Structural Dynamics Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

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Civil Engineering (CE) : Structural Dynamics Civil Engineering (CE) Notes | EduRev

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Q.1 A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time f, the equation of motion for the free vibration of the system is Structural Dynamics Civil Engineering (CE) Notes | EduRev The natural frequency of the system is    [2019 : 1 Mark, Set-I]
(a) m/k
(b) k/m
(c) Structural Dynamics Civil Engineering (CE) Notes | EduRev
(d) Structural Dynamics Civil Engineering (CE) Notes | EduRev
Ans.
(D)
Solution:
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Comparing with Structural Dynamics Civil Engineering (CE) Notes | EduRev
We get Structural Dynamics Civil Engineering (CE) Notes | EduRev

Q.2 A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 x 105 kN/m and kθ = 3 x 105 kNm/rad.
Structural Dynamics Civil Engineering (CE) Notes | EduRev
For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is___________    [2019 : 2 Marks, Set-II]
Solution:

Structural Dynamics Civil Engineering (CE) Notes | EduRev
No moment can be taken by segment FE
∴ MFE = 0
Structural Dynamics Civil Engineering (CE) Notes | EduRev

Q.3 For the beam shown below, the stiffness coefficient K22 can be written as    [2015 : 1 Mark, Set-I]
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Structural Dynamics Civil Engineering (CE) Notes | EduRev
Ans. 
(B)
Solution:
Structural Dynamics Civil Engineering (CE) Notes | EduRev

By giving unit displacement in 2nd direction without giving displacement in any other direction, the force developed RB, is,
Structural Dynamics Civil Engineering (CE) Notes | EduRev  (∴ Δ = 1)

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