STATICS

Question 1

controid of composite areas: x-axis

Answer 1

x̄ = ∑ xi Ai / ∑ Ai

Question 2

controid of composite area: y-axis

Answer 2

ȳ =∑ yi Ai / ∑ Ai

Question 3

Polar moment of inertia

Answer 3

J = Ix + Iy

Question 4

Radius of gyration: x-axis

Answer 4

rx = √ Ix / A

Question 5

radius of gyration: y-axis

Answer 5

ry = √ Iy / A

Question 6

section modulus: x-axis

Answer 6

Sx top/bottom = Ix / Cy top/bottom

Question 7

Section modulus: y-axis

Answer 7

Sy top/bottom = Iy / Cx top/bottom

Question 8

Polar section modulus (Zp)

Answer 8

Zp = J / C

Question 9

Circle (Area)

Answer 9

A = πR²

Question 10

Circle (moment of inertia):

Answer 10

I = πR⁴ / 4

Question 11

Rectangle (area):

Answer 11

A = b(h)

Question 12

Rectangle (moment of inertia): x-axis

Answer 12

Ix = b(h)³ / 12

Question 13

Rectangle (moment of inertia): y-axis

Answer 13

Iy = h(b)³ / 12

Question 14

Triangle (area):

Answer 14

A = ½ bh

Question 15

Triangle (moment of inertia): x-axis

Answer 15

Ix = b(h)³ / 36

Question 16

Triangle (moment of inertia): y-axis

Answer 16

Iy = h(b)³ / 36

Question 17

Semicircle (area):

Answer 17

A = ½ π R²

Question 18

Semicircle (moment of inertia):

Answer 18

Ix = ⅛ (π ) (R⁴ )

Question 19

Parallel axis theorem (moment of inertia): x-axis

Answer 19

Ix = ∑Ix + ∑A dy²

Question 20

Parallel theorem (moment of inertia): y-axis

Answer 20

Iy = ∑Iy + ∑A dx²