Question

The ratio of Euler’s bulking loads of column with same parameter having both end fixed to one end fixed and other is free is-
i) 1 ii) 4 iii) 8 iv) 16

Answer 1

Answer:

dont know you asked another question

Answer 2

Answer:

The correct Euler’s bulking load ratio is $16$. Option iv) is correct.

Explanation:

• Column tends to get buckle at the buckling load.
• Buckling load depends on end conditions whether they are fixed, free, or hinged.

The formula for buckling load is given by:

$P_{b}=\frac{\pi ^{2}EI }{L_{e} ^{2} }$

where, $E$ is Elasticity Young's modulus.

            $I$ is the moment of inertia.

            $L_{e}$ is effective length.

Step 1:

When both ends are fixed then  $L_{e}=\frac{L}{2}$

Substituting in the above formula we get:

$P_{b}1=\frac{\pi ^{2}EI }{(\frac{L}{2}) ^{2} }$

$P_{b}1=\frac{4\pi ^{2}EI }{L ^{2} }$

When one end is free other fixed then  $L_{e} =2L$

$P_{b}2=\frac{\pi ^{2}EI }{(2L) ^{2} }$

$P_{b}2=\frac{\pi ^{2}EI }{4L ^{2} }$

Step 2:

$\frac{P_{b} 1}{P_{b} 2} =\frac{\frac{4\pi ^{2}EI }{L ^{2} }}{\frac{\pi ^{2}EI }{4L ^{2} }}$

$\frac{P_{b} 1}{P_{b} 2} =\frac{16}{1}$

So, the required Euler’s bulking load ratio is $16$.

Option iv) is correct.