UTM FINAL EXAMINATION TON ON 2020/2021 ON 2020/2021 In the field of structural engineering, it is...
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UTM FINAL EXAMINATION TON ON 2020/2021 ON 2020/2021 In the field of structural engineering, it is crucial to understand how buildings and structures respond to seismic forces, especially in regions prone to earthquakes. The dynamic behavior of structures during earthquakes can be effectively studied through the use of mass-spring models. These models provide valuable insights into how a building responds to various modes of vibration when subjected to seismic loading. Figure 1 shows a multi-storey building that can be modeled as mass-spring system. OUTM Floor mass 1 15000 Floor mass 2 10000 Step 1 OUTM FINAL EXAMINATION OUTM FINAL EXAMINATION • Transform Floor mass 3 equation into [A]{x} =^{x} 15000 Take inverse of matrix A Project description This project centers on the analysis of a four-storey building situated in an earthquake-prone region. During an earthquake, the structure will be subjected to horizontal motion at its base, simulating the seismic forces that it may experience in reality. The building's structural characteristics, which are summarized in Table 1, include the mass of each floor, denoted as m, and the stiffness of each floor, represented by k. Figure 1: muorey building UTM Floor mass 4 m2 mm k₂ mi 10000 md ki Step 2 innovative entrepreneurial global -STM FINAL EXAMINATION Floor stiffness 1 4000 Assume X's on the LHS of the equation are equal to one and calculate eigenvalue and eigenvector OUTM SEMERTER IL SESSION 2020/2021 FINAL EXAMINATION Floor stiffness 2 1000 FINAL EXAMINATION (a) Derive the governing equation for this problem and solve the problem using in-built function code. Procedures (b) Develop a user-friendly program to solve for the Smallest eigenvalue using iterative method with 1% accuracy. Compare and discuss your answers with that in (a). 2020/2021 (c) Graphically represent the structure's vibration modes by displaying the amplitudes against building height and discuss your results. Note: normalize the amplitudes so that the displacement of the top floor is 1. Floor stiffness 3 4000 Step 3 UTM SEMESTER SESSION 2020/2021 FINAL EXAMINATION Inverse Power Method The inverse power method is used to compute the smallest (in magnitude) eigenvalue of a given square matrix A. Inverse power method is a variation of power method. It involves computing of the largest (in magnitude) eigenvalue of the inverse matrix, A-¹. OUTM • RHS is normalized so that the largest element in X's is equal to one Floor stiffness 4 1000 Smallest FINAL EXAMINATION Eigenvalu e Step 4 SINDR UTM UNYETI TEKNOLOGI MALAYSIA • Calculate leal based on the calculated eigenvalue. 11 • Repeat Step 3 if leal > Es by multiplying the matrix by the eigenvector from the previous iteration UTM FINAL EXAMINATION TON ON 2020/2021 ON 2020/2021 In the field of structural engineering, it is crucial to understand how buildings and structures respond to seismic forces, especially in regions prone to earthquakes. The dynamic behavior of structures during earthquakes can be effectively studied through the use of mass-spring models. These models provide valuable insights into how a building responds to various modes of vibration when subjected to seismic loading. Figure 1 shows a multi-storey building that can be modeled as mass-spring system. OUTM Floor mass 1 15000 Floor mass 2 10000 Step 1 OUTM FINAL EXAMINATION OUTM FINAL EXAMINATION • Transform Floor mass 3 equation into [A]{x} =^{x} 15000 Take inverse of matrix A Project description This project centers on the analysis of a four-storey building situated in an earthquake-prone region. During an earthquake, the structure will be subjected to horizontal motion at its base, simulating the seismic forces that it may experience in reality. The building's structural characteristics, which are summarized in Table 1, include the mass of each floor, denoted as m, and the stiffness of each floor, represented by k. Figure 1: muorey building UTM Floor mass 4 m2 mm k₂ mi 10000 md ki Step 2 innovative entrepreneurial global -STM FINAL EXAMINATION Floor stiffness 1 4000 Assume X's on the LHS of the equation are equal to one and calculate eigenvalue and eigenvector OUTM SEMERTER IL SESSION 2020/2021 FINAL EXAMINATION Floor stiffness 2 1000 FINAL EXAMINATION (a) Derive the governing equation for this problem and solve the problem using in-built function code. Procedures (b) Develop a user-friendly program to solve for the Smallest eigenvalue using iterative method with 1% accuracy. Compare and discuss your answers with that in (a). 2020/2021 (c) Graphically represent the structure's vibration modes by displaying the amplitudes against building height and discuss your results. Note: normalize the amplitudes so that the displacement of the top floor is 1. Floor stiffness 3 4000 Step 3 UTM SEMESTER SESSION 2020/2021 FINAL EXAMINATION Inverse Power Method The inverse power method is used to compute the smallest (in magnitude) eigenvalue of a given square matrix A. Inverse power method is a variation of power method. It involves computing of the largest (in magnitude) eigenvalue of the inverse matrix, A-¹. OUTM • RHS is normalized so that the largest element in X's is equal to one Floor stiffness 4 1000 Smallest FINAL EXAMINATION Eigenvalu e Step 4 SINDR UTM UNYETI TEKNOLOGI MALAYSIA • Calculate leal based on the calculated eigenvalue. 