Seismic response simulation and investigation on the reason for damage

Unfortunately, there is no recorded free-field ground motion in the DC region during Virginia earthquake. Therefore, the ground motions at the MSC are generated from ground motions that were recorded in Reston, VA. This process consists of conducting a deconvolution of the Reston surface ground motion into bed rock and then convoluting these motions up to ground surface of at the MSC utilizing measured soil profiles of the region. The detailed description of this method can be found in Shahidi et al. (2015).

The response spectrum of the ground motion at the bed rock and the ground surface level at MSC (rotated to the orthogonal directions of the mezzanine) are shown in Figure 3.9. It can be observed that the spectral response of 0.1s to 1s is significantly amplified by the local soil condition. It appears that soil amplification is one of the reasons that caused structural damage to the MSC, as the natural periods of the MSC fall in this range.

The tension-only model with the floor mass identified as Case I is subjected to the bidirectional ground motion at the ground surface level (Figure 3.9). Figure 3.10 shows the

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peak axial tensile stress in the diagonal braces. The peak response is in the braces along the east perimeter, where the stress is as high as 40.4 ksi, exceeding the nominal yield stress of the 36 ksi (A36 steel). In comparison, the response of the diagonal braces along the west perimeter is smaller than their counterparts in the east perimeter. This is consistent with the observed damage pattern (Figure 3.4) in which the east perimeter of the structure suffered more damage than the west side.

By close examination, this unique damage pattern can be attributed to significant coupling between the translational and torsional displacement of the floor diaphragm induced by bi- directional ground motion excitation. The effect of bi-directional excitation is clearly demonstrated by comparing the response of the structure under uni-directional and bi- directional ground motion. Figure 3.11 presents the time-history of lateral displacement in the NS direction for two braced bays located respectively at the east and west perimeter (identified within the red circles in Figure 3.10) under uni-directional ground motion in the NS, EW and bi-directional ground motion, respectively. When the ground motion strikes in the EW direction (i.e., short direction of the building; Figure 3.11 (b)), the displacement demand in the NS (i.e., long direction of the building) direction is comparable to the case when the building is subjected to ground motion in the NS direction (Figure 3.11(a)). In addition, the non-uniform response in braces in the long direction of the building is also caused by ground motion in the short direction of the building. The reason is, in this case, the CR of the first floor deviates from the CM by 13.9’ to the south and 1.2’ to the east (Table 3.1). Larger eccentricity in the long direction creates a significant component of torsion in the second and third modes (Figure 3.13). In addition, the earthquake in the short direction has much larger magnitude than its perpendicular component, especially at the

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second and third modes due to the effect of site soil amplification (Figure 3.12). Consequently, the torsional component from the second and third modes in response to the ground motion in the short direction will impose extra and non-uniform demand on the displacement response in the long direction.

Therefore, the potential causes of structural damage of steel mezzanine in Pod1 of MSC are

• Site soil amplification effect

• Combined effect of torsion and translation response • Bi-directional earthquake demand

3.4.2 Nonlinear model

In order to perform the fragility analysis, it is important to model the nonlinear behavior of the structure, which is bound to occur as structural damage limit states are reached. Thus, a nonlinear model is created in OpenSees (McKenna et al. 2000).

To include nonlinearity, the columns are modeled according to the structural drawings using nonlinear force-based beam-column elements with fiber sections. A combination of a gap element, elastic-no-compression element and nonlinear force-based beam-column element is used in series to model the tension-only behavior of the strap braces (Figure 3.14). In the same way as the SAP2000 model, the structure is modeled as a shear building with each floor modeled using a rigid diaphragm constraint. The floor mass uses the same value as the SAP2000 model (Case I).

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The model is validated using results from vibration tests and the observed damage pattern. The modal periods of the OpenSees model is compared with the results from the vibration tests in Table 3.3. OpenSees is able to calculate the modal periods based on the structural stiffness before and after brace buckling by performing an eigenvalue analysis before and after lateral load is applied to the model. The modal periods of the model with no brace buckling (i.e., pre-buckling) shows better agreement with the test result because the behavior of the braces is amplitude dependent. For the vibration test, the amplitude of the vibration is low and the braces do not buckle and can provide compressive stiffness. However, during seismic excitation the amplitude of vibration is large and the braces buckle (post buckling), and therefore are not able to provide stiffness.

The model is also subjected to ground motions from the 2011 Virginia earthquake. Figure 3.15 shows the peak axial stress response in the braces in the first story. It presents a pattern consistent with the observation (Figure 3.4) in which the axial stress in the braces along the east perimeter is larger than that along the west perimeter. The braces in the east perimeter have yielded (exceeding the nominal yield strength 36 ksi). The model appears to match well with the dynamic properties under low level of vibrations and the observed damage under higher levels of vibration, and is therefore deemed suitable for use in the fragility analysis.