Grid Strut-Tie Model – Design of Pier Coping

To examine the capability and effectiveness of the 3-D grid strut-tie model approach in the design of a concrete member with multiple load combinations, they selected a bridge pier cap subjected to three load cases with 3-D loads. The shear span-to-effective depth ratio of the cap is 1.25.

In load case 1 with the dead and live loads acting vertically, most of the design loads at loading plates 2, 3, and 4 were transferred to the pier directly by the concrete struts connecting the loading plates and column. On the other hand, most of the design loads at loading plates 1 and 5 were transferred to the pier by the curved-shaped paths described by multiple concrete struts. The pier cap subjected to load cases 2 and 3 with dead and live loads acting in three directions were designed with the same 3-D grid strut-tie model. This illustrates the versatility of the proposed approach to handle multiple loading, including 3-D loads, by using a single type of 3-D grid strut-tie model. The conditions of the strut-tie model’s geometrical compatibility under all three load cases were satisfied, and the strengths of all nodal zones were enough to transfer the strut and tie forces. Thus, the maximum cross-sectional area of a steel tie at a certain position under the three load cases was taken as the required area of the reinforcing bar that should be distributed with the effective area of the steel tie. The required areas of reinforcing bars corresponding to the other steel ties were obtained and distributed in the same way.

Design of Pier Coping-02

To compare the design results of the proposed approach, the designs of the pier cap were carried out using the ACI 318-14 flexural design method, ACI 318-14 bracket provisions, and ACI 318-99 deep beam provisions. The pier cap was also designed based on the strut-tie model approaches of current design codes, with the 2-D strut-tie models representing arch and truss load transfer mechanisms, respectively. As the 2-D strut-tie models are valid for 2-D load cases, only load case 1 was considered. The vertical positions of both nodes are the same as those of corresponding nodes of the 3-D grid strut-tie model. The horizontal positions of both nodes can be moved toward the boundary of the pier by considering the required cross-sectional areas of the concrete struts located in the pier.

From the design results, two features can be observed. First, more flexural reinforcing steel is required by the strut-tie model approach than by the other methods. This is mainly due to the positions of nodes F and G and the corresponding nodes. If these nodes are moved toward points F’ and G’ by considering the critical section defined by the ACI 318-14 flexural design and bracket provisions, similar flexural design results will be obtained. Second, more vertical shear reinforcing bars are required by the strut-tie model of truss mechanism than by the 3-D grid strut-tie model. This is because the design loads at loading plates 1 and 5 are transferred to the column mainly by truss action in the strut-tie model of the truss mechanism. On the other hand, the design loads are transferred to the pier by the combined arch and truss mechanisms in the 3-D grid strut-tie model. In other words, a portion of the design loads are transferred directly to the pier through arch-type concrete struts in the 3-D grid strut-tie model.


Reference

  1. Kim B. H. (2004) Grid Mesh Strut-Tie Model Approach for Design of Reinforced Concrete Members, Ph. D Dissertation, Kyungpook National University, Daegu, South Korea (in Korean).
  2. American Concrete Institute (2014) Building Code Requirements for Structural Concrete (ACI 318M-14) and Commentary(ACI 318RM-14), Farmington Hills, Michigan, USA.
  3. American Concrete Institute (1999). Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99), Farmington Hills, Michigan, USA.

Email : astruttie@aroad.co.kr

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