Project Information / 計畫資訊


Project ID. / 計畫代碼NCREE-R2016501
主持人張國鎮
PIKuo-Chun Chang
單位國震中心
OrganizationNCREE
計畫名稱 
Project NameExperimental study on the fundamental frequency of prestressed concrete bridge beams with parabolic unbonded tendons
Project No. / 計畫編號06105C1005
Keywords / 關鍵字concrete bridge beam, elastic modulus, fundamental frequency, prestress loss, parabolic unbonded tendon
Begin Date / 計畫啟始2016/8/1
End Date / 計畫結束2017/7/31
Abstract / 摘要 
AbstractIn this study, a laboratory experiment–based testing program was conducted on a large-scale high-strength Prestressed Concrete I (PCI) beam with a parabolic unbonded tendon, capable of simulating a typical prestressed bridge member. Specifically, the simply supported PCI beam was subjected to free transverse vibrations with different prestress forces to demonstrate that its fundamental frequency was unaffected by such force. A reference model, describing the behavior of the PCI beam as a combination of two substructures interconnected, i.e., a compressed concrete Euler–Bernoulli beam and a tensioned parabolic cable, predicts no change in fundamental frequency with increasing prestress force when variation of the concrete’s initial elastic modulus over time is taken into account. The large-scale experimental results confirmed that fundamental frequency is not an appropriate parameter for prestress loss prediction in concrete bridge beams with parabolic unbonded tendons. Accordingly, subsequent studies will be conducted for improving a static nondestructive testing method for such detection.

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Experiments / 實驗清單


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Exp 1Time–dependent elastic modulus of concrete by compression tests Time–dependent elastic modulus of concrete by compression tests NCREEReaction wall & strong floor Compression testsConcrete cylinders  A set of 100 mm × 200 mm concrete cylinders were cast to measure the time-dependent elastic modulus of the high-strength concrete through compression tests. The PCI beam and all the cylindrical specimens were maintained in outdoor laboratory spaces under the same curing environmental conditions. The elastic modulus E for each cylinder was estimated using Eq. (1), in accordance with ASTM Standards C 469/C 469M–14 [31]. The measured elastic modulus values at 28 days and those recorded during the experimental period (Section 2.2) are listed in Table 1 [dataset] [33]. The average elastic moduli Eaver and Efvt,aver were calculated on each required day by testing two cylinders. Vice versa, four specimens were tested during 28 days of curing. The elastic modulus Eaver exhibited progressive increments of 1.7%, 2.3%, and 3.8% with respect to the value obtained after 28 days. Conversely, the elastic modulus Efvt,aver registered progressive increments of 11.9%, 12.2%, and 15.9%, respectively. Thus, the average reference elastic moduli were Eref = 37,444 MPa and Efvt,ref = 41,366 MPa. The higher values for Efvt,aver were caused by the lower values of stresses σ2 assumed in Eq. (1), as reported in Table 1 [dataset] [33]. The ratio Eref / Efvt,ref = 37,444 / 41,366 = 0.91 agreed with the ratio for the secant and dynamic elastic modulus of reinforced concrete beams, where the dynamic modulus was determined through transverse vibrations on a set of concrete beam specimens [34]. The mean characteristic strength fck was 96 MPa for the compression tests at the 66th, 69th, and 70th days of curing, as detailed in Table 1 [dataset] [33]. The concrete's experimental unit weight, ρc = 24.26 kN/m3, was obtained using the average of the cylinder weights shown in Table 1 [dataset] [33].
Exp 2Free vibration testing Free vibration testing NCREEReaction wall & strong floor Vibration testing Large–scale PCI beam with a parabolic unbonded tendon  Free vibration tests were performed following application of prestress forces N0x,aver. Three test cases with N0x,aver of 1658, 1829, and 1952 kN were examined. All the servo velocity seismometers acquired acceleration data using a sampling rate of 200 Hz and a block size of 16,384 samples (Fig. 5(c)). Vibration measurements were performed three times for each imposed prestress force N0x,aver, for a total of nine experiments. Specifically, free transverse vibrations were induced by breaking a steel rebar 10 mm in diameter anchored close to the beam’s midspan (Fig. 5(a)). The rebar’s ultimate strength fsk of 540 MPa was achieved using a hydraulic oil jack of 100 kN force capacity, pulling each rebar up until rupture (Fig. 5(a)). The hydraulic oil jack was driven by a hydraulic pump of 96.53-MPa maximum pressure capacity positioned on the floor (Fig. 5(b)). The large-scale PCI beam was thus vertically excited by a release force Fd of approximately 42.4 kN (Fig. 4) and its dynamic response was measured along the strong axis. The PCI beam did not develop any cracks during testing. The applied prestress forces N0x1 and N0x2 were recorded every second for nearly 200 seconds by a data acquisition unit using a separate data log.