Center of Mass, Center of Gravity, Centroids Distributed Loads

CENTER OF MASS – locates the point in a system where the resultant mass can be concentrated so that the moment of the concentrated mass with respect to any axis equals the moment of the distributed mass with respect to the same axis.

CENTER OF GRAVITY – locates where the resultant, concentrated weight acts on a body.

Centroid The centroid (C) is a point which defines the geometric center of an object. If the material composing a body is uniform or homogeneous, the density of material is constant (ρ = constant). Hence, the resulting formulas that define the centroid of a body depend only on the geometry of the body {Volume (V), Area (A), or Length (L)}. If the material composing a body is uniform or homogeneous, the density or specific weight will be constant throughout the body, then the centroid is the same as the center of gravity or center of mass Special cases: - If a body has an axis of symmetry, C (= centroid) is on this axis - If a body has two or more axes of symmetry, C is where both axes cross - If a body is symmetric about a point, C is that point

Example-1

Example-2

Example-3 Find the centroid of the region bounded by the curve y = x3 and the lines y=0 and x=2.

Distributed loads The analysis of many engineering problems involves using the moments of quantities such as masses, forces, volumes, areas, or lines which, by nature, are not concentrated values.

Distributed loads

Distributed Loads on Beams