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Reg No.:_ Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION(S), DECEMBER 2019

Course Code: ME202
Course Name: ADVANCED MECHANICS OF SOLIDS

Max. Marks: 100 Duration: 3 Hours
PARTA

Answer any three questions, each carries 10 marks Marks
Databook is not permitted to use in the exam
1 ൭) Describe about the significance of stress invariants 2

b) Given the stress matrix

20 10 10
[०] = 10 20 10] MPa
10 10 20
(a) Determine the principal stresses and the direction cosines associated with
the maximum principal stress. 5
(b) Determine the maximum shear stress. 1
(c) Determine the octahedral stresses 2
2 93) Write down the strain — displacement relation in Cartesian Coordinate system 2
b) The displacement field for a body is given by ൮5 [2y7i+4yzj+(3+ 3
5z7)k]10~2 . Determine the strain tensor.
c) State the conditions under which the following is a possible system of strains
Exy ಲ + 9“) + 4 + 104,
Eyy = ८ + B(x? + 22) + + + y* 39 = 4 + Bxy(x? + y? —c?),yyz = 0, 5
Vex = 0 and ez, = 0.
3 a) Forsteel the Young’s Modulus 15 207x10° kPa and Rigidity Modulus 15 80x10°
kPa. For the strain tensor at a point, determine the stress tensor
0.001 0 —0.002 5
[ej] = | 0 -0.003 3
—0.002 0.003 0
b) State and explain Saint Venant’s principle for end effects 3
c Write the constitutive relation for linear elastic isotropic material 2

4 a) Obtain the stress compatibility equation for plane stress problem in the presence 5
of body force

b) Show that क = x* y + 4x*y3-y° is a valid stress function and compute the stress 5

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