ENGINEERING TRIPOS PART IA - 2012/2013

PAPER 2 - STRUCTURES and MATERIALS

Structural Mechanics

Leaders: Dr M.J.DeJong/Dr. J.M. Lees

Timing: Weeks 1-7 Michaelmas term and weeks 3-8 Lent term.

Structure: 24 lectures, 2 lectures/week

AIMS

The aims of the course are to:

• Make students aware of the key role of structures in different branches of engineering.
• Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements.
• Explain the importance of assumptions and hypotheses in the development of theory.
• Convince students of the important role of observation and experiment in the development of a proper theory of structures, and to provide practical examples of structural experiment, structural design and structural failure.
• Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, and how they deform under load, and how slender members may buckle.

OBJECTIVES

As specific objectives, by the end of the course students should be able to:

• Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
• Analyse the limiting equilibrium conditions of bodies in frictional contact.
• Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
• Determine the internal stress resultants at any section of a simple, statically determinate arch structure, and to find the maximum values of the stress resultants.
• Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate.
• Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions.
• Understand the equation of virtual work for pin-jointed frameworks and how to choose appropriate equilibrium and compatible sets.
• Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
• Explain curvature, and how it changes in an elastic beam when the bending moment changes.
• Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
• Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
• Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
• Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

SYLLABUS (Book Reference)

Introduction and Aims of the Course (1L)

1. Equilibrium in Two Dimensions (3L)

• Forces, moments and couples (3) Sect 1/1-1/5,1/7-2/5
• Resultants (3) Sect 2/6
• Free-body diagrams (3) Sect 3/1-3/2,3/4
• Polygon of forces (3) Sect 2/6, 3/3
• Two-force problems (3) Sect 3/3
• Three-force problems (3) Sect 3/3
• Distributed forces: gravity (centre of mass), pressure and hydrostatic loads (centroid) (3) Sect 1/6,5/1-5/3,5/9
• Friction(3) Sect 6/1-6/3,6/8

2. Cables, Arches and Pressure Vessels (2L) (4) Sect 5.1,5.6 (7) Ch.5

3. Two-dimensional Pin-jointed Frameworks (4L)

• Applications of frameworks in Engineering
• Triangulated frameworks, pin-jointed idealisation (3) Sect 4/1-4/2

3.1 Calculation of Bar Forces in Statically Determinate Frameworks

3.2 Calculation of Bar Elongations

3.3 Calculation of Displacements by Displacement Diagrams

4. Principle of Virtual Work (2L)

• Particles and rigid bodies in two dimensions (3) Sect 7.3
• Reactions, bar forces and displacements in pin-jointed frameworks

5. Equilibrium of Beams (2L)

• Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
• Distortion produced by internal forces
• Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
• Differential relationships between q, S, and M (5) Sect. 3.5
• Construction of bending moment diagrams
• Statical indeterminacy
• Case study

6. Deflection of Straight Elastic Beams (2L)

• Curvature and change of curvature, integration of curvature to find deflection
  (5) Sect. 8.1,8.2
• Deflection of elastic beams by integration (5) Sect. 8.3
• Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

7. Stresses in Elastic Beams (5L)

• Introduction, basic geometric concepts (5) Sect. 7.2
• Bending of beams with rectangular cross-section (5) Sect. 7.5
• Bending of beams with non-rectangular cross-section, centroid and second-moment of area
• Use of section tables
• Combined bending moment and axial force
• Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
• Shear stresses in beams (5) Sect. 7.6

8. Buckling of Columns (3L)

• Introduction, examples, hypotheses
• Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
• Critical stress
• Imperfections (6) Sect 5.2
• Design of columns

REFERENCES

Please see the Booklist for Part IA Courses for references for this module.