This set of Design of RC Structures Multiple Choice Questions & Answers (MCQs) focuses on “Axially Loaded Columns – Elastic Theory”.

1. According to Euler’s theory which one is true for an Euler column (n^{2}=P/EI)?

a) (D^{2}+n^{2})y=0

b) (D+1)y=0

c) (D^{3}+n)y=0

d) (D+2)y=0

View Answer

Explanation: According to Euler’s theory of buckling the moment of a typical column section cut at x, the moment is given as

M(x) = -Py=EI d

^{2}y/dx

^{2}

This gives: d

^{2}y/dx

^{2}+ Py/EI=0

Using differential operator and substituting n

^{2}=P/EI

(D

^{2}+n

^{2})y=0

2. A column is having effective length 4m and another column is having length of 6m respectively. What is the ratio of critical buckling load?

a) 9:4

b) 4:9

c) 5:9

d) 9:5

View Answer

Explanation: As we know that,

P

_{cr}=EI(π/l)

^{2}, here we can conclude P

_{1}/P

_{2}=(l

_{2}/l

_{1})

^{2}

= (6/4)

^{2}= 9:4.

3. The radius of gyration of two columns are respectively 200mm and 500mm.What is the ratio of critical buckling load?

a) 4:25

b) 25:4

c) 3:16

d) 16:3

View Answer

Explanation: According to recommendation of Euler theory,

P

_{cr}=EAr

^{2}(π/l)

^{2}

P

_{1}/P

_{2}= (200/500)

^{2}= (2/5)

^{2}= 4:25.

4. The assumption of the Euler’s theory is which of the following?

a) The column is bent and load is applied through point of eccentricity

b) The column is axially straight and load is applied through point of eccentricity

c) The column is bent and load is applied through point of centroid

d) The column is axially straight and load is applied through point of centroid of the section

View Answer

Explanation: If a column is axially straight then there is no eccentricity of the column about any axis. Therefore, the column is loaded through the centroid of the straight section, this is the basic assumption mentioned in Euler’s theory of buckling.

5. How the stress of the section (Ϭ) is related to the slenderness ration (l/r=k)?

a) E(π/k)^{2}

b) A(π/k)^{2}

c) E(A/k)^{2}

d) EAr^{2}(π/k)^{2}

View Answer

Explanation: As given by Euler’s theory of buckling,

P = EAr

^{2}(π/l)

^{2}

P/A = Eπ

^{2}/(l/r)

^{2}

Ϭ = Eπ

^{2}/(k)

^{2}

Ϭ = E(π/k)

^{2}.

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