Aims

Trusses, beams and frames are parts of engineering structures from bridges and building architecture to aerospace and biomaterials. Understanding how such structures deform and fail in response to loading is essential for safe and predictable designs.

There are two parts to this module:

- To understand how and why material fails, it is necessary to understand how large-scale forces and deflections lead to small-scale stresses and strains; this is an important step towards using and interpreting finite element analysis for structural design.

- A focus on trusses, beams and frames and methods for determining tensions, and how to use the principle of virtual work to calculate deflections.

Outline Of Syllabus

The syllabus is structured around two main areas:

1. Stresses and Yield (6 lectures, 3 tutorials, FF)

Engineering properties of materials, such as Young’s modulus and the yield point, are typically found from rods loaded axially, giving a very one-dimensional understanding of material response. These lectures look at the three-dimensional and interrelated nature of stress and strain and how to reduce this complexity to the von Mises stress that is useful for structural design work.

2. Trusses, beams and frames (16 lectures, 8 tutorials, SZ)

Designing safe and stable structures requires an understanding of how loads and constraints affect the deformation. These lectures cover static indeterminacy and instability of structures, how to analyse the internal distribution of forces in trusses, and how to determine bending and deflection of beams through integration. The virtual work principle is introduced and Castigliano’s method for determining deflections is illustrated. Mohr’s Circle is used as a graphical tool for solving and interpreting plane stress problems. Contact mechanics of cylinders and spheres is introduced to illustrate the impact of geometry on contact pressure and subsurface yield.

Teaching Rationale And Relationship

Lectures deliver the core engineering theory and the methods for applying this to engineering applications. Tutorials support the students' self-study in reading around the lecture material and learning to solve the practical engineering problems posed through tutorial questions.

Assessment Rationale And Relationship

The digital examination assesses the students’ ability to apply engineering principles and theory to a variety of problems covering trusses, beams, frames, thin-walled cylinders and stress in 3D. The formative assessment provides a wider range of problems with immediate feedback to aid student learning.