MCS501

Unit Description and General Aims

This unit introduces stiffness (displacement) analysis procedures of statically indeterminate structures. 

First, the basic principles for structural analysis and the basic operations of the matrix algebra are reviewed.

Then, longhand solutions are practised using matrix analysis and successive corrections (moment distribution) in the analysis of plane skeletal structures. Commercial structural analysis software SPACE GASS is then used for the analyse structures.

Finally, the Finite Element method is introduced with particular focus on the formulation of stiffness matrix equations using constitutive relations and shape functions for spring, bar and beam elements.  Finite Element software is then used to analyse practical structures with emphasis on modelling techniques and accuracy.

Learning Outcomes

On successful completion of this Unit, students are expected to be able to:

1. Evaluate beams and frames using the matrix stiffness method.

Bloom’s Level 5

2. Evaluate beams and frames using the moment-distribution method.

Bloom’s Level 5

3. Determine and derive stiffness and load matrices using Finite Element procedures.

Bloom’s Level 5

4. Synthesis 3D structures using Finite Element software.

Bloom’s Level 6

Student assessment

Prescribed and Recommended readings

Required textbook

R. C. Hibbeler, Structural Analysis, 10^th Edition. Pearson, 2019 - ISBN: 9781292247236

Recommended textbook(s)                  

Ghali, A.; Neville, A.M. and Brown, T.G.; “Structural Analysis: a unified classical and matrix approach” 7^th edition; Taylor and Francis, 2017

Kassimali A., “Structural Analysis”, 5^th edition, Cengage Learning, 2015

Cook, R. D., Malkus, D. S., Plesha, M. E., and Witt, R. J., “Concepts and Applications of Finite Element Analysis”, 4^th edition, John Wiley & Sons, 2002.

Kenneth Derucher, Chandrasekhar Putcha, Uksun Kim; “Indeterminate structural analysis”, Chapter 3.

Reference Materials

 A number of peer-reviewed journals and websites as advised below (and during lectures); 

1.     National and international technical journals: Finite Elements in Analysis and Design(https://www.journals.elsevier.com/finite-elements-in-analysis-and-design)
2.     Specific material to be advised during the lectures.

Unit Content

One topic is delivered per contact week, with the exception of part-time 24-week units, where one topic is delivered every two weeks.

Topic 1

Introduction:

1. Basic principles of structural analysis
2. Basic operations of matrix algebra

Topic 2

Stiffness Matrix Method (Part 1):

1. Fundamentals of the stiffness matrix method
2. Derivation of the stiffness matrices for beam elements
3. Analysis of beams using the stiffness matrix method

Topic 3

Stiffness Matrix Method (Part 2):

1. Analysis of frames using the stiffness matrix method.
2. BMD & SFD of Frame

Topic 4

Stiffness Matrix Method (Part 3):

1. Analysis of frames using SPACE GASS (Part 1)
2. Analysis of frames using SPACE GASS (Part 2)

Topic 5

Moment-Distribution Method (Part 1):

1. Introduction and definition of terms
2. Basic concept of the Moment-Distribution Method

Topic 6

Moment-Distribution Method (Part 2):

1. Analysis of frames: without sidesway
2. BMD & SFD of without sidesway frame

Topic 7

Moment-Distribution Method (Part 3):

1. Analysis of frames: with sidesway
2. BMD & SFD of with sidesway frame

Topic 8

Introduction to Finite Element Analysis (Part 1):

1. Fundamentals of the finite element analysis
2. Formulation of the stiffness matrix for the spring element
3. Examples: spring element

Topic 9

Application of the finite element method using commercial software:

1. Pre-processor
2. Analysis
3. Assessment of the results and their accuracy.

Topic 10

Introduction to Finite Element Analysis (Part 2):

1. Formulation of the stiffness matrix for the bar element
2. Examples: bar element

Topic 11

Introduction to Finite Element Analysis (Part 3):

1. Formulation of the stiffness matrix for the beam element
2. Examples: beam element

Topic 12

Project and Unit Review

In the final week students will have an opportunity to review the contents covered so far. Opportunity will be provided for a review of student work, to clarify any outstanding issues, and to work on finalising the major assessment report.

Software/Hardware Used

Software

• Software: SPACE GASS and ABAQUS

• Version: Student version

• Instructions:  N/A

• Additional resources or files: 

  http://www.spacegass.com/training/

  http://www.spacegass.com/student/index.htm

  https://academy.3ds.com/en/software/abaqus-student-edition

Hardware

• N/A