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Q. No. | Question | CO | RBT Level | Marks |
---|---|---|---|---|
1 | List three major applications of FEM in civil engineering and explain why FEM is preferred over other numerical methods for those cases. | CO3 | L2, L4 | 5 |
2 | Derive the stiffness relation for a linear spring element using Hooke’s law and matrix formulation. Include a neat diagram. | CO1 | L3 | 5 |
3 | Derive the stiffness matrix for a 1D bar element of length $L$, cross-sectional area $A$, and modulus of elasticity $E$. State assumptions clearly. | CO1 | L3 | 5 |
4 | Using the Minimum Potential Energy Principle, derive the FEM equation for a spring element. | CO1, CO2 | L3 | 5 |
5 | Explain the Direct Stiffness Method with the steps: (a) numbering, (b) connectivity, (c) formation of local stiffness matrices, (d) assembly. Draw a schematic. | CO1, CO4 | L2, L3 | 5 |
6 | For the spring system shown below with $k_1=50 \ \text{lb/in}$ and $k_2=25 \ \text{lb/in}$, determine the force $F_3$ required to displace node 2 by $0.75$ in. Also compute displacement of node 3. | CO1, CO3 | L3, L4 | 5 |
7 | In the spring assembly of the figure shown below, forces $F_2$ and $F_4$ are to be applied such that the resultant force in element 2 is zero and node 4 displaces an amount of 1 in. Determine: (a) the required values of forces $F_2$ and $F_4$, (b) the displacement of node 2, and (c) the reaction force at node 1. Given spring constants: $k_1 = 30 \, \text{lb/in.},\; k_2,\; k_3$. |
CO1, CO3 | L3, L4 | 5 |
8 | A steel rod as shown in figure below is modeled by two bar elements of length $0.5 \ \text{m}$ each, $E=207 \ \text{GPa}$, $A=500 \ \text{mm}^2$, subjected to a $12 \ \text{kN}$ compressive load. Determine the nodal displacements and the axial stress in each element. What other concerns should be examined? | CO1, CO3 | L3, L4 | 5 |
9 | In the two-member truss shown in below, let: • $\theta_1 = 45^\circ$, $\theta_2 = 15^\circ$ • $F_5 = 5000 \, \text{lb}$, $F_6 = 3000 \, \text{lb}$ (a) Using only static force equilibrium equations, solve for the force in each member as well as the reaction force components. (b) Assuming each member has axial stiffness $k = 52000 \, \text{lb/in.}$, compute the axial deflection of each member. (c) Using the results of part (b), calculate the X and Y displacements of node 3. |
CO1, CO3 | L3, L4 | 5 |
10 | The two-element truss in figure below is subjected to external loading as shown. Determine: • The displacement components of node 3, • The reaction force components at nodes 1 and 2, • The element displacements, stresses, and forces. Material properties: $E_1 = E_2 = 10 \times 10^6 \ \text{lb/in}^2$, $A_1 = A_2 = 1.5 \ \text{in}^2$. |
CO1, CO3 | L3, L4 | 5 |
CO # | Course Outcomes |
---|---|
CO1 | Develop stiffness matrix and load vector for a given structural element |
CO2 | Formulate finite element equation for a given problem |
CO3 | Select suitable element type and solution form in the Finite element analysis |
CO4 | Illustrate the use of FEA tools/software in obtaining the structural response of a given problem |
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