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Q. No. | Question | CO | RBT Level | Marks |
---|---|---|---|---|
1 | Derive the displacement function for a beam flexure element of length \(L\) using a cubic polynomial. Apply boundary conditions at the nodes and express in terms of nodal displacements and rotations. | CO1 | L3 | 5 |
2 | Derive the shape functions \(N_1, N_2, N_3, N_4\) for the flexure element in terms of the dimensionless coordinate \(\xi = \frac{x}{L}\). | CO1 | L3 | 5 |
3 | Compute the second derivatives of the shape functions and show how the element stiffness coefficients \(k_{mn}\) are obtained using Castigliano’s theorem. | CO1, CO2 | L3 | 5 |
4 | Using the dimensionless coordinate \(\xi\), transform the element stiffness matrix integrals and compute the final 4×4 stiffness matrix for a beam element of length \(L\) and flexural rigidity \(EI\). | CO1, CO2 | L3, L4 | 5 |
5 | For a simply supported beam of length \(L = 2\,\text{m}\) subjected to a point load \(P = 10\,\text{kN}\) at midspan, model the beam using two flexure elements. Compute: (a) nodal displacements, (b) element bending moments, (c) reactions at supports. |
CO1, CO3 | L3, L4 | 5 |
6 | A cantilever beam of length \(L = 3\,\text{m}\) with a uniform distributed load \(w = 5\,\text{kN/m}\) is modeled using two flexure elements. Determine: (a) the nodal displacements, (b) nodal rotations, (c) maximum bending moment in each element. |
CO1, CO3 | L3, L4 | 5 |
7 | A beam is subjected to a concentrated moment \(M = 20\,\text{kNm}\) at midspan. Using element load vector, determine the equivalent nodal forces and moments for a two-element discretization. | CO2, CO3 | L3, L4 | 5 |
8 | For the beam in Q6, draw the bending moment diagram and indicate the location and value of maximum stress. Compute stress at top and bottom fibers. | CO3 | L3, L4 | 5 |
9 | Explain how superposition of nodal forces and assembly of element stiffness matrices lead to the global stiffness matrix for a multi-element beam. Draw a schematic with at least three elements. | CO2, CO4 | L2, L3 | 5 |
10 | A beam of length \(L = 4\,\text{m}\) is discretized into two flexure elements. If the first element has a point load at \(x = 1\,\text{m}\) and the second element has a uniform load, determine: (a) nodal displacements, (b) nodal rotations, (c) reactions at the supports. |
CO1, CO3 | L3, L4 | 5 |
CO # | Course Outcomes |
---|---|
CO1 | Develop stiffness matrix and load vector for a given beam element |
CO2 | Formulate finite element equations for flexure elements |
CO3 | Compute nodal displacements, rotations, and stresses in beams |
CO4 | Illustrate the use of FEA tools/software in obtaining the structural response of beams |
Level | L1 | L2 | L3 | L4 | L5 | L6 |
---|---|---|---|---|---|---|
Cognitive Process | Remember | Understand | Apply | Analyze | Evaluate | Create |
Prepared by:
Dr. Yuvraj Singh
Assistant Professor, Department of Civil Engineering
Guru Nanak Dev Engineering College, Ludhiana