**2. Seismic conditions that result in structural failure**

Building seismic design codes are formulated and revised by experts in structural dynamics and soil dynamics and thus only pertain to ground vibration fortification. Hsu *et al*. [2] showed (using **Figures 1**–**3**) that the increase in the amount of shear banding during tectonic earthquakes in Taipei caused problems such as the cracking of the floor slab of the Zhenong Building, tilting and subsidence of the Yutai Building and collapse of the Dongshing Building.

As illustrated in **Figures 1**–**3**, it was determined that the seismic conditions that resulted in structural failure during tectonic earthquakes were the boundary conditions at the bottom ends of a part or all of the columns of a building gradually deviating from being a fixed end as specified in the original design, due to an increase in the accumulated amount of shear banding. The degree of damage sustained by the building increases with an increase in the extent of this deviation, *i.e.*, it increases with an increase in the cumulative amount of shear banding.

Secondly, by comparing **Figures 4a** and **b** we see that during the 921 Jiji earthquake the school building located in a non-shear banding area (**Figure 4a**) remained stable and sustained no damage; however, the school building located in a shear banding area (**Figure 4b**) could not maintain stability and suffered serious failure.

As illustrated in **Figures 1**–**4**, it has thus been determined that (1) the seismic conditions that result in structural failure during earthquakes are the boundary conditions at the bottom ends of a part of the columns or all the columns of a building being unable to maintain the fixed end conditions of the original design; (2) the seismic conditions that do not result in structural failure during earthquakes are the boundary conditions at the bottom ends of all columns of the building maintaining the fixed end conditions of the original design.

#### **2.1 Traditional pushover analysis and test results**

**Figure 5** shows the hyperbolic deformation mechanism after the bottom end of a column was set as the fixed end in a traditional pushover analysis and test, and **Figure 6** shows the deformed mesh of a school building model obtained using traditional pushover analysis.

**Figure 7a** shows that before the traditional pushover test was conducted, the boundary conditions at the bottom end of each column of the selected physical school building had the fixed end conditions of the original design after the 921 Jiji earthquake; in other words, the school building had the required seismic conditions that would not result in structural failure during a tectonic earthquake. **Figure 7b** also shows that after the traditional pushover test of the physical school building was conducted, the boundary conditions at the bottom ends of all columns maintained the fixed end conditions of the original design.

From **Figure 4b**, it can be seen that after the 921 Jiji earthquake, the boundary conditions of each column base of the physical school building of Guangfu Junior High School had deviated from the fixed end conditions of the original design, which is the seismic condition that results in structural failure during tectonic earthquakes, thus suffering serious damage. From **Figures 6** and **7b**, it can be deduced that whether traditional pushover analysis or traditional pushover testing is conduced, the boundary conditions of each column bottom in the structural analysis model maintained the fixed end conditions of the original design. Therefore, it is clear that the results obtained using these methods are not valid.

#### **Figure 5.**

*The deformation mechanism generated after the bottom end of a column was set as the fixed end in a traditional pushover analysis and test [7].*

#### **2.2 Shaking table test results**

A shaking table is a rigid thick plate capable of vibrating according to an input ground vibration acceleration history. Before a shaking table test is conducted, the bottom ends of all the columns of the building model are fixed to the shaking table; in other words, the building model is set up prior to testing under the seismic conditions

*Seismic Conditions Required to Cause Structural Failures in Tectonic Earthquakes DOI: http://dx.doi.org/10.5772/intechopen.108719*

#### **Figure 6.**

*The deformed mesh for the model of Kouhu Elementary School building, Yunlin, Taiwan, for a traditional pushover analysis [8].*

**Figure 7.**

*The traditional pushover test for the physical Kouhu Elementary School building, Yunlin, Taiwan [9]: (a) before test; (b) after test.*

in which structural failure does not actually occur. Secondly, during the shaking table test, the model is pushed down under these same seismic conditions. Therefore, the failure pattern of the building model after the shaking table test has the same flaws as the pushover analysis result shown in **Figure 6** and the pushover test result shown in **Figure 7b**, and therefore the results of the shaking table test are not valid.

It can be seen from **Figures 6** and **7b** that the failure mode of the building model during a shaking table test is that of collapse due to lateral forces under the condition of weak columns and strong beams. Since buildings designed by structural engineers must meet the requirements of the building seismic design code, this problem of weak columns and strong beams does not occur in practice; however, because the results of the shaking table test directly show that when the model fails, the bottom ends of its columns still maintain their fixed end boundary condition and fail in the weak column and strong beam mode; thus, the validity of the shaking table test results is further undermined.
