Statistical Investigation of Effective Prestress in Prestressed Concrete Bridges

The effective pretress of a strand is very important for prestressed concrete (PC) bridges because it can influence cracking and deflections. At present, the effective prestress is obtained by means of calculating the theoretical prestress loss, which is a theoretical value. However, because of uncertainty in estimating prestress losses and tensioning prestress tendons, the actual effective prestress can be very different from the theoretical values. In this paper, the transverse-tensile-incremental method (TTIM) is applied to investigate the effective prestress of prestressing tendons for PC bridges. First, a ${\mathrm{\varphi }}^{j}15.2$-type strand was tensioned with a fixed force on a machine, and the strand tensile force was tested by a specific instrument manufactured according to the TTIM. An error analysis between the fixed force and tested force was conducted to certify the instrument’s accuracy. The results showed that the error range was from 0.03 to 3.71% when the prestressing tendons tension was between 60 and 200 kN (for the ${\mathrm{\varphi }}^{j}15.2$-type strand, the tensile stress mean was from 428.6 to 1,428.6 MPa). Therefore, it can be accepted that the TTIM could be used in actual testing. Second, a total of 141 on-site measurements were collected and analyzed. A statistical parameter $K_{\mathrm{EP}}$ was introduced to be the statistical objective for the effective prestress of a strand. This parameter was defined as the ratio of mean effective prestress from the testing value to that from theoretical calculation. A statistical analysis was carried out to determine an appropriate probability distribution for the $K_{EP}$ using commercially available software. Based on the collected specimens, a normal distribution was found to be an appropriate probability distribution, and the distribution parameter $K_{EP}$ is $\sim N(0.983,0.066)$. Finally, an example of a reliability assessment was demonstrated using a simply supported T-beam. The anticrack reliability index for the section bottom of the midspan is $\beta =1.223$ when the uncertainty of effective prestress was considered, whereas $\beta =2.488$ if the uncertainty is neglected. Therefore the anticrack reliability would be overestimated if the uncertainty of effective prestress is not included. The method proposed in this paper can provide a way to properly consider the uncertainty of effective prestress and subsequently be used in anticrack reliability assessments for PC bridges.