Polymorf - Knowhere - Moment of inertia of columns

Finally, consider a solid wood column that is 2.828 in. x 2.828 in. and has the same cross

sectional area of the 2 x 4 shown previously.

e) model of 2.828 x 2.828		f) model of 2 x 4

Area = 8 in.²		Area = 8 in.²
I = 2.828 in. (2.828 in.)³		Ι = 4 in. (2 in.)³
12		12
= 5.33 in.⁴		= 2.67 in.⁴
.
Fig. 132 - Moment of inertia of solid columns with the same cross sectional area

Notice that the moment of inertia of the 2.828 inch square solid column is twice that of the

2 x 4 column despite the fact that their cross sectional areas are equal. Regardless whether

it is solid or hollow, a column with a square cross sectional area will have a larger moment

of inertia and load bearing capacity than a rectangular column of equal cross sectional

area, all other factors being equal. For this reason, structural columns are usually square

or circular in cross section and are often hollow because this design affords the greatest

load bearing capacity for the amount of materials used. Of course if the walls of the hollow

column get too thin their tendency to buckle locally, or crinkle, will increase.

The other dimensional component of a column is its length. To repeat, increasing its length

decreases a column's load bearing capacity by the square of the increase. For example in

Fig. 133 as the length of the columns is doubling the loading capacity is decreasing by a

factor of four. Notice that the cross-sectional areas of these columns do not change. Thus


.	.
Fig. 133 - The load bearing capacity of	S.R. narrow face = 14.4 in. / 2 in. = 7.07
columns with doubling lengths	S.R. wide face = 14.4 in. / 2.828 in. = 5
(visualization models)	Fig. 134 - Slenderness ratio of a column

the longer columns are more slender than the shorter ones, which obviously accounts for

their relative weakness. Engineers have combined the forgoing factors that determine a

column's strength into a single, simplified measure called the slenderness ratio. The

slenderness ratio is simply the column's length divided by its width, i.e. L / D. For columns

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