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ARCHITECTURAL Centroids 1Lecture 11

S^ TRUCTURES

I:

STATICS AND

STRENGTH OF

MATERIALS

lecture eleven centers ofgravity- centroids

Centroids 2Lecture 11

A

Center of Gravity •^ location of equivalent weight •^ determined with calculus •^ sum element weights

ΔW^1 ΔW^4

ΔW^2 ΔW^3

W ∑Δ

y x z

=^ dW^ ∫ W

Centroids 4Lecture 11

A

Centroid •^ “average” x & y of an area •^ for a volume of constant thickness^ –

where

is weight/volume

-^ center of gravity = centroid of area

(^

) Ax A x^

∑= (^

) Ay A y^

At ∑= W^

γ

Centroids 5Lecture 11

A

Centroid •^ for a line, sum up length

ΔL

(^

) Lx L x^

∑= (^

) Ly L y^

Centroids 7Lecture 11

A

n

Symmetric Areas •^ symmetric aboutan axis •^ symmetric abouta center point •^ mirrored symmetry

Centroids 8Lecture 11

n

Composite Areas •^ made up of basic shapes •^ areas can be negative •^ (centroids can be negative for any area)

• (-)

⇒

Centroids 10Lecture 11

n

Area Centroids •^ Table 7.1 – pg. 242

h^ b

b^3 right triangle only