An axial load P = 400kN is applied at 30oC to the rod as shown in figure. The temperature is raised to 70oC. Assume quadratic shape function for element selection.?

Question

Answer

Problem Statement: An axial load P = 400kN is applied at 30oC to the rod as shown in figure. The temperature is raised to 70oC. Assume quadratic shape function for element selection.

Explanation:

Assumptions:

Linear Elastic Material

2D Plane Stress Condition

Uniform Temperature Gradient Across the Rod

Quadratic Shape Function for Element Selection

Steps:

Divide the rod into elements with quadratic shape function.

Calculate the nodal coordinates and degrees of freedom.

Calculate the stiffness matrix [K] and load vector {F} for each element.

Assemble the global stiffness matrix [K] and load vector {F}.

Apply boundary conditions.

Solve for the displacements using the equation [K]{U}={F}.

Calculate the strains and stresses at each element.

Calculate the total elongation of the rod due to the applied load and temperature change.

Formulas:

Strain: ε = (du/dx)

Stress: σ = Eε

Elongation: ΔL = LαΔT + PL/AE

Results:

The total elongation of the rod due to the applied load and temperature change can be calculated using the above formula.

The stresses and strains at each element can be calculated using the nodal displacements.

The axial force and deformation at any point in the rod can be calculated using the shape functions and nodal displacements.

Similar GATE Doubts

The current flowing through a certain P-n junction at room temperature when reverse-biased (bias voltage being very large in comparison to VT) is 0.15μA. Determine the current (in μ

The sensing element of a thermocouple at its hot junction is provided with a shield while taking measurements in a high-temperature gas. The principal reason for giving the shield is

The sensing element of a thermocouple at its hot junction is provided with a shield while taking measurements in a high-temperature gas. The principal reason for giving the shield is (2002)

Top Courses for GATE

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Other Engg Branches

Related Exams

Company