CIVIL ENGINEERING FORMULAS

FIGURE 2.1 Geometric properties of sections.

Section

Equilateral polygon

A = Area

r = Rad inscribed circle

n = No. of sides

a = Length of side

Axis as in preceding section

of octagon

R = Rad circumscribed

circle

Moment of inertia

b 1 b 1

22

c

b

h

I =(6R^2 −a^2 )

6 R^2 −a^2

24

12 r^2 +a^2

48

12 b^2 + 12 bb 1 + 2 b 12

6 (2b+ b 1 )

R

2

≈

A

24

=I

r

I

c

I = h^3

6 b^2 + 6 bb 1 +b 12

36 (2b+b 1 )

=

180 °

n

I

Rcos

c = h

3 b+ 2 b 1

2 b+b 1

= h^2 h

6 b^2 + 6 bb 1 +b 12

12 (3b+ 2 b 1 )

I

c

=A(12r^2 +a^2 )

48

= (approx)

AR^2

4 = (approx)

AR

4

Section modulus Radius of gyration

1

3

13