By engaging in this module, the students will understand and appreciate the difference between large/small initial curvature on the theoretical solutions to bending of initially curved beams. The geometry of curved bars has an important bearing on the bending stress distribution and is an extension to previously examined bending theory and but includes the movement of the neutral axis. Euler theory on buckling of struts will be extended to include the Rankine theory, and also the solution of problems associated with struts with initial curvature, and struts laterally loaded. This will required prerequisite knowledge of the solution to second order differential equations. Students will apply work, strain energy and complementary energy principles to structural analysis, including statically indeterminate systems. The module will introduce the concept of transverse shear and calculate the shear stress distribution in loaded beams. The module will review stresses and strains in 2D, and extend these principles into 3D in an elastic body subjected to various loading conditions, and to understand how to apply stress functions to problems in bending, contact stress and pure shear. The laboratory element of the module will inform the students of the principles of practical strain measurement techniques, from strain gauges to Digital Image Correlation and compare these experimental results to numerical and theoretical solutions, associated with stress concentrations. This module will build on and enhance the students' knowledge of the fundamentals of mechanics of solids (i.e. from introductory modules in this space such as Mechanics of Solids 1 & 2), and students should have also knowledge of the fundamentals of Finite Element Analysis.

By engaging in this module, the students will understand and appreciate the theoretical solutions to: bending of initially curved beams, movement of the neutral axis; Euler theory on buckling of struts, to include the Rankine theory, and also the solution of problems associated with struts with initial curvature, and struts laterally loaded; Work, strain energy and complementary energy principles applied to structural analysis, including statically indeterminate systems; Transverse shear stress and the shear stress distribution in loaded beams; Review stresses and strains in 2D, and extend these principles into 3D in an elastic body subjected to various loading conditions, and to understand how to apply stress functions to problems in bending, contact stress and pure shear; the laboratory element of the module will inform the students of the principles of practical strain measurement techniques, from strain gauges to Digital Image Correlation and compare these experimental results to numerical and theoretical solutions, associated with stress concentrations.

On successful completion of this module, students will be able to: 1. Contextualise, analyse and determine the bending stress distribution in curved beams subjected to various external loads and appreciate that the neutral axis can move; 2. Apply their mathematical knowledge and understanding to determine the particular integrals and complementary functions required to solve second order differential equations to determine the deflection characteristics of struts when buckled; 3. Employ energy methods for the structural analysis of complex truss structures, appreciate various methods for establishing deflections of loaded structures by the principles of virtual work, total complementary energy, fictitious loads. These methods will be applied to statically determinate and indeterminate structures, including self-straining or thermal straining; 4. Develop expressions for the transverse shear stress distribution in beams and identify and evaluate the location and magnitude of shear stresses at various locations along a beam cross-section; 5. Develop expressions for the stress and strain tensor and given the stress or strain tensor be able to calculate the 3 principal values and their direction cosines, evaluate the state of stress on a plane and transform the state of stress to different planes. Demonstrate that there are 3 principal stresses, strains. 6. Evaluate, by combining and comparing, experimental and numerical methods for the strain analysis of a complex structural artefact including a stress concentration subject to external loading.

1. Interact with technicians, the lecturer and fellow class-mates to understand how they together constitute an engineering team and critically compare experimental results to theoretical ones (group work and a written journal style paper based on laboratory work); 2. Identify and assess experimental constraints, intricacies and deficiencies associated with each strain measurement technique; 3. Appreciate the Health and Safety regulations and rules associated with laboratory work.

1. With great hand-eye coordination and dexterity affix strain gauges to engineering artefacts and mechanically test them under load. 2. Apply a carefully controlled artificially applied speckle pattern to an engineering artefact using acrylic spray or aerosol paint to perform Digital Image Correlation - this requires very careful dexterity to successfully achieve a consistently uniform but random speckle pattern of up to 10 pixels in size.

Normal lectures will be used for the students to acquire most of the learning outcomes. The laboratory work will be a platform for the dissemination and appreciation of learning outcomes also. New advances (and research by the module leader) in strain measurement techniques and capital investment in the acquisition of these techniques will add to the students' experiences. The module is aligned to the following UL graduate attributes: Knowledgeable: Students will apply their knowledge, understanding and mathematical abilities to the subject of the mechanics of solids to structurally analyse components theoretically but also to apply this knowledge to experimental tasks and results. Proactive: the students will be given allocated time slots in a dedicated computer laboratory to produce, on their own, Finite Element Analysis results to compare with experimental data. Responsible: Have a thorough understanding of the importance of the health and safety in the laboratory setting. Collaborative and articulate: Students will engage with faculty, technicians and team members to complete the laboratory tasks/assignments and author and submit a journal style report based on their experimental experiences, in contract to their numerical analyses.