11 • Repeat Step 3 if leal > Es by multiplying the matrix by the eigenvector from the previous iteration UTM FINAL EXAMINATION TON ON 2020/2021 ON 2020/2021 In the field of structural engineering, it is crucial to understand how buildings and structures respond to seismic forces, especially in regions prone to earthquakes. The dynamic behavior of structures during earthquakes can be effectively studied through the use of mass-spring models. These models provide valuable insights into how a building responds to various modes of vibration when subjected to seismic loading. Figure 1 shows a multi-storey building that can be modeled as mass-spring system. OUTM Floor mass 1 15000 Floor mass 2 10000 Step 1 OUTM FINAL EXAMINATION OUTM FINAL EXAMINATION • Transform Floor mass 3 equation into [A]{x} =^{x} 15000 Take inverse of matrix A Project description This project centers on the analysis of a four-storey building situated in an earthquake-prone region. During an earthquake, the structure will be subjected to horizontal motion at its base, simulating the seismic forces that it may experience in reality. The building's structural characteristics, which are summarized in Table 1, include the mass of each floor, denoted as m, and the stiffness of each floor, represented by k. Figure 1: muorey building UTM Floor mass 4 m2 mm k₂ mi 10000 md ki Step 2 innovative entrepreneurial global -STM FINAL EXAMINATION Floor stiffness 1 4000 Assume X's on the LHS of the equation are equal to one and calculate eigenvalue and eigenvector OUTM SEMERTER IL SESSION 2020/2021 FINAL EXAMINATION Floor stiffness 2 1000 FINAL EXAMINATION (a) Derive the governing equation for this problem and solve the problem using in-built function code. Procedures (b) Develop a user-friendly program to solve for the Smallest eigenvalue using iterative method with 1% accuracy. Compare and discuss your answers with that in (a). 2020/2021 (c) Graphically represent the structure's vibration modes by displaying the amplitudes against building height and discuss your results. Note: normalize the amplitudes so that the displacement of the top floor is 1. Floor stiffness 3 4000 Step 3 UTM SEMESTER SESSION 2020/2021 FINAL EXAMINATION Inverse Power Method The inverse power method is used to compute the smallest (in magnitude) eigenvalue of a given square matrix A. Inverse power method is a variation of power method. It involves computing of the largest (in magnitude) eigenvalue of the inverse matrix, A-¹. OUTM • RHS is normalized so that the largest element in X's is equal to one Floor stiffness 4 1000 Smallest FINAL EXAMINATION Eigenvalu e Step 4 SINDR UTM UNYETI TEKNOLOGI MALAYSIA • Calculate leal based on the calculated eigenvalue. 11 • Repeat Step 3 if leal > Es by multiplying the matrix by the eigenvector from the previous iteration UTM FINAL EXAMINATION TON ON 2020/2021 ON 2020/2021 In the field of structural engineering, it is crucial to understand how buildings and structures respond to seismic forces, especially in regions prone to earthquakes. The dynamic behavior of structures during earthquakes can be effectively studied through the use of mass-spring models. These models provide valuable insights into how a building responds to various modes of vibration when subjected to seismic loading. Figure 1 shows a multi-storey building that can be modeled as mass-spring system. OUTM Floor mass 1 15000 Floor mass 2 10000 Step 1 OUTM FINAL EXAMINATION OUTM FINAL EXAMINATION • Transform Floor mass 3 equation into [A]{x} =^{x} 15000 Take inverse of matrix A Project description This project centers on the analysis of a four-storey building situated in an earthquake-prone region. During an earthquake, the structure will be subjected to horizontal motion at its base, simulating the seismic forces that it may experience in reality. The building's structural characteristics, which are summarized in Table 1, include the mass of each floor, denoted as m, and the stiffness of each floor, represented by k. Figure 1: muorey building UTM Floor mass 4 m2 mm k₂ mi 10000 md ki Step 2 innovative entrepreneurial global -STM FINAL EXAMINATION Floor stiffness 1 4000 Assume X's on the LHS of the equation are equal to one and calculate eigenvalue and eigenvector OUTM SEMERTER IL SESSION 2020/2021 FINAL EXAMINATION Floor stiffness 2 1000 FINAL EXAMINATION (a) Derive the governing equation for this problem and solve the problem using in-built function code. Procedures (b) Develop a user-friendly program to solve for the Smallest eigenvalue using iterative method with 1% accuracy. Compare and discuss your answers with that in (a). 2020/2021 (c) Graphically represent the structure's vibration modes by displaying the amplitudes against building height and discuss your results. Note: normalize the amplitudes so that the displacement of the top floor is 1. Floor stiffness 3 4000 Step 3 UTM SEMESTER SESSION 2020/2021 FINAL EXAMINATION Inverse Power Method The inverse power method is used to compute the smallest (in magnitude) eigenvalue of a given square matrix A. Inverse power method is a variation of power method. It involves computing of the largest (in magnitude) eigenvalue of the inverse matrix, A-¹. OUTM • RHS is normalized so that the largest element in X's is equal to one Floor stiffness 4 1000 Smallest FINAL EXAMINATION Eigenvalu e Step 4 SINDR UTM UNYETI TEKNOLOGI MALAYSIA • Calculate leal based on the calculated eigenvalue. 11 • Repeat Step 3 if leal > Es by multiplying the matrix by the eigenvector from the previous iteration
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