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  BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH (Declared as Deemed to be University under section 3 of UGC Act, 1956, vide notification No.F.9-5/2000-U.3 ) BHARATH INSTITUTE OF SCIENCE AND TECHNOLOGY EPARTMENT OF ERONAUTICAL E NGINEERING Selaiyur, Chennai  –  600 073 Phone: 044 2229 0125 / 2229 9007  Mob: +91 9840844425  Fax: 91 044 22290742  Mail:  hodaero@bharathuniv.ac.in  IMPORTANT QUESTIONS BAN 504 THEORY OF ELASTICITY PART A (Two mark questions) UNIT I 1.   Define the term “Elasticity”.   2.   Write the assumptions made in elasticity problems. 3.   Give the generalised stress strain relation for a continuous material. 4.   Define Principal stress and Principal plane. 5.   State St. Venant’s Principle 6.   Give Equilibrium equation in 3D form in Cartesian coordinate 7.   State the stress compatibility equation for three-dimensional stress state. 8.   State the strain compatibility equation for three-dimensional stress state. UNIT II 1.   Write down the Airy’s stress function for two -dimensional problem in Cartesian co-ordinate system. 2.   Write down the Bi-harmonic eqn. 3.   Give the condition for plane stress and plane strain problems. 4.   What is stress tensor 5.   What is Lame’s constant.   6.   Give the strain displacement equation. 7.   Give the stress displacement relation 8.   Relation between Elastic Constants. UNIT III 1.   Give the suitable stress function for cantilever beam carrying point load at the free end. 2.   State the boundary conditions for finding stress distribution for cantilever beam. 3.   State the boundary conditions for finding displacement for cantilever beam. 4.   Sketch the displacement variation in cantilever. 5.   Explain St. Venant’s  theory on torsion. 6.   Explain  Navier’s theory on torsion . 7.   Explain Prandtl ’ s theory on torsion. 8.   Give the Poisson equation for torsion. UNIT IV 1.   Define anisotropy. 2.   Explain monoclinic material. 3.   Write the material property transformation law. 4.   What is meant by Fracture mechanics? 5.   Define fracture toughness. 6.   What is meant by rupture? 7.   What is meant by Brittle fracture and Ductile fracture? 8.   Define stress intensity factor. UNIT V    BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH (Declared as Deemed to be University under section 3 of UGC Act, 1956, vide notification No.F.9-5/2000-U.3 ) BHARATH INSTITUTE OF SCIENCE AND TECHNOLOGY EPARTMENT OF ERONAUTICAL E NGINEERING Selaiyur, Chennai  –  600 073 Phone: 044 2229 0125 / 2229 9007  Mob: +91 9840844425  Fax: 91 044 22290742  Mail:  hodaero@bharathuniv.ac.in  1.   What are the assumptions made in classical plate theory? 2.   Write the equation of equilibrium for plates. 3.   State boundary conditions for problems on plates. 4.   Write the Navier’s  method of solution for simply supported rectangular plates? Part B (Sixteen Marks questions) UNIT I 1.   (a) Derive the equation of equilibrium for three-dimensional state of stress. (12) (b) Obtain Cauchy’s stress formula in three-dimensional stress field. (4) 2.   The state of stress at a point is given by the following array of terms; 9 6 36 5 23 2 4 . Determine the maximum principal stress and its direction cosines. (16) 3.   The state of stress at a point is given by the following array of terms; −800 400 500400 1200 −600500 2 −400 . Determine the normal and shear stress on a plane whose direction cosines are  =  , =  . (16) 4.   (a) A rectangular bar of cross-section 30mm x 25mm is subjected to an axial tensile force of 180 kN. Calculate the normal, shear and resultant stress on a plane whose normal is given by direction cosines  =  =  √   and  = 0.  (10) (b) Define the term strain. Obtain the normal and shear strain expression for three-dimensional element. (6) UNIT II 1.   Derive the equation of normal stress and shear stress in an inclined plane for plane stress condition. Also obtain the expression for principal stress and its direction for the above mentioned condition. (16) 2.   Derive the equilibrium equation for two-dimensional stress condition in polar co-ordinates. (16) 3.   At a particular point in a structural member a two- dimensional stress system exits where σ x = 60 N/mm 2 , σ y  = -40 N/mm 2   and τ xy  = 50 N/mm 2 . If young’s modulus  E = 200 kN/mm 2 , shear modulus G = 76.9 kN/mm 2  and  poison’s ratio ν = 0.3. Calculate the normal and shear strain also calculate the principal strains, their directions and maximum shear strain. (16) 4.   A cantilever beam of length L and depth 2h is in a state of planer stress. The cantilever is of unit thickness and is loaded by UDL (q N/unit area) throughout the length. For the stress function ϕ  = ax 2 + bx 2 y + cy 3  + d (5x 2 y 3    –   y 5 ) evaluate the constants a, b, c and d for above given condition. (16) UNIT III 1.   Briefly explain St. Venant’s principle.  2.   Briefly explain Prandtl’s theory on torsion.  3.   Find the shear stress and the axial twist of the section shown in the fig.1 when subjected to the torque of 1x10 8   Nmm. Thickness of the section is 5mm and shear modulus is 0.8x10 5  N/mm 2 .  BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH (Declared as Deemed to be University under section 3 of UGC Act, 1956, vide notification No.F.9-5/2000-U.3 ) BHARATH INSTITUTE OF SCIENCE AND TECHNOLOGY EPARTMENT OF ERONAUTICAL E NGINEERING Selaiyur, Chennai  –  600 073 Phone: 044 2229 0125 / 2229 9007  Mob: +91 9840844425  Fax: 91 044 22290742  Mail:  hodaero@bharathuniv.ac.in  fig.1 4.   A rolled steel channel with height of 400mm, width of 100mm and thickness of 10mm is subjected to a torque of 2kNm. Evaluate the maximum shear stress developed and angle of twist per unit length. Shear modulus is 12 kN/mm 2 . (16) UNIT IV 1.   Derive the elastic constant relation for monoclinic, orthorhombic and tetragonal material. (16) 2.   Briefly explain different types of material based on material symmetry. 3.   Derive the expression for stress component and stress intensity factor near crack tip for Mode-I fracture. 4.   Determine the principal stress and the maximum shear stress close to a crack tip loaded in Mode I. The material is linearly elastic with Poisson’s ratio ν = 0.3. The stress components close to the crack tip are:      =   √ 2[2(1− 2sin32 )]      =   √ 2[2(1+ 2sin32 )]      =    √     sin   cos     (16) UNIT V 1.   A cantilever plate contains a crack of length 0.04 m as shown in fig.2. If the length of the plate is 0.32 m, width of the plate is 0.08 m, thickness of the plate is 0.03 m. Determine at which value of load P failure will occur if the fracture toughness of the material is 50 MN/m 3/2 . (16)  BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH (Declared as Deemed to be University under section 3 of UGC Act, 1956, vide notification No.F.9-5/2000-U.3 ) BHARATH INSTITUTE OF SCIENCE AND TECHNOLOGY EPARTMENT OF ERONAUTICAL E NGINEERING Selaiyur, Chennai  –  600 073 Phone: 044 2229 0125 / 2229 9007  Mob: +91 9840844425  Fax: 91 044 22290742  Mail:  hodaero@bharathuniv.ac.in  2.   Briefly explain the classical plate theory. (16) 3.   Find Levy’s solution f  or simply supported and uniformly loaded rectangular plates. (16)
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