main girder of the examined span. In the Fig. 9 two examples of such dependence for the half-span point on the span 4-5 of structure No 1 and on the span 4-5 of structure No 2 have been presented.

15. 15 Fig.9. Dependence load – deflection for half-span point: a) on the span 4-5 of structure No 1 and b) on the span 4-5 of structure No 2 In each of two figures both curves are similar and close to linear dependence, and the values of deflections do not exceed theoretical values. It means, that level of prestressing assured such structural behavior of the tested part of girder, that we may assume there is no tension in concrete in main direction of bending.

16. 16 CONCLUSION Improper level of prestressing may be a cause of excessive deflections, cracks and corrosion processes and at last a cause of sudden collapse of prestressed concrete bridge structure. The most important from the safety point of view is to distinguish the case of reduction of bearing capacity of structure, which may produce a danger of collapse from the case of reduction serviceability of structure. The real cause of excessive reduction of prestressing force may be established on the ground of a broad basis, including chemical and physical tests.

17. 17 THANK YOU FOR THE ATTENTION