Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

GATE : Civil Engineering (CE) Notes | EduRev

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Q.1 A column of height h with a rectangular cross-section of size a x 2a has a buckling load of P. If the cross-section is changed to 0.5 a x 3a and its height changed to 1.5h, the buckling load of the redesigned column will be    [2018 : 1 Mark, Set-I]
(a) P/12
(b) P/4
(c) P/2
(d) 3P/4
Ans. 
(a)
Solution:
For column,  Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
For new column,
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev

Q.2 Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young’s modulus 2 x 105 MPa, square cross- section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler’s theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is _____.    [2017 : 2 Marks, Set-I]
Solution:

 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
∴ Required ratio =  Civil Engineering (CE) Notes | EduRev

Q.3 In a system two connected rigid bars AC and BC are of identical length, L with pin supports at A and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, k. The system initially assumes a straight line configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to a transverse load, P applied at C is    [2015 : 2 Marks, Set-II]
(a) PL/4k
(b) PL/2k
(c) P/4k
(d) Pk/4L
Ans. 
(A)
Solution:
Deflection under load P= θL
Work done by force  Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
Strain energy stored in spring
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
⇒ θ = PL/4k

Q.4  If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
If a is amplitude constant for y, then   [2014 : 2 Marks, Set-I]
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
Ans. 
(C)
Solution:
 Civil Engineering (CE) Notes | EduRev
∴ Solution of above differential equation is,
y = a sin mx + b cos mx
at = x = 0, y = 0
⇒ b = 0
at x = L, y = 0
⇒ 0 = sin mL
⇒ mL = nπ
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev

Q.5 The possible location of shear centre of the channel section, shown below is,    [2014 : 1 Mark, Set-I]
 Civil Engineering (CE) Notes | EduRev
(a) P
(b) Q
(c) P
(d) S
Ans.
(A)
Solution:
 Civil Engineering (CE) Notes | EduRev
For no twisting
V x e = H x h
 Civil Engineering (CE) Notes | EduRev
Hence possible location of shear centre is P.

Q.6 Two steel column P (length L and yield strength fy = 250 MPa) and Q (length 2L and yield strength fy = 500 MPa) have the same cross-section and end condition the ratio of buckling load of column P to that of column Q is    [2013 : 1 Mark]
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
Ans.
(D)
Solution:
Buckling load,
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev
 Civil Engineering (CE) Notes | EduRev

Q.7 The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to    [2012 : 1 Mark]
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
Ans.
(D)
Solution:
Eulars critical load,
 Civil Engineering (CE) Notes | EduRev 

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