# Verification of Actual Prestressing in Existing Pre-Tensioned Members
## 2 Monitoring of Prestressing Force  
Nowadays, several methods for monitoring the prestressing force value are available. These approaches fall into two main categories: direct and indirect methods. The principle of direct methods is the evaluation of the prestressing force directly from the results of the measurement (elasto-magnetic method, vibration-based methods, etc.) [19]. The benefit of these techniques is the possible real-time monitoring of the prestressing force. Unfortunately, the application of direct methods in existing structures is very limited [20]. Therefore, the implementation of indirect methods for determining the state of prestressing on prestressed concrete structures in service appears to be a suitable alternative. On one hand, direct methods are mainly non-destructive, but on the other hand, indirect methods can be both non-destructive and destructive (or semi-destructive). Classification of indirect methods according to their influence on the investigated structure is in some cases problematic and depends on the point of view of the author. Generally, the techniques with only a local effect on the structure can be considered as non-destructive or semi-destructive, as damages caused by their application can be properly and easily repaired without any long-term impact on the structure's integrity and durability. Indirect methods for determining the state of prestressing include, for example, methods based on stress relief in a concrete member such as the saw-cut method, stress-relief coring technique (or drilling method), strand-cutting method (or wire-cutting method), exposed strand method, and structural response methods (crack initiation method and crack reopening method) [21; 22; 23]. The presented paper is focused on the study of the non-destructive saw-cut method performed on seven prestressed concrete sleepers. Subsequently, obtained results are verified using MBN and compared with values of prestressing force determined using standard calculation. The concept of the saw-cut method is the isolation of a concrete block from acting forces caused by saw-cuts. The value of the prestressing force is then derived from stress (or strain) change monitored in the area adjacent to performed saw-cuts. It can be stated that the concrete block is fully isolated if the increasing depth of the performed saw-cuts no longer initiates any significant change of the measured stress (strain). Recorded stress is the basis for the evaluation of the residual prestressing force value in the examined structure. If it is possible to determine the ratio of the released stress, e.g., by application of validated results of numerical analysis, full isolation of the concrete block is not necessary. This approach is used in the case of old structures with considerably low concrete cover, which limits the maximal depth of the applied saw-cuts. Consequently, saw-cuts have only a negligible local impact on the prestressed concrete structure. For  
Figure 1: Stress in a prestressing tendon over time. this reason, the saw-cut method is considered a non-destructive indirect method [23; 24]. When using the saw-cut method on an unloaded structure, the residual prestressing force can be determined according to Equation (1). This equation is applicable in the case of an uncracked member with a linear distribution of stress. Nevertheless, if the investigated prestressed concrete structure is loaded by the external load, additional stress resulting from this load has to be considered. In Equation (1), \(\sigma_{\text{c,0}}\) represents the initial stress in the concrete member, \(\text{M}_{\text{G}}\) is the bending moment due to dead load, \(\text{e}_{\text{pi}}\) is the eccentricity of prestressing reinforcement from the neutral axis of an ideal cross-section, while \(\text{I}_{\text{yi}}\) (second moment of inertia), \(\text{A}_{\text{i}}\) (cross-sectional area), and \(\text{z}_{\text{i}}\) (position of neutral axis from the edge of the cross-section) are characteristics of the ideal cross-section.