# Civil Engineering with Architecture BEng/MEng

## Mechanics of Solids 3 ENG3037

• School: School of Engineering
• Credits: 10
• Level: Level 3 (SCQF level 9)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

This course develops the principles of stress and strain in three dimensions and illustrates the 2D plane stress and plane strain states as special cases of the 3D scenario. Stress and strain transformations in 3D and 2D are studied and special stresses and strains such as principal stresses and strains in 3D etc. are discussed. Equilibrium, compatibility and constitutive relationships are developed.  Experimental stress analysis is treated in conjunction with laboratory exercises and the course concludes with a treatment of yield criteria and plasticity including assessment of the likelihood of failure in practical stress analysis scenarios such as in members undergoing combined bending and torsion and in pressure vessels.

### Timetable

2 lectures per week, 1 tutorial every two weeks

None

None

### Assessment

85% Written Exam

15% Written Assignment

Main Assessment In: December

### Course Aims

The aims of this course are to:

■ introduce stress and strain in 3D, 3D transformation laws for stress and strain (geometric, matrix, and tensor index notation approaches), principal stresses and strains in 3D, maximum shear stress and strain in 3D, octahedral stresses and strains, hydrostatic stress and strain, deviatoric stress and strain, plane stress and plane strain and Mohr's circle for 3D and 2D stress states;

■ develop equilibrium, compatibility and constitutive relationships in continua;

■ study experimental stress analysis techniques (including strain gauges, digital image correlation etc.);

■ explain brittle and ductile yield criteria and discuss the mechanisms and mechanics of plasticity (as applied to 3D and 2D stress states);

■ introduce design against failure: determination of whether yield will occur in practical scenarios such as in members undergoing combined bending and torsion and in pressure vessels.

### Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ define stress and strain in two and three dimensions;

■ calculate principal stresses (and strains) and maximum shear stress (and strain) in 3D and 2D;

■ define and calculate octahedral planes, octahedral stresses, hydrostatic stresses and deviatoric stresses (and strains);

■ undertake transformations of stress and strain in 3D (and 2D) using geometric, matrix and index notation approaches;

■ use Mohr's circle in 3D and 2D to determine stresses and strains at various orientations, to determine principal stresses (and strains) and to determine maximum shear stress (and strain);

■ explain equilibrium, compatibility and constitutive relationships in materials;

■ explain the available methods for assessing stress fields experimentally (particularly strain gauging and digital image correlation), including solving 2D strain gage problems;

■ explain the various yield criteria for brittle and ductile failure (Maximum principal stress, Tresca, Von Mises etc.) and the fundamental mechanisms and mechanics of plasticity;

■ calculate the possibility of yield occurring for various 3D and 2D stress states arising from practical stress analysis problems (such as in members undergoing combined bending and torsion and in pressure vessels etc.).

### Minimum Requirement for Award of Credits

Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.

Students must attend the timetabled laboratory classes.