9 | Centroids, Centers of Mass, & Distributed Loads

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

  1. Find area and centroid of 2D shape defined by a function using calculus

  2. Find area/volume and centroid of composite 2D/3D shape using the tabular method

    • Calculate centroid and area of common shapes

    • Find the center of mass of non-homogeneous objects

  3. Simplify distributed loading into point load(s) in correct location(s)

Centroids

Integration Method

Hibbeler 12e 9.10: Finding Centroid Using Calculus and Vertical Strips

Hibbeler 12e 9.25: Finding Centroid Using Calculus with Varying Top and Bottom of Strips

Hibbeler 12e 9.18: 2D Equilibrium with Unknown CoM Location

Tabular Method for Centroids

Hibbeler 12e 9.60: Finding Centroid of Shape with Hole Using Tabular Method

Hibbeler 12e 9.59: Finding Centroid of Shape with Cutout Using Tabular Method

Tabular Method for Center of Mass

Hibbeler 12e 9.65: Center of Mass of 3D object

Distributed Loads

Hibbeler 13e 4.145: Uniform- and triangularly-distributed load

Hibbeler 13e 7.18: Triangularly-distributed load on a compound beam

Hibbeler 12e F4.38: Equilibrium with Uniform- and triangularly-distributed load

Hibbeler 12e F4.42: Equilibrium with Functionally-Defined Distributed Load

Hibbeler 12e 7.61: Multi-Body Equilibrium with Distributed Load

Mathematica Code