Last Updated S012019


Unit Name Strength of Materials - Advanced Topics
Unit Code BCS204S
Unit Duration 1 Semester

Bachelor of Science (Engineering)

Duration 3 years    

Year Level Two
Unit Creator / Reviewer N/A
Core/Elective: Core
Pre/Co-requisites BCS106S
Credit Points


Total Course Credit Points 81 (27 x 3)

Mode of Delivery Online or on-campus. 
Unit Workload (Total student workload including “contact hours” = 10 hours per week; 5 hours per week for 24 week delivery)
Pre-recordings / Lecture – 1.5 hours
Tutorial – 1.5 hours
Guided labs / Group work / Assessments – 2 hours
Personal Study recommended – 5 hours

Unit Description and General Aims

The objective in presenting this unit is to impart to students the key components of study into the strength of materials, particularly the mechanics of structures and stress analysis, with an emphasis on advanced topics and analysis.

The subject matter covered in this unit will include mathematical models used to describe the effects of forces on simple structures under combined actions; the concepts of stress and strain transformation, Mohr circles and combined stresses and aspects of stability.

At the conclusion of this unit, students will have acquired the requisite specialised knowledge to undertake the design and analysis of many different structures. Furthermore, the acquisition of the information from this unit will provide students with a basis on which more advanced forms of analysis and design skills can be further developed in later units.

Learning Outcomes

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

  1. Design structures for axial loads and direct shear and analyse shear stress in simple beams.
    Bloom’s Level 6
  2. Determine, assess and validate beam deflections and bending stresses/strains in composite beams.
    Bloom’s Level 4
  3. Design, analyse and interpret combined stresses in simple structures
    Bloom’s Level 6
  4. Design and specify simple column analysis and interpret results to provide solutions to specific problems.
    Bloom’s Level 6
  5. Analyse and assess statically indeterminate beams and trusses by the Flexibility (Force) method.
    Bloom’s Level 4

Student assessment

Assessment Type When assessed Weighting (% of total unit marks) Learning Outcomes Assessed

Assessment 1

Type: Multi-choice test / Group work / Short answer questions / Practical / Remote Lab / Simulation

Example Topic: Tension, Compression, and Shear Stresses, Axially Loaded Members & Torsion, Beam Bending, Shear Stresses in Beams

Students may complete a quiz with MCQ type answers and solve some simple equations to demonstrate a good understanding of the fundamental concepts.

Due after Topic 3 15% 1

Assessment 2

Type: Multi-choice test / Group work / Short answer questions / Practical / Remote Lab / Simulation

Example Topic: Stress Transformation, Deflections of beams & columns.

Students may be asked to provide solutions to simple problems on various topics.

Due after Topic 6 20% 2, 3

Assessment 3

Type: Multi-choice test / Group work / Short answer questions / Practical / Remote Lab / Simulation / Project

Example Topics: Tension test of mild-steel and aluminium; Torsion test of mild-steel and aluminium; Impact test of mild-steel and aluminium; Bending test of steel/timber beams; Shear test of steel beam; and, Buckling test of steel column.

Students may complete a quiz with MCQ type answers or solve some simple problems or use software to complete a practical.

Due after Topic 9 20% 5

Assessment 4

Type: Examination

Example Topic: All topics with an emphasis on Logarithms and Matrices

An examination with a mix of detailed report type questions and/or simple numerical problems to be completed in 3 hours

Final Week 40% 1 to 5

Attendance / Tutorial Participation

Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application.

Continuous 5% 1 to 5

Prescribed and Recommended Readings

Required textbook(s)

• R. C. Hibbeler, Mechanics of Materials, 10th Edition. Prentice Hall, 2018 ISBN 978-1292178202

Reference Materials

• M. Gere, B. J. Goodno, Mechanics of Materials, 9th Edition. Cengage, 2020 ISBN: 978-0357377857
• Wilkinson, Tim (2007). Structural Mechanics, 2/E, Sydney: University of Sydney

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

Beam Bending

• Basics of bending
• Types of beams
• Graphical representation of SFD and BMD
• Bending deformation of a straight member
• Flexure (bending) formula
• Composite beams - transformed section method
• Composite beams (advanced topic)
• Doubly symmetric beams with inclined loads (advanced topic)
• Bending of unsymmetrical beams (advanced topic)
• Bending of unsymmetrical beams (direct method)

