The Study On Moment Magnification Factor Of Reinforced Concrete Arch Bridge

In design calculation of the reinforced concrete arch bridge, bending moment from linear elastic calculation of arch ring cross-section multiplied by bending moment magnification factor is often used to reflect geometric and material nonlinear effects. But it is always challenge to define the right moment magnification factors. Here is focused on how to define moment magnification factors under the cross-section carrying capacity limit state of reinforced concrete arch bridge.The carrying capacity limit state of reinforced concrete arch bridge exists in cross-sections and overall bridge, the latter one is usually greater than the former one, except for rare cases like under earthquake. Therefore, reinforced concrete arch bridge should be designed to have overall bridge carrying capacity limit state no greater than that of the cross-section. This dissertation combined theoretical analysis, model test and geometric nonlinear analysis of stiffness reduction, to study moment magnification factor of reinforced concrete arch bridge.The static equilibrium analysis was conducted in reinforced concrete hingeless arch. The bending moment of reinforced concrete arch bridge from the nonlinear calculation is greater than that from the linear calculation. The greater moment resulted from the extra bending moment generated from the interaction of horizontal thrust against vertical displacement, vertical reaction force against horizontal displacement, external load against displacement. Under normal rise-span ratio, the arch foot vertical reaction force and horizontal thrust is generally at the same order of magnitude, and the horizontal and vertical displacement of the section is also at the same order of general magnitude. Therefore the extra bending moment from vertical reaction force and horizontal thrust could not be ignored. Based on the analysis of isolation body arch section, external load may increase or decrease the non-linear bending moment.Separation method of arch abutment could be applied to measure the bending moment of arch cross section. Firstly separating arch abutments of hingeless arch feet from ground base to form separated arch abutments. Secondly to measure the vertical reaction force and the horizontal thrust with the integrated pressure sensors to figure out the arch feet’s vertical reaction force, the horizontal thrust and the bending moment, with the reference of relative factors, then to calculate the bending moment, axial force and hearing force of any arch cross section.Moment zero point method could be applied to measure the bending moment of Arch feet. As arch feet horizontal thrust and the vertical reaction force was not impacted by the nonlinear calculation, the liner elastic calculation result could be used as measured value. If limited to conditions, there is no need to measure horizontal thrust and the vertical reaction force or to separate arch abutments. The moment zero point from Nonlinear calculation or actual measurement of the closest point of arch feet, could be used as the first moment zero point. The arch between hingeless arch feet and first moment zero point could be set as isolation body, to analyze its static equilibrium and combine with measured value of relative arch axis displacement, and then could calculate the nonlinear moment of arch feet.Axial force method could be applied to measure the bending moment of arch ring section. The axial force of reinforced concrete arch ring is generally not impacted by nonlinear calculation. Based on the loading test of the section bearing capacity under limit state, its linear elastic axial force could be calculated. The section N-M bearing capacity could also be calculated based on arch ring section size, reinforcement, applied linear elastic axial force, and define its moment of section bearing capacity under limited state. Such moment could be also used as its nonlinear bending moment or measured bending moment.Model test on reinforced concrete arch bridge were made to study the bending moment magnifier. Similarity relation model was adopted to have constant load internal force similar to real bridge and infection line method was adopted to load moving load. Model test was finally reached to requirements of design code JTG D62-2004for concrete elastic modulus, through material selection and mix ratio and complicated treatment process of C40concrete elastic modulus. Intelligent fine-tuning jack were used in loading and measurement, the pressure was accumulated into axial strength stem through pressure sensors, to ensure the pressure sensors are concentric, reducing the errors of loading test. The bending moment from bending moment zero method, bending moment zero method and Axial force method are respectively1.039,1.046and1.050, which are very close to one another.Using geometric nonlinear analysis of stiffness reduction, based on eccentric compression test on test98reinforced concrete straight columns, eccentric compression test on16reinforced concrete curved columns and model test on4reinforced concrete arches, comparing with the value from the relative codes, stiffness reduction factor of eccentric compressed straight columns was0.195～0.934, average value was0.540, while stiffness reduction factor from straight columns’non-liner calculation was0.230. Stiffness reduction factor of eccentric compressed curved columns was0.225～0.465, average value was0.336, while stiffness reduction factor from curved columns’non-liner calculation was0.225. Stiffness reduction factor of reinforced concrete arch was0.432～0.645, average value was0.512. Stiffness reduction factor of reinforced concrete arch if calculated on eccentricity formula will be smaller. Here suggested using0.4as Stiffness reduction factor.The stiffness reduction of reinforced concrete arches was analyzed in geometrically nonlinear methods under the loading test of4model arches5reinforced concrete ribbed arch bridge. The geometrically nonlinear analysis shows that the inner force could be directly used to section design, not need to consider the nonlinear factor of bending moment magnification factor. The moment magnification factor from nonlinear calculation was less than the values documented in the6design code, such as JTG D62-2004, etc.It was also analyzed on how sensitive the bending moment was responding to stiffness reduction. It was shown that the moment magnification factor of arch ring section was increasing with the decreasing of stiffness reduction. The lower stiffness reduction was, the stronger the nonlinear impact was, the more sensitive the bending moment to stiffness reduction. When stiffness reduction is more than0.4, the nonlinear bending moment increase less, while when stiffness reduction is less than0.4, the nonlinear bending moment increase more. The axial force from linear elastic calculation could be directly used to design the arch ring section size and reinforcement. The design of reinforced concrete arch bridge could be based on axial force design.The linear elastic buckling stability coefficient of reinforced concrete arch bridge more than4-5, could not ensure its safety of bearing capacity. Based on the result analysis of geometrically nonlinear calculation on stiffness reduction of arch structure, the simplified formula was proposed for the moment magnification factor. The N-M bearing capacity calculation of arch ring sections in Bridge of Damotan, Shitian reservoir bridge, Heishuidang Bridge, West River Bridge of Nanchong City, Longdongbei Bridge, except Heishuidang Bridge needs reinforcement treatment, the other4bridges didn’t need reinforcement.The three different methods applied in the calculation of bending moment of reinforced concrete arch ring section, showed reasonable results and its application value, including separation arch support method, bending moment zero method and axial force method. The geometrically nonlinear methods to calculate the stiffness reduction of reinforced concrete arches showed accurate and efficient, so that could be applied to arch bridge design calculation.