Objectives:

Understand understanding of structural behaviour.
Understand the differences in numerical, analytical results.

Part A: Matrix analysis method

Consider the following structural system shown in Figure 1.

Use the Matrix analysis method to analyse the structural response of the portal frame.

E=4500ksi, I=3500in⁴, Poisson Ratio=0.1 and Area=180 in².

a) Determine slope and vertical deflection at point “B”

b) Find reactions and draw BMD, SFD for the Frame Structure.

Part B: Structural behaviour

1) Use Matrix analysis method and STAAD. PRO to determine internal force diagrams (bending moments, shear and axial forces), reaction forces and sway (horizontal displacement of beam) of the following four systems:

B.1 uniform frame and offset load (Figure 2)

B.2 nonuniform frame and offset load (Figure 3)

B.3 nonuniform frame and centric load (Figure 4)

B.4 uniform frame and centric load (Figure 5).

Sectional properties 1: Solid rectangular cross-section with a depth of 2 mm and an out of plane thickness of 15 mm (Calculate the corresponding A₁ and I₁).

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Sectional properties 2: Solid rectangular cross-section with a depth of 1.5 mm and an out of plane thickness of 15 mm (Calculate the corresponding A₂ and I₂).

Load: Force F = 4.9 N

Material properties: Young’s modulus E = 100,000 N/mm²

Figure 2: System B.1: uniform frame and offset load

Figure 3: System B.2: nonuniform frame and offset load.

Figure 4: System B.3: nonuniform frame and centric load.

Figure 5: System B.4: uniform frame and centric load.

2) Discuss differences in internal force distributions (axial force, shear force and bending moment diagrams) and reaction forces for the systems B.1 to B.4

3) Discuss how the sway of the frame (sway is the horizontal displacement of the horizontal beam) is influence by position of the load and the nonuniform properties of the frame.

4) Investigate the importance of the axial stiffness on the STAAD.PRO results for the system with the largest sway. Would it acceptable to assume that the members are inextensible?

5) Summarise the key results in the form of all reactions and the sway for all 4 systems in a table

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Report

The report should contain the following minimum contents:

PART A

Description of the problem
Summary of the results in the form of a comparison of reaction forces and internal force diagrams (BMD, AFD, SFD) of the reference solution and the solution of the force method. Comment on any differences in the solution.
Description of calculation steps, intermediate internal force diagrams and reaction forces for the auxiliary systems.

PART B

Description of the problem.
Matrix analysis B.1 ~ B.4 Frame and calculate the reaction forces, draw internal force diagrams.
Comparison of the internal force diagrams, reaction forces and sway of STAAD.PRO analyses
Discussion of the influence of load position and cross-sectional properties on the response of the frame
Conclusions

STAAD.PRO screenshots are only permitted in the report if a white background is used and the labels are clearly readable!

You are very welcome to include hand written calculations and hand drawn internal force diagrams in your report.

Submission Guidelines

Please note that standard rules for late submission of coursework apply.

Reduction of two subgrades (e.g. B1 to B3) for each working day late, up to a maximum of 5 days.
Zero mark if more than 5 days late.
It is essential that you still submit any late coursework, even if you are going to get zero marks for it (otherwise you cannot obtain any credits for this course).

Remember that the mark for CVE2221 counts towards your degree classification.

Marking

The marking will take into account in equal weights the presentation of the results and the understanding.

Concerning the presentation, aim for the following:

The main steps of the computation and calculation are well presented
Results are clear and easily accessible
The writing is accurate
Good English
All references to figures and equations are correct
Enough information is provided to allow others to reproduce your results

Concerning the understanding, aim to provide sufficient comments to show that you have understood the underlying theory, which give you the presented results.

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