# Development of a New Rubber Buckling-Restrained Brace System for Structures
## 3 Details of Material Implemented in the Design of RBRB
### Steel Design  
The maximum elongation of the core is essential for estimating the dimensions of the rubber cubes to be placed in the gap between the concrete and dividers. This ensures that the rubber components function in unison with the core displacement, generating resistance. It is important to note that, based on the actuator setup framework in the laboratory, the distance between the actuator head and the fixed support was 1500 mm. Therefore, the initial length of the BRB and RBRB prototypes was set to this value.  
The range of the cross-section area of the core has been calculated based on the formulation of [PERSON]'s law in Equation (1) [81; 82]. It should be mentioned that based on actuator setup safety regulation, the maximum employed force has to be less than 300 kN, based on the following formulation:  
\[A=\frac{PL}{\delta E} \tag{1}\]  
where \(P\) is the maximum yielding force, which is considered 300 kN; \(L\) is the length of the sample, which is 1500 mm; \(\delta\) is yielding deformation of the core, which is 15%; \(A\) is the core cross-section area; and E represents [PERSON]'s modulus of steel 200 MPa.  
Three different thicknesses of steel sections of 5 mm, 6 mm, and 8 mm (Figure 4) were chosen based on the aforementioned calculation. To evaluate their tensile capacity, the cross-section area can be between 30 mm\({}^{2}\) and 50 mm\({}^{2}\). The steel components were certified based on A36 [83]; also, all the coupon tests result for the steel samples were provided by the same supplier.  
Figure 4: Steel plate sample cores.  
Figure 3: RBRB performance under tension.  
These three samples were fixed in the UTM machine and pulled up to their ultimate capacity, as indicated in Figure 5.  
Based on the test results, as shown in Figure 6, all samples exhibited a similar pattern up to the yield strength of the steel. However, due to their different cross-sectional areas, they displayed varying strain hardening behaviors to reach ultimate strength. The 5 mm and 6 mm samples achieved maximum displacements of 43 mm and 73 mm, respectively. For the 8 mm steel sample, the maximum load reached 95 kN at a displacement of 14 mm. The test was then stopped due to the tensile testing machine's (UTM) limitation of a maximum tensile strength of 100 kN.  
As can be seen in Table 1, the maximum strain for the 5 mm and 6 mm steel samples at their peak load measured 10.93% and 13.90%, respectively. For the 8 mm sample, due to the test being stopped before reaching the maximum load, the strain measured 3.68%. Additionally, the tensile test results indicate that the maximum tensile stress for  
Figure 5: UTM testing device.  
Figure 6: Steel samples result.  
the 5 mm sample is 564 MPa, while it is 491 MPa and 475 MPa for the 6 mm and 8 mm samples, respectively.  
Due to the dynamic actuator's limitations, the maximum elongation considered for prototype testing had to be within 150 mm. Therefore, it was necessary to determine the steel core elongation value within this range (with an ultimate force capacity of 300 kN). Based on the aforementioned values, the sample with dimensions of 6 \(\times\) 25 \(\times\) 420 mm was selected due to its compatibility with the dynamic actuator's maximum displacement limitations. The 6 mm sample reached a displacement of 73 mm. Considering the UTM limitation, all samples were cut in half, necessitating doubling the deformation value in calculations. Consequently, a maximum sample displacement of 150 mm was determined to be appropriate, ensuring that the device would fail before reaching the actuator's maximum displacement.