Abstract
The compression or tension-controlled failure mode of concrete beams prestressed with unbonded FRP tendons is governed by the relative amount of prestressing tendon to the balanced one. Explicit assessment to determine the balanced reinforcement ratio of a beam with unbonded tendons ( rho_{pfb}^{U} ) is difficult because it requires a priori knowledge of the deformed beam geometry in order to evaluate the unbonded tendon strain. In this study, a theoretical evaluation of rho_{pfb}^{U} is presented based on a concept of three equivalent rectangular curvature blocks for simply supported concrete beams internally prestressed with unbonded carbon-fiber-reinforced polymer (CFRP) tendons. The equivalent curvature blocks were iteratively refined to closely simulate beam rotations at the supports, mid-span beam deflection, and member-dependent strain of the unbonded tendon at the ultimate state. The model was verified by comparing its predictions with the test results. Parametric studies were performed to examine the effects of various parameters on rho_{pfb}^{U} .
Highlights
Carbon Fiber Reinforced Polymers (CFRPs) have a number of valuable advantages: corrosion-free; high strength in tension; lower unit weight than steel; and low linear expansion coefficient
In order to find a fixed point of unbonded tendon strain at the ultimate state, equivalent curvature blocks are iteratively refined as given in the following algorithms
(1) The model based on three equivalent curvature blocks was validated by comparing its predictions with test results: the average and standard deviation of the ratios of the predicted to the measured beam strengths at the ultimate state were 0.96 and 0.09 (1.07 and 0.06), respectively
Summary
Carbon Fiber Reinforced Polymers (CFRPs) have a number of valuable advantages: corrosion-free; high strength in tension; lower unit weight than steel; and low linear expansion coefficient. A section is regarded as the tension-controlled section if the FRP tendon rupture governs the beam failure with a prestressing ratio (qpf) less than the balanced ratio of the prestressing tendon (qpfb). If concrete crushing governs beam failure where qpf is greater than qpfb, the section is regarded as the compression-controlled section (ACI 440.1R-03 2003; ACI 440.4R-04 2011). The balanced reinforcement ratio of bonded FRP tendons (qBpfb) is presented in ACI 440.4R-04 (2011), and was developed based on the compatibility at a section. CFRP tendon (qUpf ) greater than qBpfb would preserve the compression-controlled section with a higher degree of plasticity, avoiding an abrupt brittle failure. This may result in overdesign and underutilize maximum tensile capacity of unbonded tendon. The model is modified and the iterative algorithm determining qUpfb is presented
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