CIVIL ENGINEERING FORMULAS

88 CHAPTER THREE

Thekernis the area around the center of gravity of a cross section within

which any load applied produces stress of only one sign throughout the entire

cross section. Outside the kern, a load produces stresses of different sign.

Figure 3.5 shows kerns (shaded) for various sections.

For a circular ring, the radius of the kern r D[1(d/D)^2 ]/8.

For a hollow square (Handhlengths of outer and inner sides), the kern is

a square similar to Fig. 3.5(a), where

(3.3)

For a hollow octagon,RaandRiare the radii of circles circumscribing the outer

and inner sides respectively; thickness of wall0.9239(Ra–Ri); and the kern is an

octagon similar to Fig. 3.5(c), where 0.2256Rbecomes 0.2256Ra[1 (Ri/Ra)^2 ].

COLUMNS OF SPECIAL MATERIALS*

Here are formulas for columns made of special materials. The nomenclature for

these formulas is:

rmin

H

6

1

 2 

1 

h

H

2

0.1179H^1 

h

H

2



h

4

b

b

3 h

1

(e) (f)

(b)

R R

.226R

(a)

2 r

min.

(c)

d

D

2 r

r 2

r 1

3

b

3

b

b

3

h

b

3

h

h

6

h

6

h

3

h

3

h

h

4

d

d

(d)

4 h

1 3

(^2) h
FIGURE 3.5 Column characteristics.
*Roark—Formulas for Stress and Strain, McGraw-Hill.