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QUESTION: 1

For a circular column having its ends hinged, the slenderness ratio is 160. The l/d ratio of the column is

Solution:

If radius R then radius of gyration = R/2.

Now , L ÷ (R/2)=160,

-) L ÷ (D/4)=160,

So, L/D= 40.

QUESTION: 2

For the case of slender column of length 'l’ and flexural rigidity EI built in at its base and free at the top, the Euler's buckling load is

Solution:

Euler’s buckling load,

For a column fixed at base and free at the top,

∴

QUESTION: 3

Rankine-GordonTormulafor buckling is valid for

Solution:

QUESTION: 4

The resultant cuts the base of a circular column of diameter ‘d’ with an eccentricity equal to one-fourth of 'd'. The ratio between the maximum compressive stress and the maximum tensile stress is

Solution:

For a solid circular section, the maximum eccentricity for no tension is d/8.

The stress

for e = d/4

The minus sign is due to opposite nature of forces.

QUESTION: 5

A column of length 2.4 m area of cross-section 2,000 mm^{2} andmoment of inertia of I_{xx }= 720 x 10^{4} mm^{4} and I_{yy }= 80 x 10^{4} mm^{4} is subjected to buckling load. Both the ends of the column are fixed. What is the slenderness ratio of column?

Solution:

Slenderness ratio of column is given by,

QUESTION: 6

A hollow circular column, has D = 100 mm, d = 80 mm. What is its radius of gyration

Solution:

QUESTION: 7

If diameter of a long column is reduced by 20%, the percentage reduction in Euler’s buckling load is

Solution:

Euler buckling load P is given by,

QUESTION: 8

A rectangular bar as shown in the figure below carries a tensile load of 1 kN as shown in the figure. Under this load the maximum value of stress over the mean value will increase by

Solution:

Mean value of stress,

Maximum intensity of stress

∴ Increase in stress

QUESTION: 9

A hollow circular column of internal diameter 'd' and external diameter '1.5 d’ is subjected to compressive load. The maximum distance of the point of application of load from the centre for no tension is

Solution:

QUESTION: 10

Given that

P_{E} = The crippling load given by Euler

P_{C} = The load at failure due to direct compression

P_{R} = The load in accordance with the Rankine's criterion of failure

P_{R} is given by

Solution:

### Theory of Columns

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