PSI - Issue 44

Masoud Pourmasoud et al. / Procedia Structural Integrity 44 (2023) 590–597 M. Pourmasoud et al. / Structural Integrity Procedia 00 (2022) 000–000

592

3

where α is the confinement exponent that is 0.25 for low confinement, 0.55 for medium confinement, and 0.90 for high confinement. Fig. 1 compares the trends regarding Eq. 1 (dashed lines) with the data obtained for each confinement category. The proposed confinement exponents in Eq. 1 were obtained to provide the best agreement with the presented results using a regression statistical optimization method. 2. Recommended equation to estimate a lead core’s yield strength Fig. 1 illustrates the general trend of (      versus the influential factor of (      . However, to obtain specific values, the confinement conditions as well as the yield/character strengths under zero axial loads (Q 0 , σ y0 ) shall be also taken into account. This section addresses the conditions that can be used to define confinement levels. The two main influential factors are the slenderness ratio (       and the area ratio (       , where H is the lead core height, D l is the lead core diameter, A l is the cross area of the lead core, and A b is the bonded area of the isolator. In addition, the slenderness ratio over the area ratio is defined as Influential Factor Ratio (IFR) according to Eq. 2.   (       (       (2) Fig. 2 illustrates the trend for σ y0 versus IFR when an accurate yield strength is known. This diagram is extracted from testing isolators under zero axial load and obtaining the corresponding yield strength of the lead core based on the confinement condition. The diagram has a steep slope for IFRs less than one but changes to a smoother slope with increasing IFR, which indicates that the axial load influence is more significant for fewer IFRs. In other words, better confinement results in less variation of yield strength regardless of the axial load. To obtain the yield strength under zero axial load, Eq. 3 can be employed:    0.35 ln( + 6 (3)

7.5

7.0

6.5

σ y0

6.0

5.5

5.0

0

2

4

6

8

10

IFR

Fig. 2. The trend of yield strength versus IFR based on 0 = 0.35 ln( + 6

(3.

Combination of Eq. 2 and 3 results in the following equation to calculate the yield strength of lead rubber bearings as a function of their configuration, the imposed axial loads, and other influential factors.    [0.35 ln( + 6]     (4) Eq. 4 provides a practical perspective regarding the actual yield strength of the lead core before running the prototype tests. This equation can help to narrow the gap between upper/lower bounds of λ test and λ spec mentioned in (ASCE 7-16 2022), which is beneficial for the design of super-structures as discussed before.

3. Validation

This section validates the accuracy of the developed equation to estimate the yield strength of a lead rubber bearing. To this end, seven lead rubber bearings subjected to various axial loads and lateral displacements were employed. Table 1 shows the physical dimensions and applied axial loads. Table 2 shows the applied axial loads and lateral displacements. The isolators were