Page 150 - Civil Engineering Formulas

88 CHAPTER THREE

h
h 3
6
h h
2r 3
h min. h
6 h
3
h
b b b .226R
3 3 3 R R
b
(a) (b) (c)
1 h 2 h
3 1 3
D 4 h

b
b
2r 4
d
4 d
r 1
d r 2
h
(d) (e) (f)
FIGURE 3.5 Column characteristics.

The kern is 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.
2
For a circular ring, the radius of the kern r D[1 (d/D) ]/8.
For a hollow square (H and h lengths of outer and inner sides), the kern is
a square similar to Fig. 3.5(a), where
2
2
h
h
H 1
r min 1 0.1179H 1 (3.3)
6 2 H H
For a hollow octagon, R a and R i are the radii of circles circumscribing the outer
and inner sides respectively; thickness of wall 0.9239(R a – R i ); and the kern is an
2
octagon similar to Fig. 3.5(c), where 0.2256R becomes 0.2256R a [1 (R i /R a ) ].
COLUMNS OF SPECIAL MATERIALS*
Here are formulas for columns made of special materials. The nomenclature for
these formulas is:

*Roark—Formulas for Stress and Strain, McGraw-Hill.