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

2. 2 USE OF CRACK PATTERN Crack pattern should be taken into account for comparative analysis of structure with existing cracks. In this case, as a model, we often use the deep beam analogy with additional line elements, simulating prestressing tendons. Such approach has been done in case of girder No 4 of Grunwaldzki Bridge in Cracow. The calculation has been done using the finite element method. The stiffness of the three span deep beam model was like stiffness of the three span single girder of the bridge, with the same spans, prestressed in the same way as the real girder (Fig.2). Figure 2 Grunwaldzki Bridge in Cracow SIDE ELEVATIONLONGITUDINAL SECTION SUPPORT Girder No4 CROSS - SECTION SPAN

3. 3 The main target of analysis was to establish the real state of prestressing of the bridge spans. For such reason they have been taken into account over 60 combination of loads and states of structure. They have been taken into account different combinations of: loads, e.g. dead load, superimposed load, partial live load and full live load according to the Polish standard, using influence line or influence surface of load distribution; vertical displacement of supports, e.g. -0.2, -0.1, -0.05, 0, 0.1, 0.2 m; different prestressing forces e.g. 50, 70, 85 and 100% of design value; different creep coefficients for permanent loads, e.g. 0, 2 and 3. Creep of concrete has been included for permanent load by modification of modulus of elasticity using following formula: (3) where: E c - modulus of elasticity for short-time loads,  - creep coefficient for concrete.

4. 4 Since all computation has been performed with the help of standard computer program ‘Micro Strains’, designed for structure built from homogeneous material within elastic range, in the procedure ‘step by step’ method has been used. Use of such standard program there is an advantage, because it enables application much more accessible tool for engineers. In that way after each step of calculation values of principal tensile stresses  1 have been checked in all elements. When the value in the element exceeds of limit value, taken as 0.6f ctk, modulus of elasticity for the concrete in the element has been reduced according with formula: (4) As a limit value has been assumed 60% of characteristic tensile strength of concrete because of fatigue effect.

5. 5 Figure 3 Reduction of modulus of elasticity for concrete after cracking Figure 4 Stresses in concrete deep beam after cracking As the deep beam is working as two dimensional structure, we should realise that we reduce stiffness of element simultaneously in both directions. Baumann has indicated that in general case even in cracks tensional stresses may arise thanks to equilibrium of an element (Fig.4). Presence of reinforcement increases considerably tensional forces along trajectory of stresses  1.

6. 6 For the combinations of loads they were created maps of stresses, than the maps have been compared with the real crack pattern of analysed girder. Figure 5 Scheme of ½ length of Grunwaldzki Bridge Girder No 4 with partition into elements The load combination No 23 corresponded to characteristic load comprised: self weight, superimposed load, 70 % of designed prestressing, 50 % of the maximum live load and settlement of the pier -0.1 m. According to many observation assumed value of live load was close to the frequent value of variable load for the bridge. In Fig. 6 we have example of map of principal tensile stresses  1 for 1/2 of length of deep beam for the load combination No23. as one of the most probable cases which might create existing crack pattern in the girder.

7. 7 Figure 6 Principal stresses σ 1 in ½ length of deep beam They have been also taken into account deflections of model beam and the real girder No4. As a result of comparative analysis, they have been established hypothetical values of prestressing forces existing in the structure, corresponding to the load combination No 23. The average value of prestressing force in whole structure has been estimated as 70% of designed value, however the closer analyse allows us to assume, they are some differences in the reduction of prestressing forces in whole structure.

8. 8 Figure 7 General view of Pokój Bridge in Wrocław

9. 9 Because procedure of comparison of maps of stresses and real crack pattern, became rather tedious and not very precisely, in case of next application the method has been improved. For the Pokój Bridge in Wrocław instead of maps of principal stresses, the maps of elements have been used (Fig.8). Such maps have been prepared, and also using ‘step by step’ procedure, according to the same criteria ‘0.6f ctk ’, a map of elements endangered by cracks have been prepared (Fig. 9). Figure 8 Maps of elements for a part of girder

10. 10 Figure 9 Part of deep beam with shadowed elements endangered by cracks In the map have been shown also the real cracks discovered in the girder of the bridge. The maps of elements became much more precise and practical in use. The average value of prestressing force, corresponding to the picture of endangered elements for girder 1,has been estimated as 65 % of design value, it means about 36 % of assumed characteristic strength of cables.

11. 11 The conformation of the result of analyse is comparison between calculated deflection of the end of cantilever of girder No 1 under self weight of structure, which is z self =0.144 m and measured real value – z m =0.150 m. In the calculation values of E , according with equation (3) have been applied. After statement of an excessive reduction of prestressing force in the structure we should establish the reason of such situation. That is the most important problem from the point of view of the safety of structure. Damages caused by intensive corrosion process of prestressing steel may be extremely dangerous because that process very often produces internal changes in the steel and as a result of these it may create unexpected collapse, having sudden and brittle character.

12. 12 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. They have been presented some way of analysis, based on the comparison of computed for the model of structure values with those confirmed in the real 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.

13. 13 THANK YOU FOR THE ATTENTION