Chapter-13 IES-8.
Theories of Column
S K Mondal’s
Match List-I (End conditions of columns) with List-II (Equivalent length in terms of length of hinged-hinged column) and select the correct answer using the codes given below the Lists: [IES-2000] List-I List-II A. Both ends hinged 1. L
B. One end fixed and other end free 2. L/ 2 C. One end fixed and the other pin-pointed 3. 2L D. Both ends fixed 4. L/2 Code: A B C D A B C D (a) 1 3 4 2 (b) 1 3 2 4 (c) 3 1 2 4 (d) 3 1 4 2 IES-8. Ans. (b) IES-9. The ratio of Euler's buckling loads of columns with the same parameters having (i) both ends fixed, and (ii) both ends hinged is: [GATE-1998; 2002; IES-2001] (a) 2 (b) 4 (c) 6 (d) 8 IES-9. Ans. (b) Euler’s buckling loads of columns 4π 2EI (1) both ends fixed = 2 l π 2EI ( 2 ) both ends hinged = 2 l
Euler's Theory (For long column) IES-10.
What is the expression for the crippling load for a column of length ‘l’ with one end fixed and other end free? [IES-2006; GATE-1994] (a) P =
IES-10. Ans. (b)
2π 2 EI l2
(b) P =
π 2 EI 4l 2
(c) P =
4π 2 EI l2
(d) P =
π 2 EI l2
IES-11.
Euler's formula gives 5 to 10% error in crippling load as compared to experimental results in practice because: [IES-1998] (a) Effect of direct stress is neglected (b) Pin joints are not free from friction (c) The assumptions made in using the formula are not met in practice (d) The material does not behave in an ideal elastic way in tension and compression IES-11. Ans. (c) IES-12.
Euler's formula can be used for obtaining crippling load for a M.S. column with hinged ends. Which one of the following conditions for the slenderness ratio
l is to be k
satisfied?
[IES-2000]
(a) 5 <
IES-12. Ans. (d)
l <8 k
(b) 9 <
l < 18 k
(c) 19 <
l < 40 k
(d)
l ≥ 80 k
IES-13.
If one end of a hinged column is made fixed and the other free, how much is the critical load compared to the original value? [IES-2008] (a) ¼ (b) ½ (c) Twice (d) Four times IES-13. Ans. (a) Critical Load for both ends hinged = π 2EI/ l 2 And Critical Load for one end fixed, and other end free = π 2EI/4l2 IES-14.
If one end of a hinged column is made fixed and the other free, how much is the critical load compared to the original value? [IES-2008] (a) ¼ (b) ½ (c) Twice (d) Four times π 2EI Page 373 of 429 IES-14. Ans. (a) Original load = 2 I