ABSTRACT

A lamina is a thin flat sheet having uniform thickness. The centre of gravity of a lamina is the point where it balances perfectly, i.e. the lamina’s centre of mo-

At the end of this chapter you should be able to:

• define a centroid • define first moment of area • calculate centroids using integration • define second moment of area • define radius of gyration • state the parallel axis and perpendicular axis theorems • calculate the second moment of area and radius of gyration of regular sections using a table of standard results • calculate the second moment of area of I, T and channel bar beam sections

Why it is important to understand: First and second moment of areas The first moment of area is usually used to find the centroid or centre of gravity of a two-dimensional shape or an artefact. The position of the centroid and centre of gravity is fundamental and often it is very important in very many branches of engineering. The second moment of area can be described as the geometric ability of a two-dimensional figure or lamina to resist rotation about an axis through its plane. It is extensively used in structures, where it measures the geometric ability of the structure to resist bending. Likewise in the hydrostatic stability of ships and yachts, the second moment of area of a yacht or a ship’s water plane is a measure of the yacht or ship to resist rotations, such as those due to ‘heeling’ and ‘trimming’. This chapter starts by defining the first and second moments of area of twodimensional figures and laminas, and extends this to shapes that are useful in engineering, such as the shapes of the cross-sections of beams. For example, I beams, Tee beams and channel cross-sections are all very important in structural engineering. First and second moments of force are of much importance in calculating bending stresses in buildings, bridges, ships, etc.