static equilibrium

newtons first law of motion

an object remains at rest or in uniform motion in a straight line unless acted on by a resultant of net force

applied forces

on structure affect the distribution of force within the structure

force acting on mass(W)

W=mg=m x 9.81

conditions of equilibruim in 2D

all horizontal force in balance

$\sum F_x=0$

all vertical force in balance $$\sum F_y=0
$$

in plane moments $$\sum M=0
$$

all out of plane forces as $$\sum F_x=0
$$

3D conditions for equilibrium

also need the following

all out of plane force $$\sum F_x=0
$$

alll out of plane moments as $$\sum M_x=0 $$ and $$\sum M_y=0$$

beams

simple supprted beam

cantilever

one end on the beam is fixed and one unsupported

force act

vertically x-y plane

cantilever

vertical direction $$\sum F_y=0$$

$$R_y=P+mg$$

no horizontal forces $$R_x=0$$ no horzontal loads$$\sum M=0$$

$$M=PL+mg\frac{L}{2}$$

amount the structure deflects - stiffness

curvature of beam

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