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Background
The use of post-tensioning in girders causes high bearing and compressive stresses in the anchorage zone. In this study, the behavior of the anchorage zone and the interaction between the local and general zone are investigated. The variables included different reinforcements for both the local and general zones for a block of two anchor...

## Contexts in source publication

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... typical anchorage zone has been shown in Fig. (1), which is defined as the volume of concrete through which the concentrated pre-stressing force at the anchorage device spreads transversely to a more linear stress distribution across the entire cross-section at some distance from the anchorage device [7 -9]. Within the anchorage zone, the bending theory is not valid because the ...

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... the transverse dimensions of the concrete block. This method recommends a minimum edge distance of 1.5 times the corresponding lateral dimension, "a", of the anchorage plate for a proper stress distribution of the anchorage zone. Moreover, the depth of the block was selected to be within the limits recommended by AASHTO specifications (refer to Fig. 1). Duct holes were made by using 30 mm diameter aluminum tubes with a negligible strength. This diameter represented a scale of one-third of the duct diameter of 90 mm required for the number of strands for anchorage devices VSL E 5-19 [21]. The final dimensions of the specimen were 300 mm x 450 mm x 600 ...

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... Rσ=4 and Rε=4 may be used, σ c is the effective stress, ε c is the effective strain, E c is the initial modulus of elasticity and ε is the concrete strain at peak stress which was assumed to be 0.0025. The curve of the stress-strain relationship for compression in this study is shown in Fig. ...

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... strength of the concrete (peak stress). The direct tensile strength of concrete is 0.5 to 0.7 of its splitting tensile strength [35]. In this study, the direct tensile strength is assumed as 0.6 of the tested splitting tensile strength mentioned in Table 1, providing a result of 2.82 MPa. The tensile stress-strain curve for this study is shown in Fig. ...

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... solid members (concrete, anchorage plates and wedge plates) were meshed using eight nodes bricks type C3D8R, reduced integration and hourglass control, as shown in Fig. (12). These are first-order hexahedral elements that provide good results for minimum cost in three-dimensional analyses. A two-node, three-dimension truss element type T3D2 was used for the reinforcement (spirals and ties). The general size of the elements was 10 mm. The square shape of the anchorage plate with a circular hole at the ...

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... ( 13 and 14 ) show the load-vertical displacement relationship for the specimens in different groups. Initially, the specimens showed the same linear behavior and then approximately the same non-linear relationship, especially for the specimens with a spiral reinforcement. ...

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... can be observed in Figs. (13 and 14) that FEA values of stiffness are greater than the experimental results. This difference is justified for many reasons that include the ...

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... bottom of the specimens. This, in addition to the secondary displacement mentioned before, has an effect on the precision which is expected when comparing the displacement, and hence the stiffness, among different experimental specimens, taking into consideration that the required displacement to be measured at the linear stage was parts of 1 mm. Fig. (13). Load-displacement relationship for the specimens in different groups. Fig. (14). Load-displacement relationship for the specimens arranged in additional groups. ...

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... before, has an effect on the precision which is expected when comparing the displacement, and hence the stiffness, among different experimental specimens, taking into consideration that the required displacement to be measured at the linear stage was parts of 1 mm. Fig. (13). Load-displacement relationship for the specimens in different groups. Fig. (14). Load-displacement relationship for the specimens arranged in additional groups. ...

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... groups G1 and G2 in Fig. (13) show greater stiffness for the specimens with stronger tie reinforcement in the general zone. In group G1, the specimens SP1 (with ϕ6 mm tie reinforcement) and SP2 (with ϕ5 mm tie reinforcement) have more stiffness than SP3 (with ϕ4 mm tie reinforcement) and SP4 (without tie reinforcement). In group G2, and for the same reason, the ...

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... the precision that is expected due to the points mentioned in this section, the other curves in Figs. (13 and 14) show a close stiffness among most of the experimental specimens of the same group, except SP8 in Fig. ...

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... the precision that is expected due to the points mentioned in this section, the other curves in Figs. (13 and 14) show a close stiffness among most of the experimental specimens of the same group, except SP8 in Fig. ...

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... versus axial strain curves for the ties for the short and long direction are shown in Figs. (15 and 16), respectively. The strain considered was at the center of the second ties for both the short and long direction, which represented the critical location for the tensile stresses. There is a good agreement in these curves as observed from the FEA and the experimental ...

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... of ϕ6 mm for both the spirals and ties. For the same direction, the maximum tie strain at ultimate load was 2112 micro-strain for the specimen SP15, which had the minimum reinforcement of ϕ4 mm for ties, and had no spiral reinforcement. In order to have a clearer picture of the axial stresses distribution in ties and spirals at ultimate load, Fig. (17) shows the FEA results of this type of stress for all specimens that have tie reinforcement. S11 in Fig. (17) represents the axial stresses in ties and spirals. For all the specimens, tie axial stresses at ultimate load were less than the yielding stress of the reinforcement of 401 MPa, 495.5 MPa and 428 MPa for the bar size of ϕ6 mm, ...

**Context 15**

... 2112 micro-strain for the specimen SP15, which had the minimum reinforcement of ϕ4 mm for ties, and had no spiral reinforcement. In order to have a clearer picture of the axial stresses distribution in ties and spirals at ultimate load, Fig. (17) shows the FEA results of this type of stress for all specimens that have tie reinforcement. S11 in Fig. (17) represents the axial stresses in ties and spirals. For all the specimens, tie axial stresses at ultimate load were less than the yielding stress of the reinforcement of 401 MPa, 495.5 MPa and 428 MPa for the bar size of ϕ6 mm, ϕ5 mm and ϕ4 mm, respectively, a matter which well agrees with the experimental results. Meanwhile, the axial ...

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... ( 18 and 19 ) show the load-strain relationship for concrete for the short and long direction, respectively. The experimental and FEA results are close. ...

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... and within a depth close to the direction length. Previous studies [7,8,19] provided a similar distribution and location for these stresses. Bursting stresses distribution was almost the same for all specimens, which indicated that the studied variables had no effect on this kind of stresses at the elastic range. Only group G1 was included in Fig. (19) as the other groups had similar stress distribution. Fig. ( 21 ) shows the cracking pattern of the experimental specimens included in this study. ABAQUS FEA program does not have a tool to display the cracks extent of the model, but other parameters like plastic strain, logarithmic strain or tensile damage can be used as an indication ...

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... studies [7,8,19] provided a similar distribution and location for these stresses. Bursting stresses distribution was almost the same for all specimens, which indicated that the studied variables had no effect on this kind of stresses at the elastic range. Only group G1 was included in Fig. (19) as the other groups had similar stress distribution. Fig. ( 21 ) shows the cracking pattern of the experimental specimens included in this study. ABAQUS FEA program does not have a tool to display the cracks extent of the model, but other parameters like plastic strain, logarithmic strain or tensile damage can be used as an indication of crack development. In this study, the tensile damage parameter ...

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... study. ABAQUS FEA program does not have a tool to display the cracks extent of the model, but other parameters like plastic strain, logarithmic strain or tensile damage can be used as an indication of crack development. In this study, the tensile damage parameter DAMAGET has been used as an indication of crack propagation. For every specimen in Fig. (21), the first image is the tensile damage diagram from ABAQUS FEA, and the other three are the experimental cracking patterns in the long direction, short direction and top surface, respectively. For the FEA, the red color indicates that the tensile damage ratio is more than 80% in the elements. ...

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