JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II FUNDAMENTALS OF STRUCTURAL ANALYSIS Previous Question Paper (July/August - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive expressions for compatibility for a two dimensional problem.
Answer
In a two-dimensional elasticity problem, the state of stress at a point is defined by the stress components σx, σy, and τxy. The compatibility equations ensure that the strain components are geometrically consistent, meaning they correspond to a single-valued, continuous displacement field (u, v). For a 2D plane stress or plane strain problem, the strain-displacement relations are:
To derive the compatibility condition, we differentiate the strain components to eliminate the displacement functions u and v. By taking the second partial derivative of the shear strain with respect to x and y:
Using the expressions for normal strains:
Substituting these into the expression for the shear strain derivative, we obtain the Saint-Venant compatibility equation for 2D problems:
In terms of stress, using Hooke's Law for plane stress (where E is Young's modulus and ν is Poisson's ratio), the equation is expressed as:
This result, known as the Beltrami-Michell compatibility equation, implies that the sum of normal stresses in a 2D body under equilibrium must satisfy the Laplace equation, ensuring the physical validity of the stress distribution.
Explain about:
Saint Venant principle
Answer
Saint-Venant's principle states that the difference between the effects of two different but statically equivalent load systems applied to a small part of a body becomes negligible at distances sufficiently far from the region of application. Specifically, if a set of forces acting on a small area of a body is replaced by a statically equivalent system (same resultant force and moment), the stress distribution in the body is significantly altered only in the immediate vicinity of the loading area. At distances greater than the characteristic dimension of the loaded area, the stress distribution is essentially independent of the actual mode of application of the load and depends only on the resultant force and moment.
Construction of Mohr’s circle.
Answer
Sign in to view the complete answer paper.
A simply supported continuous beam is subjected to two point loads and uniformly distributed load as shown in Figure. Calculate the support reactions using Clapeyron's theorem. EI = constant.
Answer
Sign in to view the complete answer paper.
List some examples of technical problems where in the concept of beams on elastic foundations are used in the analysis.
Answer
Sign in to view the complete answer paper.
An infinitely long steel beam of unit width and 200mm thick is resting on a elastic foundation whose modulus of foundation is 10 N/mm2. A concentrated load of 8 KN is applied at a point on the beam. Determine the maximum deflection of the beam and the maximum bending stresses. Take E = 2 × 105 N/mm2, ν = 0.28.
Answer
Sign in to view the complete answer paper.
Deduce a formula for the Euler’s critical load of a column having both ends hinged.
Answer
Sign in to view the complete answer paper.
A hollow cylindrical cast iron column 150 mm external diameter and 20 mm thick is 6 meter in length having both ends hinged. Find the load using Rankine’s formula. Compare this load with that given by Euler’s formula. Take σc = 550 N/mm2 and (rankine’s constant) a = 1/160.
Answer
Sign in to view the complete answer paper.
Derive Bredt-Batho formula for a thin walled single cell closed section.
Answer
Sign in to view the complete answer paper.
Explain the step by step procedure of the application of unit load method.
Answer
Sign in to view the complete answer paper.