Reg No.:

Max. Marks: 100

1 a)
b)

2

3 a)
b)

4 2)
b)

6 a)
b)

02000ME202052001

Pages: 3

Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Fourth semester B.Tech examinations (S), September 2020

Course Code: ME202
Course Name: ADVANCED MECHANICS OF SOLIDS (ME)

Data-books are not allowed to use

PARTA

Answer any three full questions, each carries 10marks.
If the stress tensor at a point is given by 0,x=0, 6,५50, 6,/50, ൩510, ൩൧൭ -10,
Tyz=20, find stress invariants, characteristic equation, principal stresses and the
principal plane associated with the maximum principal stress.
Find magnitude of normal and shear stress on an octahedral plane for the state of
stress specified in part (a) above.
If the displacement field is (उ+) i+ (312 1+ (422 +>) k, obtain the displaced
position of a point originally at (2,1,1). Also determine the strain-displacement
gradient matrix and corresponding strain tensor at (2,1,1).
Deduce the constitutive relation for a linear elastic isotropic material
Derive the compatibility equation in terms of Airy’s stress function for a two
dimensional elastic problem. Assume body forces are not acting

Differentiate plane stress and plane strain problems with suitable examples.
‏وف‎
‎Verify whether the function (x,y) = त (x+y? ) + Coxy, (C1 and C2 are constants)

is a valid Airy’s stress function. If valid, formulate stresses from it.

PART 8
Answer any three full questions, each carries 10marks.
Derive equilibrium equations in (1,0) coordinates; Modify it to axi-symmetric case

For a 2D axi-symmetric problem, if ടെ ವೆ [4(1 + 1/) - 5 (1-v)]; 6055
E B ⋅
↕∀−⇄− [4(1 ‏(بد+‎ + 2 (1 — v)], evaluate A and ए for pressures P, and Py at inner

radius ‘a’ and outer radius ‘b’ respectively. Then modify 6; and og accordingly.

Reduce the above equations for a case with external pressure alone. Plot the

variation of stresses across the thickness of the wall.

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Duration: 3 Hours

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