1to7 Plate and Shell-Quest

Total No. of Questions : 6] [Total No. of Pages : 2

[3665] - 462M.E. (Civil / Structures)

THEORY OF PLATES AND SHELLS(2008 Course) (Semester - II) (501408)

Time : 4 Hours] [Max. Marks : 100

Instructions to the candidates:1) Attempt any two questions from each section.2) Answers to the two sections should be written in separate books.3) Neat diagrams must be drawn wherever necessary.4) Figures to the right indicate full marks.5) Use of non programmable electronic calculator is allowed.6) Assume suitable data, if necessary.

P1648

SECTION - I

Q1) a) Differentiate between thin and thick plate bending under lateral loads.Give explanation of the various assumptions made in small deflectiontheory. [8]

b) State the 4th order differential equation for a thin plate. Find expressionsfor moments, shears using various boundary conditions. [5]

c) Obtain the expression for strain energy stored in the small element of athin plate subjected to bending and twisting moments. Describe theprocedure to obtain the deflected surface of the plate under a given loadingby Raleigh-Ritz approach. [12]

Q2) a) A window of a high rise building is approximated by a rectangular platesimply supported over its edges. The plate is subjected to uniform windload intensity of P

o. Derive the expression for the deflected surface using

Navier’s method. [19]b) State the advantages of Levy’s method over Navier’s method. State the

constants of Levy’s method. [6]

Q3) A circular plate of radius ‘a’ is having fixed edges. Find the maximum valuesof radial and tangential moments for the following loading conditions :a) Central load P.b) Central circular patch load over a area of radius a/4 with intensity p

o per

unit area.c) Axisymmetric triangular load with zero intensity at the centre and p

o per

unit area at the edges. [25]

P.T.O.

SECTION - II

Q4) Derive the equation of equilibrium of shell of revolutions with axisymmetricloading. Apply the same to determine the membrane forces in a R.C.Chemispherical dome of radius of 8 m and thickness 120 mm supported on itslower edge by roller supports all along the periphery. Plot the variation ofinternal forces along any meridian. Consider self weight only. Is there anybending effect to be considered near the lower edge? Comment on your answer.

[25]

Q5) a) Derive the equations of equilibrium for a small element of a cylindricalshell. Show the stress resultants on this element for general loading. [14]

b) Explain in brief different theories of bending in cylindrical shells. [6]c) With neat sketches classify shell surfaces based on Gaussian curvature.

[5]

Q6) a) Describe the principles of Lundgren’s beam theory for thin shells. Discussthe advantages and limitations of the theory. [8]

b) Using Lundgren’s beam theory, analyze a semicircular cylindrical shellof 3 m radius and simply supported over a span of 10 m. The shell issubjected to a uniformly distributed load of intensity of 1.8 kN/m2. Thisintensity is inclusive of the self weight. Calculate the maximumcompressive stress at the crown in the mid-span section and compare thevalue with the value obtain by membrane theory. Comment on the resultsby both theories. [17]

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[3665] - 462 -2-

Total No. of Questions : 6]

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[4165] - 464

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P.T.O.

Total No. of Questions : 6] [Total No. of Pages : 2

[3965]-463

M.E. (Civil) (Structures)

THEORY OF PLATES & SHELLS

(2008 Course) (501408) (Sem. - II)

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Total No. of Questions : 6] [Total No. of Pages :2

[4065] - 464M.E. (Civil) (Structures)

THEORY OF PLATES & SHELLS

�(2008 Course) (501408) (Sem. - II)Time : 4 Hours] [Max Marks : 100

Instructions to the candidates :1) Attempt any two questions from each section.2) Answers to the Two sections should be written in separate books.3) Neat diagrams must be drawn wherever necessary.4) Figures to the right indicate full marks.5) Use of non programmable electronic calculator is allowed.6) Assume suitable data, if necessary.

SECTION-I

Q1) a) Explain clearly assumptions made in Classical Plate Theory (CPT)and hence derive displacement model of CPT. [8]

b) Classical Plate Theory is applicable only for thin plates and not forthick plates. Write your comments. [7]

c) Differentiate clearly difference between Navier’s and Levi’s solutionin the analysis rectangular plates. [10]

Q2) a) A rectangular plate of length 1000 mm is simply supported on allsides and carries uniformly distributed load of intensity 30 N/mm2.Determine maximum displacement and maximum stress in the plate.E = 2 × 105 N/mm2, v = 0.30. [20]

b) Explain how the accuracy in the results of central displacement in theNavier’s solution can be achieved and hence discuss convergence ofresult. [5]

Q3) Derive an expressions for transverse displacement, moments and shearingforces for edge simply supported circular plate subjected to uniform lateralloading. [25]

P.T.O.

P 1244

SECTION-II

Q4) a) Derive equations of equilibrium for thin shells with neat diagram ofgeometry and stress resultants. [18]

b) Explain Membrane Theory for shells. [7]

Q5) a) Determine ,Nφ N forces for a spherical dome of constant thickness

under its own weight. [15]

b) Explain Lundgren’s beam theory for cylindrical shells. [10]

Q6) a) Derive equations of equilibrium for cylindrical shells. [15]

b) Determine Nx, N and xN forces for a horizontal circular cylindrical

shell filled with liquid and supported at ends. [10]

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[4065]-464 - 2 -

SECTION - I

Q1) a) Differentiate between : [10]

i) Thin and Thick plate bending.

ii) Beam and Plate analysis.

b) A square plate with 350 mm sides and 8 mm thickness is subjected touniformly distributed pure couple of 400 Nm on all the edges. If theplate is simply supported on its four corners, find the lateraldisplacement at the midpoints of the edges. Take E = 210 GPa and

3.0=ν . [15]

Q2) a) Differentiate between Navier’s and Levy’s theories for analysis of thinrectangular plate in bending. [6]

b) Using Levy’s method, obtain the expression for lateral displacementof a rectangular plate simply supported on edges, of sides a × b undera uniformly distributed load ‘q’ per unit area. [19]

Q3) A circular clamped plate of radius ‘a’ is subjected to axisymmetric triangularloading of intensity zero at the center and q0 at the edge. Develop fromfirst principles, expression for maximum deflection. [25]

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SECTION - II

Q4) a) A thin conical shell tank carries water upto a height ‘d’ from the vertex.It is supported at the top edge by a ring beam. Derive the expressionfor the membrane stresses Nθ and Nϕ in the shell. Also find the locationsof the maximum values of stress resultants, with their magnitude.[20]

b) What are the limitations of the membrane theory in the analysis ofshells? [5]

Q5) a) Derive the expressions for displacements in symmetrically loaded shellhaving the form of a surface of revolution. [12]

b) A semicircular thin cylindrical shell roof of uniform thickness has lengthL and radius R. It is simply supported along the straight edges and freealong the curved edges. Derive the expressions for the stress resultantsNx, Nϕ and Nxθ considering its self weight only. [13]

Q6) Analyze a cylindrical tank of uniform thickness filled with liquid usingbending theory for shells for axisymmetric loading. The tank is open atthe top and rigidly fixed at the bottom. [25]

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1to7 Plate and Shell-Quest