1
CV6103 Structural Dynamics
Homework
Instructions:
– This homework is part of continuous assessment. It accounts for 15% of total course mark.
– The total mark of this homework is 100. 20 marks will be deducted for every day of late submission
(so no need to submit if 5 days late).
– Written/presentation quality will be taken into consideration in marking. Present your
assumptions/steps clearly but in a concise manner. Irrelevant/conflicting materials will be penalised.
– Submit by 10 Nov 2019 (Sun) 23:59hrs the following files by uploading to ‘hwk01’ page under
‘Assignments’of the course website:
o ‘[Surname_INITIALS].pdf’: PDF file (e.g., generated from MSWORD) of solutions (with tables
and figures, if applicable) to questions
o ‘[Surname_INITIALS].xlsx’: Excel file used in performing the calculations
E.g., for Siu-Kui AU, the file names should be AuSK.pdf and AuSK.xlsx.
Question 1 [60 marks]
Consider a ground motion XYZ (say), whose acceleration time history sampled at 50 Hz for 30 sec is
given in the worksheet ‘XYZ’ in the Excel file ‘hwk01.xlsx’. The latter can be downloaded from the
Contents folder of the course website. You may perform calculations using the same Excel file as part of
submission; create additional worksheet if necessary. Time-stepping response calculations should be
performed in Excel using Newmark linear acceleration scheme.
a) [5 marks] Plot the acceleration time history of XYZ.
b) [25 marks] Plot the displacement response time history of an SDOF structure with a natural
frequency of 1 Hz and a damping ratio of 1%.
c) [30 marks] Assume 1% damping. Complete the following table and hence draw the displacement
response spectrum (Sx) and pseudo-acceleration response spectrum (Sa) of XYZ.
| Natural period T [sec] | Max. abs. displacement response Sx [mm] | Pseudo-acceleration response Sa [%g] |
| 0.1 | ||
| 0.2 | ||
| 0.3 | ||
| 0.4 | ||
| 0.5 | ||
| 0.6 | ||
| 0.7 | ||
| 0.8 | ||
| 0.9 | ||
| 1.0 | ||
| 2.0 | ||
| 3.0 | ||
| 4.0 | ||
| 5.0 |
2
Question 2 [40 marks]
Consider a four storey shear building whose lateral resisting system can be considered to comprise four
columns. The mass and stiffness properties of the building are given in the table below. Using a first
mode approximation with 5% damping and a linear mode shape, i.e., one that increases with height,
estimate the maximum base shear of the building when subjected to ground motion XYZ. You may make
use of the Excel spreadsheet developed in Question 1.
| Floor | Mass [tonnes] | Storey | Height [m] | Stiffness [kN/mm] | |||
| Column 1 | Column 2 | Column 3 | Column 4 | ||||
| 1 | 1000 | 1 | 4.0 | 200 | 400 | 400 | 300 |
| 2 | 1000 | 2 | 3.5 | 200 | 400 | 400 | 300 |
| 3 | 800 | 3 | 3.0 | 150 | 380 | 380 | 200 |
| 4 | 800 | 4 | 3.0 | 150 | 380 | 380 | 200 |