Samenvatting statica formuleblad handig bij Tentamen en basistoets

Geometric Properties of Line and Area Elements Center of Gravity and Mass Mome
Centroid Location Centroid Location Area Moment of Inertia
z
y y
L = 2θ r A = θ r2
r r Ix = 14– r 4 (θ – 12– sin 2)θ
θ θ
x x V = 43– π r 3 r
θ C θ C
G
Iy = 14– r 4 (θ + 12– sin 2 ) θ
r sin θ
—––– 2– r sin θ
—–––
θ 3 θ y

Circular arc segment Circular sector area
x
Sphere
y
Ixx = Iyy = Izz = 25– mr 2
L = π2– r L = πr A = 14– πr2 –1– π r 4
Ix = 16
4r
r 2r C r r —
3π
C —
π C Iy = 16
1
πr4 z
x ––
4r
—
3π

Quarter and semicircle arcs Quarter circle area
V = 23– π r 3
G
r y
a A= –1h (a + b) y π r2
2 A= —–
2
h C 4r
x 3– r
x —
3π
Ix = 18– π r 4 8
r
2 a+ b
1– ——— h C x Hemisphere
b 3 a+b
Ixx = Iyy = 0.259mr2 Izz = 5 mr
2– 2
Iy = 8π r
1– 4

Trapezoidal area Semicircular area
y
A= 2– A = πr2
b 3 ab

r z
a C 3– Ix = 14– π r 4 z'
5a x
C
G
Iy = 14– π r 4
–3 b r
8
y
Semiparabolic area Circular area
x
Thin Circular disk
y A = bh
Ixx = Iyy = 4 mr
1– 2 I = 1– mr2 I
zz 2 z'z' = 2– mr
3 2
A=—
1 ab
Ix = 12 bh
3 —1 3
b h x
C
C
10 b
—3
b
4a
3–
Iy = 12 hb
—1 3 z
a
Exparabolic area Rectangular area

a r
A= –1 bh
2 G
b y
C h C
x Ix = 36 bh
1 3
1
— x