Question

Slenderness ratio of 5m long column hinged at both ends and having a circularcrosssection with diameter 160mm is

Answer 1

Answer:

The slenderness ratio is 125.

Step-by-step explanation:

Given data:  

Effective length of the column, L = 5 m

Diameter of circular cross section, D = 160 mm

To find: Slenderness Ratio  

Let the least radius of gyration be “K”.

The Area of the column be “ A” = πD²/4

And, Moment of Inertia be “I” = πD⁴/64

Therefore,  

K = √ (I/A)

Or, K = √ [{πD⁴/64} / {πD²/4}]

Or, K = √ [{D²/64} / {1/4}]

Or, K = √ [(160*160)/16]

Or, K = √ [1600]

Or, K = 40 mm = 0.04 m

Now,

Slenderness Ratio = (Effective length) / (least radius of gyration)

Slenderness Ratio = L / K

                                 = 5 / 0.04

                                  = (5 * 100) / 4

                                    = 125