Centroids and Force Vectors

1st law of motion

an object in rest remains in rest unless acted upon by another force

2nd law of motion

force = mass times acceleration

3rd law of motion

for every action there is an equal and opposite reaction

centroids x coordinate

xiai/ai

centroids y coordinate

yiai/ai

right triangle x centroids

b/3

right triangle y centroids

h/3

semicircle x centroids

r

semicircle y centroids

4r/3pi

rectangle x centroids

b/2

rectangle y centroids

h/2

Ai 1

BH

Ai 2

pir^2/2

Ai 3

bh

F

pounds

beam deflection equation

change in max=FL^3/48EI

equation for I

b(h)^3/12

L

inches

E

psi (lb/in^2)

I=

in^4

magnitude

angle between a reference axis and an arrows line of action

direction

in relation to axis(angle)

sense

common sense (direction of top arrow)

SOHCAHTOA

use to find force vectors - flip to match part found

Fw

always down

normal force

up

converting inches to feet

divide by 12

free body diagram steps

1. sketch isolated object
2. sketch forces
3. label