Global Journal of Researches in Engineering, E: Civil & Structural, Volume 23 Issue 2

Fig. 7: Topology optimal for deep beam with opening: classical model (a) [28]; (b) [45] In Fig. 8 it can be seen that the SESO formulation (Fig. 8a) results in a setting similar to the classical model, but the VFLSM formulation (Fig. 8b) presents a model with a discretely simpler setting, with the internal strut in the vertical direction, unifying at a lower point the two ties. This setting simplifies the design procedure and the reinforcement detailing of the reinforced concrete structure, in the practical and executive sense, although the classic model makes it possible to calculate the complementary reinforcement around the opening. Fig. 8: Strut-and-tie models: (a) SESO; (b) VFLSM b) Example 2 – Pile Cap In this example, a building foundation structure is dimensioned as a pile cap according to the dimensions shown in Fig. 9, for consideration as a rigid block and to enable the analysis by the STM concept. The pile cap is subjected to a vertical force of 4,000 kN located at the center of the upper face. The material properties used are the compressive strength of the concrete cylinder is 32 MPa. The Young's modulus of the concrete E c = 25,000 MPa and Poisson's coefficient = 0.15 . The filter radius = 1.5 mm and the volume fraction of 22.5%, a rejection ratio, RR = 1% and the evolution ratio ER = 2% were specified in the optimization process. Global Journal of Researches in Engineering © 2023 Global Journals ( ) E Volume XxXIII Issue II Version I 30 Year 2023 Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models