Question

For a circular column having its ends hinged, the slenderness ratio is 160. The 1/d ratio of the column is
A. 80
B. 57
C. 40
D. 20

Answer 1

Hint: We have been provided with a circular column whose ends hinged. We have given the slenderness ratio which is 160. Now to calculate the $\dfrac{1}{d}$ ratio of the column, use the formula of slenderness ratio which will be the relation of distance d. Put value and get answers.

Complete answer:
We have a circular column whose ends hinged. The slenderness ratio is 160.
Now we need to calculate the $\dfrac{1}{d}$ ratio of the column.
Slenderness ratio is given by,
Slenderness ratio = $\dfrac{1}{d}$
Where, r is the ratio of gyration
$r=\dfrac{d}{4}$
$\dfrac{1}{d}=\dfrac{160}{4}=40$
Hence the $\dfrac{1}{d}$ ratio of the column is 40. Therefore option (C) is the correct option.

So, the correct answer is “Option C”.

Additional Information:
Radius of gyration measure the distribution of mass about the axis of rotation. Small value of radius of gyration shows that the mass of the body is distributed close to the axis of rotation so that moment of inertia will be small. For a large value of radius of gyration, the distribution of mass of the body is at a large distance from the axis of rotation, so that moment of inertia is large.

Along with circular columns, we have many types of columns and depending on size or spread, the slenderness ratio changes. For a short steel column, the range of slenderness ratio does not exceed 50 while the intermediate length steel column has slenderness ratio ranging from 50 to 200. For a long steel column, slenderness ratio is greater than 200.

Note:
For a given body, mass always remains constant. If we change the axis of rotation, the distance of particles also changes. Due to this the radius of gyration also changes and hence slenderness ratio also changes. The radius of gyration depends upon the shape and size of the body.