Karunya Advanced Structural Analysis Question Bank 2025
Download Karunya Institute of Technology and Sciences, Advanced Structural Analysis [21AE3002] Question Bank Nov/Dec 2025 PDF Free Online.
Download Karunya Advanced Structural Analysis Question Bank 2025
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Karunya Advanced Structural Analysis Questions
Part – A : (5 X 16 = 80 Marks)
(Answer any five from the following)
1. a Derive the two-dimensional strain compatibility condition for a linearly elastic body under small deformations. CO1 A
b. A two-dimensional elastic body has the following strain components: ε_x =αy^2+2y, ε_y =4x+6y and γ_xy =2x+4y. Using the 2-D strain compatibility equation, determine the value of α that ensures a continuous displacement field exists. CO1 A
2. A plane stress element has normal stresses σx, σy and shear stress τxy. Using Mohr’s circle, derive the general expressions for the stresses (σx′, σy′ and τx′y′) on an oblique plane rotated by an angle θ from the x-axis. CO2 An
3. A cantilever beam of length L = 2.0 m has a rectangular cross-section with a width of b = 50 mm and a depth of h = 100 mm. The beam is subjected to an axial compressive load N = 15 kN and a vertical concentrated load P = 800 N acting downward at the free end. Take the positive x-axis along the beam’s length and the y-axis vertically upward from the neutral axis. Assuming linear elasticity and small deformations, determine (a) the normal stress distribution σx(y) and (b) the location of the neutral axis with respect to the centroidal axis. CO3 An
4. Starting from the two-dimensional equilibrium equations of elasticity (neglecting body forces), prove that ∇^2 (σ_xx+σ_yy)=0 for plane strain conditions. CO4 A
5. Solve the equation for a beam under pure bending as shown in the figure, and using the theory of elasticity (Airy’s stress function approach), show that the resulting stresses satisfy equilibrium and boundary conditions. CO5 A
6. A thick cylinder with inner radius ‘a’ and outer radius ‘b’ is subjected to internal (p_i) and external (p_o) pressure. Determine the stresses induced in the cylinder.
7. The displacement field components at a point are given by:
u=-0.0001y^2+0.0015xyz, v=0.0002x^2 y+0.0003x^2 z,
w=0.0015xyz+0.0002x^2 yz. Determine the strain tensor at a point (2, 3, 1). CO1 A
Part – B (1 X 20 = 20 Marks): [Compulsory Question]
8. Show that Airy’s stress function ϕ=A(xy^3-3/4 xyh^2 ) represents the stress distribution in a cantilever beam loaded at the free end with a concentrated load P. Determine the value of A if the shear stress τxy = 0 at y = ±h/2, where b and h are the width and depth of the beam, respectively. CO4 An
Course Outcomes:
• CO1 Understand stress and strain compatibility conditions.
• CO2 Derive Stress-strain relationship of a lamina.
• CO3 Differentiate the symmetrical and unsymmetrical bending.
• CO4 Determine the shear center in various open and closed section of aircraft structures.
• CO5 Analyze the buckling of plates to predict the critical stress.
• CO6 Design aircraft composite panel for aerospace applications.
