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[A-11]

[EPRSE 201]

M.Tech. DEGREE EXAMINATION

Structural Engineering & Natural Disaster Management

II SEMESTER

STABILITY OF STRUCTURES(Effective from the admitted batch 200809)

Time: 3 Hours Max.Marks: 60

-------------------------------------------------------------------------------------Instructions: Each Unit carries 12 marks.

Answer all units choosing one question from each unit.

All parts of the unit must be answered in one place only.Figures in the right hand margin indicate marks allotted.

---------------------------------------------------------------------------------------------

UNIT-I

1. a) Starting from fundamentals concepts, taking the solution of

partial differential equation in the form Y= A Cos Kx + B

Sin Kx + PI for a beam column acted upon by a concentrated

load Q at a distance c from right end, show that Maximumdeflection is given by

maxtan

2 2 2

Q kl kl

pk

6

b) Show that Maximum bending moment Mmax =tan

4

QL u

u6

OR

2. a) Starting from fundamentals, derive expressions for crippling loadof a column with one end fixed and other end hinged 6

b) Discuss the change in crippling load value with change end

conditions 6

UNIT-II

3. a) Explain Raliegh-Ritze method for the solution of buckling

problem 6

b) Using Raliegh-Ritze technique show that approximate buckling

load for a column fixed at one end and hinged at the other end isgiven by Pcr=3EI/L

2 6

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OR

4. A steel section shown in figure is used as column of length 8m.

Estimate the Crippling load of the column if it is subjected to axial

compressive load if (i) both ends are hinged (ii) both ends are

fixed. Modulus of elasticity of the material of the rod is

2 x 105

N/mm2

12

UNIT-III

5. a) Discuss buckling shapes of frames with infinite and zero beam

stiffness by sway and non sway mode 6

b) Derive expression for Pcr of a frame with Non symmetric mode 6

OR

6. a) Explain Lateral buckling in beams and performance of the beam

subjected to lateral buckling 6b) Show that critical moment of resistance of an I beam subjected to

lateral buckling is given by Mcr= yEI GJl

6

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UNIT-IV

7. Considering finite difference expression for the equation governing

bending of plate in Cartesian coordinates, derive expression for the

central deflection in a plate clamped along the pair of opposite edges

and simply supported along other two opposite edges. Divide plateinto appropriate number of equal squares. Use Finite Difference

Approach 12OR

8. a) Derive the governing differential equation for the plate buckling

problem 4

b) Discuss the buckling of simply supported rectangular plate of

dimensions a and b subjected to compressive forces in one

direction 8UNIT-V

9. a) Explain Modes of buckling of portal frames 4

b) Explain procedure for calculation of Crippling frame for a

symmetric frame using matrix approach 6

c) Calculate Cripling load for the frame in figure using above

concept 2

OR

10. a) Explain Critical load on frame using Neutral Equilibrium

approach 6

b) Explain procedure for assessment of critical load for multi bar

frames with an example 6

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