Question

Compare the crippling loads calculated by Rankine’s theory and Euler’s theory for a 4 m long hollow steel column having inner and outer diameter of 50 mm and 46 mm respectively. Consider both the ends of the column are pin jointed, yield strength = 310 MPa, Rankine’s constant= 1/7500 and E = 210 GPa.

Answer 1

Answer:

Step-by-step explanation:

Correct option is B)

Given

Y

B

​

Y

A

​

​

=

4

7

​

        L

A

​

=2m      A

A

​

=πR

2

L

B

​

=1.5m             A

B

​

=π(2mm)

2

A

F

​

=Y(

L

ℓ

​

)

given F and ℓ are same ⇒

L

AY

​

 is same

L

A

​

A

A

​

Y

A

​

​

=

L

B

​

A

B

​

Y

B

​

​

⇒

2

(πR

2

)(

4

7

​

Y

B

​

)

​

=

1.5

π(2mm)

2

.Y

B

​

​

R=1.74mm

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