**Assignment Task**

**Task **

**1 Task 1 – To Be Defined****2 Task 2 – Generation of elastic response spectrum**

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Get Help Now!Acknowledgement: This assessment uses ground motion acceleration data, which is publicly available to download via the Pacific Earthquake Engineering Research Center (PEER). Consider the ground motion time history signal shown in Fig. 1. As earthquake loading is not a deterministic load (i.e. it cannot be described analytically) and is highly transient, a corresponding structural response is often calculated with the use of a response spectrum.

A response spectrum is a plot of period versus acceleration, which shows the maximum response of a linear single degree of freedom (SDOF) system for a given component of an earthquake ground motion. Using MATLAB or other general programming language you are asked to generate an elastic response spectrum based on ground motion data. Fig. 2 visually illus

**Figure 2: a) 5 ?mped elastic spectrum according to EC8, and b) single degree of freedom systems with different natural periods (from left to right the oscillator is stiffer and therefore has a lower period).**

In this assignment you are asked to compute the displacement, velocity and acceleration response spectra for a given ground motion, considering the period range between 0.1 s and 4 s. Keeping the mass constant, vary the stiffness of the oscillator to obtain the desired period. Consider also that the oscillator is initially at rest and has a damping ratio ? = 5 %. As mentioned above, the response of a structure subjected to ground motion has no analytical form, and has therefore to be approximated numerically. There are numerous methods available, each with different levels of convergence, stability and accuracy. For the present assignment you will be primarily supported to implement and use Newmark’s method. You are free to use any routine available online, as long as you provide appropriate reference. However, extra marks will be awarded if you are able to implement and justify the use of an alternative method.

The ground motion shown in Fig. 1 is an example for illustration — you have been assigned a data set that is individual to you and whose filename is listed in column 2 of Table 1. Your data file can be downloaded directly from Blackboard. Note that each data file has header lines (to be ignored), five columns of acceleration data (only the first column is to be considered), data is in g-force units, and the sampling period is ?t = 0.01 s.

**Validation**

To validate the numerical routine that you have chosen it is useful to compare its outputs against the analytic solution of a problem of similar complexity. One suggested route is to implement a damped SDOF oscillator driven by three superimposed harmonic loads of different amplitude and excitation frequency. Then the total response is obtained by combining the response of the starting transient with the steady state response for each individual load. The total load can be denoted as

where pi and ?i are the amplitude and excitation frequency for each harmonic i = 1, 2, 3 of the total load, respectively. Finally, the analytic total response should be compared (in terms of displacement, velocity and acceleration) against a numerical approximation with the same input parameters.

To aid you in the validation process, a load and total response analytic time history plots are provided in Fig. 3. These plots have been obtained for a load with p1 = 1, p2 = 0.5, p3 = 0.1 (kN), ?1 = 2, ?2 = 10, ?3 = 12 (rad/s) and a linear oscillator with parameters k = 13 kN/m, ?n = 5 rad/s, ? = 5 %, u0 = 0.3 m and v0 = 0 m/s, where k, ?n, ?, u0 and v0 correspond to the stiffness, natural frequency, damping ratio, initial displacement and velocity of the oscillator, respectively.

**The following workflow is suggested****1**. Carry out the validation process by implementing the analytic solution first. Implement the transient and steady state responses separately. If necessary, start considering a single harmonic of the total load and then progress to add the other two;**2**. Validate the analytic solution against the provided solution and then against the numerically approximated solution;**3**. Read and post-process the ground motion data into your programming environment.**4**. Use your validated method to approximate the response of a SDOF driven by ground motion, within a loop which changes its dynamic properties (period).**5**. Plot the vectors of peak acceleration, velocity and displacement response against each period that you have generated. The resulting plots are the elastic response spectra for your ground motion/SDOF.

**Your report should include**

- A background overview of the design philosophy of response spectra, and its appropriateness for seismic analysis;
- Validation of the method that you have adopted for numerical integration of the equation of motion.
- A discussion of the obtained elastic response spectra and the algorithm/method that you have implemented to obtain it, including a pseudocode/flowchart and relevant criteria

**Task 3 – Seismic design of a steel framed structure**

In this task you are asked to carry out a seismic analysis and design a steel framed structure against a seismic event using Autodesk Robot software or other FE package, see Fig. 4. You have to design the structure following the guidelines prescribed in the Eurocode 8 for a nonlinear pushover analysis. To support the design of your steel framed structure, you are expected to produce a report including CAD/BIM drawings of the designed frame.

**3.1 Requirements****The structure should have the following geometrical/material requirements:****• **have a specific number of portals that is individual to you and is listed in column 3 of Table 1;**• **have a minimum distance between portals of 2.5 m;**• **have a minimum clear height of 4.2 m;**• **each portal of the frame should have a clear span of 8 m;**• **you have to consider the self-weight of the structure, a dead load of 4 kN/m and a live load of 1.6 kN/m on the roof beams.**• **be made of steel grade S235 with a perfectly plastic material model.

In addition to these requirements, you can add as many bracing elements and roof beams as you find suitable, as long as the bracing do not obstruct passage across the portals. You should design the structural element profiles so that the structure is safe against a seismic event of type 1, ground type as listed in Table 1, importance class II and damping coefficient ? = 5 %, as prescribed by the Eurocode 8 (see EN 1998-1:2004 3.2.2.5).

**The following workflow is suggested**

- Pre-design your structure based on the geometrical/material requirements and vertical loads;
- Model your structure in a specialised FE software to obtain its capacity curve;
- Separately, use the Annex B of the EC8 to determine the target displacement that your structure has to reach, using the required response spectrum for the above seismic action;
- If the pushover curve stops before the target displacement, the structure has to be redesigned so that its limit displacement is increased, e.g., by reducing the stiffness of the system;
- When the pushover curve stops after the target dispacement, use your FE software to calculate the internal forces at that displacement, and carry out ultimate limit state (ULS) verification (bending and shear failure checks at the minimum).

**Your report should include**

- A detailed overview of the modal and pushover analyses required to obtain the capacity curve of the structure, namely mode shapes and used options (material model, consideration of geometric nonlinearities, used Newton-Raphson algorithm, etc.);
- The target displacement, response spectrum for the seismic event detailed above, and the corresponding description of plastic hinges formation, performed safety checks;
- a maximum of three pdf files of A3 size showing a 3D CAD/BIM view of the frame, 2D CAD/BIM views and constructive details of the designed frame. The views should be to scale, annotated with dimensions, have a border page and a title box. The box should contain a title block in the bottom right hand corner listing the title, student number, date and scale;

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