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Centroid

The centroid is the point where the whole weight of a body can be thought to act. For composite areas you find it by weighting each part area with its own position. Common shapes, such as the triangle, have a standard centroid location worth remembering.

\bar x = \dfrac{\sum A_i x_i}{\sum A_i}

centroid of a composite area

y_C = h/3

triangle, measured from the base

Symbols

$A_i$	part area $i$	m²
$x_i$	centroid of part area $i$	m
$h$	height of the triangle	m

Example

A triangle with height $h = 0.9$ m:

$y_C = h/3 = 0.3$ m from the base.

The centroid of a triangle lies one third of the height above the base, where the medians meet.

Practise trusses and friction for free →

← Friction · Kinematics →

Part of Statics and Dynamics: Trusses and friction.