GATE CE exam:gate PYQs & Answers — Page 86

Questions 851–860 of 1300. Imported answers require independent review unless marked reviewed.

For the Ordinary Differential Equation

, with initial conditions

and

, the solution is

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An ordinary differential equation is given below

The general solution of the above equation (with constants

and

), is

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A continuous function

is defined. If the third derivative at

is to be computed by using the fourth order central finite-difference scheme (with step length = h), the correct formula is

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A 4×4 matrix

is given below

The eigenvalues of

are

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0, 3, 6, 6

1, 2, 3, 4

3, 4, 5, 7

1, 2, 5, 7

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Distributed load(s) of 50 kN/m may occupy any position(s) (either continuously or in patches) on the girder PQRST as shown in the figure (not drawn to the scale). The maximum negative (hogging) bending moment (in kN.m) that occurs at point R, is

Diagram for Civil Engineering question 28

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22.50

56.25

93.75

150.00

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A prismatic linearly elastic bar of length

, cross-sectional area

, and made up of a material with Young’s modulus

, is subjected to axial tensile force as shown in the figures

. When the bar is subjected to axial tensile forces

and

, the strain energies stored in the bar are

and

, respectively.

is the strain energy stored in the same bar when subjected to an axial tensile force

, the correct relationship is

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A rigid weightless platform PQR shown in the figure (not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by the weightless member OJ and four weightless, frictionless rollers. Points O and J are pin connections. A block of 90 kN rests on the platform as shown in the figure. The magnitude of horizontal component of the reaction (in kN) at pin O, is

Diagram for Civil Engineering question 29

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120

150

180

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The planar structure RST shown in the figure

is roller-supported at S and pin-supported at R. Members RS and ST have uniform flexural rigidity

and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffness.

When the structure is subjected to a concentrated horizontal load

at the end T, the magnitude of rotation at the support R, is

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A cantilever beam PQ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at R as shown in the figure. The deflection at the free end Q is

Diagram for Civil Engineering question 30

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Joints I, J, K, L, Q and M of the frame shown in the figure

(not drawn to the scale) are pins. Continuous members IQ and LJ are connected through a pin at N. Continuous members JM and KQ are connected through a pin at P. The frame has hinge supports at joints R and S. The loads acting at joints I, J and K are along the negative Y direction and the loads acting at joints L and M are along the positive X direction.

The magnitude of the horizontal component of reaction (in kN) at S, is

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GATE CE exam:gate PYQs

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29

Question 30

Question 30