Topic 2

Shear Stresses in Beams

• Bending of beams - Shear Stress Theory
• Curvature of a beam
• Longitudinal stains in beams
• Normal stresses in beams
• Shear stresses in beams
• Shear stresses in beams of rectangular cross-section
• Shear stresses in beams of circular cross-section
• Shear stresses in the webs of beams with flanges
• Shear flow in built-up beams
• Beams with axial loads

Topic 3

Shear-Centre Concept

• The shear-centre concept (advanced topic)
• Shear stresses in beams of thin-walled open cross sections
• Shear stresses in wide-flange beams
• Shear centres of thin-walled open sections (advanced topic)

Topic 4

Stress and Strain Transformation

• Introduction to plain stresses
• Plane stresses
• Transformation of plane stresses
• Principal stresses and maximum shear stresses
• Mohr’s circle for plane stress
• Hook’s law for plane stress
• Triaxial stress
• Transformation of plane strain

Topic 5

Application of Plane Stresses

• Spherical Pressure Vessels
 Stresses at the outer surface
 Stresses at the Inner surface
 Important points to note
• Cylindrical Pressure Vessels
 Circumferential stress
 Longitudinal stress
 Stresses at the outer surface
 Stresses at the Inner surface
• Maximum Stresses in Beams
 Beams of Rectangular cross section
 Wide flange beams
• Combined Loading
 Method of analysis
 Illustration of the method
 Selection of critical points

Topic 6

Deflection of Beams Part 1

• Differential Equations of a Deflection Curve
 Beams with small angles of Rotation
 Non-Prismatic Beams
 Prismatic Beams
 Exact Expression for Curvature
• Deflection by Integration of Bending Moment Equation
• Deflection by Integration of the Shear Force and Load Equation
• Method of Superposition
 Tables of Superposition
 Distributed Loads
 Principles of Superposition
• Moment-Area Method
 Second-moment area theorem
• Non-prismatic Beams

Topic 7

Deflections of beams Part 2

• External work and Strain Energy
• Strain Energy Density
• Elastic Strain Energy for Normal Stresses
• Elastic Strain Energy for Shearing Stresses
• Strain Energy for a general state of Stress
• Conservation of Energy
• Impact Loading
• Deflections produced by Impact
• Discontinuity Functions

Topic 8

Deflections of beams by energy methods

• Principles of Virtual work
• Method of Virtual forces applied to Trusses
• Method of Virtual forces applied to beams
• Castigliano’s Theorem
• Deflection by Castigliano’s Theorem
• Castigliano’s Theorem applied to Trusses
• Castigliano’s Theorem applied to Beams
• Deflection of Trusses by Unit Load method
• Temperature Effects

Topic 9

Statically Determinate and Indeterminate Beams

• Classification of Structures
• Statically Indeterminate Beams and Shafts
• Statically Indeterminate Beams and Shafts-Method of Integration
• Statically Indeterminate Beams and Shafts-Moment-Area Method
• Statically Indeterminate Beams & Shafts-Method of Superposition
• Analysis of Statically Indeterminate Beams by Force method
• Analysis of Statically Indeterminate Trusses by Force method

Topic 10

Column buckling

• Introduction to Columns
• Buckling and Stability of Columns
• Columns with pinned ends
• Columns with other support conditions
• Columns with concentric loading
• Column with eccentric loading
• The Secant formula and applications for columns
• Elastic & Inelastic Behavior of Column
• Inelastic Buckling

Topic 11

Centroids and Moment of Inertia

• Centroids of Plane areas
• Centroids of Composite areas
• Moments of Inertia of Plane areas
• Radius of gyration
• Parallel-axis theorem for moment of Inertia
• Polar Moment of Inertia
• Products of Inertia
• Moment of Inertia of Inclined Axes
• Mass moment of Inertia
• Principal Axes
• Principal Points
• Principal moments of Inertia

Topic 12

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 students’ work and to clarify any outstanding issues.

Software/Hardware Used


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