Supplementary Lecture Handouts (ABZ)
Stress and Strain (2007-8)
Recommended Textbook: J.M. Gere. Mechanics of materials. 6th edition. Brooks/Cole – Thomson Learning, London, 2004. Chapters 1, 2, 7, 8 (8.1 - 8.3 only).
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Tension and compression
Introduction to mechanics of materials. Normal stress and strain of a prismatic bar and limitations of the theory. Mechanical properties of materials and stress-strain diagrams. Linear elasticity, Hooke’s law, and Poisson’s ratio. Elasticity and plasticity. Strain energy and strain energy density.
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Axially-loaded members
Stiffness and flexibility of springs and prismatic bars. Factor of safety, allowable stresses and loads. Changes in length of prismatic bars under non-uniform conditions: intermediate axial loads, prismatic segments, continuously varying loads or dimensions. Elasto-plastic analysis.
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Statically indeterminate structures
Determinate and indeterminate structures. Equations of equilibrium and compatibility. Force-displacement relations. Temperature effects. Misfits and pre-strains. Bolts and turnbuckles. Use of displacement diagrams in statically indeterminate problems.
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Stresses on inclined sections
Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke’s law in shear. Normal and shear stresses on inclined sections. Maximum stresses on a bar in tension. Introduction to stress elements.
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Plane stress transformation equations
Stress elements and plane stress. Stresses on inclined sections. Transformation equations. Principal stresses, angles, and planes. Maximum shear stress.
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Mohr's circle for plane stress
Another look at the transformation equations for plane stress. Procedure for constructing Mohr’s circle. Stresses on an inclined element. Principal stresses and maximum shear stresses. Introduction to the stress tensor.
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Applications and further development
Hooke’s law for plane stress. Relationship between the elastic constants. Volume change and bulk modulus. Spherical and cylindrical pressure vessels.
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Plane strain
Plane stress versus plane strain. Transformation equations. Principal strains and maximum shear strains. Mohr’s circle for plane strain. Strain measurements; rosettes.