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The objective of the proposed work will be to identify the factors that influence the dimensions, strength and stiffness of struts, ties, and nodal zones and to develop relationships and determine values that quantify these effects. At least six types of experiments, coupled with analytical studies, will be conducted.
Table 1 provides a summary of these experiments. The background and proposed work for each of the six types of experiments is described below. A total of about 80 experiments are anticipated.
2.3.1 Type A: Behavior of Concrete Compressive Struts
Background: Four factors are considered to most greatly influence the behavior of compressive struts.
Shape of the Strut: If the stress trajectories in a strut are parallel, then the strength of that strut is close to that of the concrete test cylinder. However, if the strut is within the core of the D-Region, such as shown in
Figure 6a, then the strut will spread out as it moves away from the nodal zones. This “bottle-shaped” strut, see
Figure 6b, may fail due to splitting of the strut, at a stress that is far less than the peak cylinder compressive strength.
Imposed Transverse Strain: One factor that influences the splitting strength of the strut is the magnitude of tensile strain that is transverse to the strut. This strain may be induced by a crossing tie or another effect.
Crack Control: The splitting of the compressive strut, due to either the spreading of the compressive stresses or imposed transverse strain, can be controlled by the use of distributed reinforcement.
Confinement: In addition to crack control reinforcement, the performance of the strut will be enhanced by confinement provided either by specially designed confinement reinforcement or by mass reinforced concrete that surrounds the strut.
Previous experimental research [17-20] to study the impact of these factors is limited.
Proposed Work: A selection of simple tests as described in
Figure 6c would be conducted to evaluate the influence of geometry (L/B, B/b, b/t ratios), induced transverse applied by tensioning transverse reinforcement, crack control reinforcement, and confinement on the load-deformation response of struts.
Table 1
Summary of Experimental Research Plan
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Figure 6 Example of an Experiment to Evaluate Compressive Strut Behavior
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2.3.2 Type B: Behavior of Steel Tension Ties
Background: The capacity of a tie is simply equal to the strength of the reinforcement. However, it is of interest to understand the factors that influence the load-deformation response of the tie for a least two reasons.
(1) If the stiffness characteristics of the ties and struts are known, then the distribution of load in statically indeterminate structures may be predicted. An example of a statically indeterminate truss is shown in
Figure 7 where the point load is considered to be transferred to the support by two distinct load paths: (i) A direct strut from the point of loading to the support, and (ii) A path consisting of two steeper struts connected by a steel tie. The portion of the load taken in each direction will be in proportion to the stiffness of the two paths.
(2) As illustrated in Figure 7, a tie may cross the path of a compressive strut. The strength of the strut will be influenced by the straining and cracking induced by the tie that crosses its path. By examining the factors that influence the tension stiffening effect [21-22] and distribution of cracking in ties, the capacity and response of struts can be better understood.
Proposed Work: In this experimental study, the influence of the size and distribution of the tie reinforcement, as well as the characteristics of the surrounding reinforced concrete, on the response of the tie will be studied. The distribution of strain in the steel and on the concrete surface, and on cracking characteristics, will be closely monitored. A typical test specimen is shown in
Figure 8.
Figure 7 Statically Indeterminate Truss
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Figure 8 Evaluate the Behavior of Tension Ties
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2.3.3 Type C: Anchorage and Distribution of Tie Reinforcement
Background: The use of the strut-and-tie design method draws attention to how forces are transferred at the ends of simply supported members. As illustrated in
Figure 9, the ability to transfer the horizontal component of a diagonal strut to the tie is clearly influenced by the manner in which the tie reinforcement is distributed and anchored.
Figure 9 Examples of Various Tie Anchorage Conditions
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The ability to transfer this force in the nodal zone depends on numerous factors, such as:
- Bar size and roughness
- Lateral spacing of bars
- Vertical spacing of bars
- Angle of compressive strut
- Width of bearing plate
- Use of confinement
- Length of bar
- Anchorage of bar (i.e. hook, plate)
- Use of fibers
The PI participated in a series of experiments that were conducted [23-24] to begin to examine the influence of a few of these factors on the performance of anchorage zones. A picture of a typical one of these test specimens and of a typical anchorage zone is shown in
Figure 10.
Figure 10 Tests Conducted to Study Anchorage and Steel Distribution Requirements [24]
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Proposed Work: In the proposed experimental program, the scope of the tests will be expanded to study the influence of the identified factors on the ability to transfer load. Both “cut-away” specimens similar to those shown above and companion “filled-in” specimens will be tested.
2.3.4 Type D: Size, Shape, and Strength of Complex Nodal Zones
Background: The anchorage detail examined in the preceding section illustrated some of the complexity of load transfer in nodal regions. These regions may have a large variation in their configurations and thus become quite difficult to understand [25, 26]. Some the factors that define nodal zones are listed below.
- Type of truss member forces (compressive or tensile)
- Number of intersecting truss members
- Distribution of tie reinforcement
- Confinement and use of fibers
- Level of transverse straining
- Volume and condition of surrounding concrete
- Anchorage conditions of ties
Proposed Work: Obtaining a detailed understanding of the behavior of complex nodes is a challenge that goes beyond the immediate scope of this program. The objective of this part of the experimental program will be to test a series of relatively representative complex nodes in order to test the validity of simplified design assumptions. An example of test of a complex nodal region is shown in
Figure 11.
Figure 11 Test of Complex Nodal Zone
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2.3.5 Type E : Complex Truss Models and Distributed Reinforcement Requirements
Background: As applied to the strut-and-tie design approach, the lower bound theory of plasticity [27-29] suggests that if an internal truss is created that can support that applied loading then the capacity of the structure will be greater than or equal to the capacity of the internal truss. This provides the practicing engineer with considerable freedom in the selection of the strut-and-tie model. If the designer chooses a truss that proposes an “unrealistic” load path, then the structure will have to undergo significant deformation to support the load in the envisioned manner. Just as with the strip method for the design of two-way slabs, a minimum amount of distributed reinforcement should be provided to give the structure sufficient ductility and to avoid serviceability problems.
If an unlikely load path is chosen, Rogowsky and MacGregor [30] suggest that an undesirably large amount of distributed reinforcement may be required to ensure the ductility of very stiff sections. They suggest that designers should give careful consideration to the selection of the most suitable strut-and-tie model. In their 1986 paper, they state "Selecting an appropriate truss model is of great importance in design. An appropriate truss model is one which correctly identifies the reinforcement which is at yield at failure of the beam and discounts the remaining reinforcement."
Proposed Work: In this aspect of the experimental program, structures will be designed with internal trusses that rely upon the ductility of the structure to be effective. An example of such a test is shown in
Figure 12.
Figure 12 Example of Test to Evaluate Minimum Reinforcement Requirements
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2.3.6 Type F: Demonstration Projects
The experimental program supported by this award would culminate with the testing of a few large, geometrically similar, complex structures in which different trusses were idealized as the load carrying mechanisms. This would serve to illustrate that this design method is conservative, the importance of good truss model selection, and the benefits of good detailing practice. An example of this type of structure is shown in
Figure 13.
Figure 13 Example of a Demonstration Test
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