The University of Southampton
Courses

# CENV2030 Structural Analysis

## Module Overview

This module is aimed to develop and deepen knowledge already gained in FEEG1002 of understanding of how structural elements behave, and can be analysed. Students will also learn principles of structural dynamics and the applications of fundamental dynamic modelling. The module provides a firm basis for all subsequent modules in these areas in later years.

### Aims and Objectives

#### Module Aims

• Extend understanding of how structures behave, and can be analysed. • To recognise the concepts of stress-state, strain-state by considering the behaviour of simple structures. • Explain the elastic analysis of statically indeterminate structures, and to show key implications of redundancy. • Understand the use of plastic theory for analysis of simple structures. • To understand the analysis of moving loads. • Explain principles of dynamics and introduce and apply fundamental dynamic modelling. • To understand the nature of stiffness, mass and damping in civil engineering structures. • Analyse systems with more than one degree of freedom.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Apply the concept of stress-state and strain-state.
• Solve the standard-form equations for the response to simple harmonic, free damping and forced dynamics systems.
• Obtain and solve differential equations for systems with more than one degree of freedom.
• Analyse statically indeterminate truss, beam and frame structures.
• Apply matrix method of analysis of structures.
• Apply the influence line analysis for beams and 2-D trusses.
• Apply the Tresca and von Mises yield criteria.
• Find upper bound estimate of the failure load of beams, 2D frames and slabs.
• Find lower bound estimate of the failure load of beams.
• Solve stability (i.e. buckling) problems of columns.
• Know the fundamental assumptions of lumped parameter mass, stiffness and damper models.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Apply analytical skills to practical problems.
• Problem analysis and problem solving.
• Read flexibly and with purpose.
• Self-management (e.g. time management).
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Determine stiffness matrix of a simple model structure.
• Experiment on dynamic response of an idealised multi-degrees-of freedom simple structure.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Understand and appreciate the subject as an essential structural design tool.
• Identify appropriate analytical technique to determine failure load of structures.
• Estimate safe design loads for a range of key structural elements.
• Determine free/forced vibrations of single degree/ multi degrees of freedom systems.

### Syllabus

Statics (24 lectures + 1 short lab and associated course work + 4 tutorials) (10 Credits) 1. Revision of basic statics (1L) Stress, strain, Hooke's law (1D/2D/3D) • Static determinacy • Shear force and bending moment diagrams • Engineering’s Bending Theory • Concept of virtual work 2. Elastic Structural Analysis (8L) • Statically indeterminate trusses, analysis by the force method. • Stiffness method of analysis of structures • Matrix method of structural analysis • Moment distribution method • Statically indeterminate 2D frames 3. Influence lines (3L) • Introduction to moving loads. • Influence lines (simply supported beams) • Muller-Breslau method • Influence lines due to a series of point-loads / uniformly distributed load • Influence lines in 2D trusses. 4. Plastic Structural Analysis (8L) • Review of collapse mechanisms for statically determinate / indeterminate beams • Tresca, von-Mises yield conditions. • Upper bound analysis of beams / frames. • Yield lines analysis of plates. • Lower bound analysis of beams. • Lower bound principle as a justification for elastic analysis. 5. Introduction to non-linear analysis (4L) • Geometric non-linearity. • Buckling of ideal columns. • Euler buckling theory. • Buckling of slender columns • Rankine Theory. • Buckling of columns with initial imperfections. Dynamics (12 lectures + 1 short lab and associate coursework + 2 tutorials) (5 Credits) Dynamic equilibrium of structures, Response of a single degree of freedom system to dynamic excitation, Free vibration, Forced vibration, Multi degrees of freedom systems, Solving the free/forced vibration equation (analytical and numerical), Forced response of multi-degree of freedom systems, Numerical analysis of dynamic systems, Eigenvalue problems, Introduction to the seismic response of buildings.

#### Special Features

Supported computer sessions are provided for the coursework exercise and a licenced version of the software is available for students to use off-campus.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include • Lectures • Tutorials • laboratory supervisions • worked examples Learning activities include • lectures • laboratory classes • problem assignments • private study PowerPoint slides, tutorial sheets and solutions available from Blackboard

TypeHours
Tutorial5
Preparation for scheduled sessions20
Revision37
Lecture36
Follow-up work36
Supervised time in studio/workshop6
Total study time150

D. Brohn (2005). Understanding Structural Analysis.

JW Smith (1988). Vibration of Structures: application in civil engineering design.

S.S. Rao. Mechanical Vibrations.

Megson, T.H.G (2005). Structural and Stress Analysis.

### Assessment

#### Assessment Strategy

Repeat Method - External repeat as per referral method.

#### Summative

MethodPercentage contribution
Coursework 10%
Coursework 10%
Examination  (120 minutes) 80%

#### Referral

MethodPercentage contribution
Examination  (120 minutes) 100%

#### Repeat Information

Repeat type: Internal & External