Undergraduate Course: Theory of Structures 3 (CIVE09015)
|School||School of Engineering
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 9 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||This course introduces the analysis of two-dimensional indeterminate elastic structures composed of line elements. The types of structure that are studied in detail are continuous beams and rigid-jointed plane frames both with and without translating joints.
L1 Overview of structural analysis
Introduction: key differences between determinate and redundant structures; methods of determining level of redundancy in flexural beams and frames.
L2 Analysis of simple redundant beams using Macaulay brackets and superposition.
Macaulay brackets treatment of simple continuous beams. Free and reactant bending moment diagrams. Rigorous deduction of deflected shapes. Simple redundant structures:superposition. Application to beams of varying cross-section.
L3 Bending moment diagrams and relationships for redundant structures:
Construction of bending moment and shear force diagrams for redundant structures. Consequences of element stiffnesses on resulting forms.
L4 Introduction to Slope Deflection:
Introduction to slope deflection: notation and sign conventions. Derivation of slope deflection equations for a straight member. Fixed end moments and their derivation. Examples of fixed end moments for given loads. Inversion of SD equations to give rotations as subject.
L5 Application of Slope-Deflection to beams and simple frames:
Continuous beams subjected to generalised loading conditions; settlement of supports; bending moment and shear force diagrams for continuous beams.
L6 Sway and No-sway Frames;
Distinction between flexural frames that carry loads by joint displacement and those that use truss action instead. Identification of number of independent sway modes.
L7 Slope-Deflection for No-Sway Frames;
Plane frames with zero joint translations; bending moment diagrams. Reduction of number of unknowns in special conditions; bending moment, shear force and thrust diagrams.
L8 Analysis Principles for Sway Frames
Application to two dimensional structures with joint translations; general sway treatment; bending moment and shear force diagrams; symmetry and anti-symmetry. Formulation of stiffness matrices. Sway equilibrium equations for two dimensional structures. Application to simple rectangular structures.
L9 Moment Distribution: Introduction
Fundamental concepts, terminology, notation and sign convention; application to continuous beams; bending moment and shear force diagrams.
L10 Moment Distribution: Derivation
Derivation of the key parameters of moment distribution from the slope deflection equations.
L11 Moment Distribution: Continuous beams and faster convergence;
Application to continuous beams with fixed ends, pinned ends and overhangs; reduced stiffness for faster calculations; settlement of supports; bending moment and shear force diagrams.
L12-13 Moment Distribution: No-sway plane frames;
Moment distribution procedure for two dimension plane frame without joint rotation; bending moment, shear force and thrust diagrams.
L14 Moment Distribution: Continuous beams and support settlement; symmetry and antisymmetry. Moment distribution procedures for beams. Support settlement and its affects.
L15 Simple sway frames
Planar sway frames: general procedure for joint translation; bending moment, shear force and thrust diagrams. Single storey frame subjected to wind or lateral loading; sway displacement evaluation; bending moment and shear force diagrams.
L16 More complex sway frames; superposition of solutions;
Planar sway frames with multiple modes of joint translation in multiple directions: general procedure in structural analysis for addressing problems involving superposition of more complex treatments. Multi-storey frames and pitched-roof structures; sway displacement evaluation; bending moment and shear force diagrams.
L17 A substantial worked example on a complex unsymmetrical frames with inclined members.
Tutorial 1 Determinate structures: BMs and SFDs
Revision tutorial to ensure that the student has a good grasp of bending moment and shear force diagrams in determinate structures.
Tutorial 2 Simple Redundant Structures and Slope Deflection
The concept of redundancy and its use in determining forces in simple structures. A few simple questions using Slope Deflection.
Tutorial 3 Moment Distribution Analysis of Continuous Beams
The moment distribution method applied to beam structures.
Tutorial 4 Moment Distribution Analysis of No-Sway Frames
The moment distribution method applied to simple frame structures in 2D.
Tutorial 5 Sway Frames
The moment distribution method applied to simple sway frames in 2D.
Information for Visiting Students
|Pre-requisites||Structural Mechanics/Analysis to 2nd year undergraduate level or similar
|High Demand Course?
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- calculate the elastic pattern of stress resultants in a 2D redundant beam or flexural frame structure by hand;
- calculate the joint displacements of sway frames by hand;
- sketch the deformed shapes of redundant beams and frames under a wide variety of load patterns;
- draw appropriate bending moment, shear force and axial force diagrams.
|Coates, R.C., Coutie, M.G. & Kong, F.K.|
Structural analyses, 3rd Edition
Van Nostrand Reinhold (UK), Wokingham, (1988).
Other texts defined in the lecture notes.
|Graduate Attributes and Skills
|Course organiser||Dr Ahmad Al-Remal
|Course secretary||Mrs Lynn Hughieson
Tel: (0131 6)50 5687