CEN4030- N: Advanced Structural Analysis with Dynamics Report Writing - IT Assignment Help

Assignment Task:

Task:

Question 1
For the two-storey shear frame shown in Figure Q1, perform the following tasks considering the design data given in Table Q1.
1. Provide the equivalent mechanical model. [3 Marks]
2. Formulate the mass matrix [M]. [3 Marks]
3. Formulate the stiffness matrix [K]. [8 Marks]
4. Estimate the natural periods T of the system. [8 Marks]
5. Estimate the vibration modes {φ} of the system. [8 Marks]

[Total: 30 Marks]

Figure Q1: Two storey shear frame
Table Q1: Design data
Floor height h (cm) 350
Floor 1 mass m1 (kg) 3600
Floor 2 mass m2 (kg) 2000

Second moment of area (Floor 1) I1 (cm4) 25000

Second moment of area (Floor 1) I2 (cm4) 10000
Damping ratio ξ (-) 0.05 h

School of Computing, Engineering & Digital Technologies Page 3 of 11
Question 2
The steel tapered cantilever shown in Figure Q2 is subjected to a harmonic uniform line load p(t). The mass m(x) and second moment of area I(x) vary linearly along the length of the cantilever. The damping coefficient is constant and equal to c0. The design data for the problem is given in Table Q2.
Assuming that the cantilever vibrates with a deflected shape φ = x
2 L
2 ⁄ , perform the

following tasks:
1. Write the equation of motion in terms of generalized parameters.
[15 Marks]
2. Estimate the natural period T of this generalized SDOF for the given shape
function. [5 Marks]
3. Discuss what is the necessary condition for the cantilever to be in resonance.
[3 Marks]
4. Estimate the anticipated amplification factor in the case of resonance.
[4 Marks]
5. Estimate the damping coefficient c0.

Question 3
A six-member truss is subjected to two concentrated loads as shown in Figure 3a. It is intended that the matrix method of analysis is performed to find the member forces of the truss. For the purpose of analysis, the nodes and members of the truss have already been numbered as shown in Figure 3b. Perform the following tasks as part of the analysis for the truss.
a. Write the load vector for the given loads [5 Marks]
b. Determine the member stiffness matrices for all six members [15 Marks]
c. Determine the structural stiffness matrix for the entire truss

Question 4
a. Explain why defining appropriate boundary conditions is important for a finite element analysis. [4 Marks]

b. List what are the main types of boundary conditions used in a finite element formulation and explain how they are incorporated in the formulation. [4 Marks]

c. In finite element modelling, loads can be applied on the solid model or on the finite element model.

i. Discuss the advantages and disadvantages of applying loads on the finite element model instead of a solid model. [4 marks]
ii. Which load application approach did you use to model your structure for this module? [4 marks]
d. Write a short description of the approach taken in the application of the finite element method to the modelling and analysis of a continuous plate. [7 marks]
e. Explain how progressive collapse analysis is performed for a multi-storey building. Present three engineering design measures that can be adopted to reduce the probability of progressive collapse of a structure. [7 marks]

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