CIVE5522 F24 HW 1 Solutions

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Northeastern University**We aren't endorsed by this school

Course

CIVE 5522

Subject

Mechanical Engineering

Date

Dec 19, 2024

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CIVE 5522 STRUCTURAL SYSTEMS MODELING Homework No. 1 – Solutions 1) Briefly explain the three fundamental relationships for structural analysis. The analysis of structures involves the following fundamental relationships: 1) equilibrium equations, 2) compatibility conditions and 3) constitutive relations. Equations of static equilibrium are based on Newton’s laws. Compatibility conditions ensure that all parts of the structure will fit together, and no boundary conditions will be violated when the final displaced configuration is obtained. The constitutive relations refer to the stress-strain relationships of the structural material. 2) Identify a case study where it was feasible that the engineers did not comply with the fundamental relationships listed above resulting in errors in hand calculations and/or computer modeling. In the simplest explanation possible, what do you think went wrong? Answers will vary. Hard Rock New Orleans collapse discussed in lecture. 3) Given the continuous beam, determine and sketch the dof’s / independent displacements on a separate diagram for each response. a. What is the degree of static indeterminacy? b. What is the degree of kinematic indeterminacy? c. If the effects of axial deformations are neglected, what is the degree of kinematic indeterminacy?

4) Given the plane frame, determine and sketch the dof’s / independent displacements on a separate diagram for each response. a. What is the degree of static indeterminacy? b. What is the degree of kinematic indeterminacy? c. If the effects of axial deformations in the columns and beams are neglected, what is the degree of kinematic indeterminacy?

5) Given the plane truss, determine and sketch the dof’s / independent displacements on a separate diagram for each response. a. What is the degree of static indeterminacy? b. What is the degree of kinematic indeterminacy? Solve Problems 6 and 7 by hand using the matrices given below: 6) If the operation cannot be performed, write “nonsense”, and explain why. a. [A] + [B] b. [A] – [C]

c. [A][C]Td. [D][E] e. [B][D] f. [D][B] 7) Determine [D]-1by the Gauss-Jordan method.

8) Given the following matrices, show that the triple matrix product XTA Xis symmetric. For Problems 9,10, and 11, you will be using MATLAB. If you have little experience with MATLAB or need a refresher, do the MATLAB Onramp tutorial and read through the document “MATLAB for CIVE 5522” provided in Module 1. 9) Using the functions provided in MATLAB, redo problems 6 and 7. Provide a pdf printout of the MATLAB steps and results. 10) Using the flowchart presented in class, develop a computer program (script) to solve a system of simultaneous equations of any size by the Gauss-Jordan method. a. Check the program by solving the class example (Example 2.11) and comparing the computer-generated results to those determined by hand. b. Your program should perform a check at the end by solving the example using the MATLAB function x = A/B (solves the system of linear equations Ax = B). The program should be general, the input data should not be hard coded in the script, but rather your program should ask the user for the input data interactively. Provide a pdf printout of the programming details and results. 11) Repeat Problem 10 but, instead of entering the input data interactively, the program should read the input from a file (Excel or text file). To read from Excel, use the command xlsreador readmatrix. To read from a text file, use the command fscanfor readmatrix. You may also use any other command you are familiar with. For the project you will need to be abel to read input data from a file, so this is good practice. Provide a pdf printout of the file, programming details, and results.

563669-1288-74-39

35 6 -39 -1 28 -7 4668-39

A=5.00006.00003.00009.0000-1.00002.00008.0000-7.00004.0000B=66.00008.0000-39.0000After solving, G=1.00000.00000.00001.2128-0.00001.00000.00008.57450.00000.00001.00002.8298