03-LoadsAssignment-1

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Auburn University *

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3610

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Mechanical Engineering

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Apr 3, 2024

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CIVL 3610 Laboratory p. 1 of 4 Spring 2024 Roueche Loads Assignment Due: See Canvas A. Read Canvas course notes under Loads . Read Section 1.3 in the Structural Analysis textbook. B. Read and perform the Impact Testing and Live Load Testing procedures of Exercise 25 in the lab manual. In place of the Resonant Testing procedure, read and perform the following Shake Table Dynamic Testing procedure: Shake Table Testing Objectives : To demonstrate dynamic loading effects using a shake table and varying heights of single degree of freedom systems. Background Information on Single Degree of Freedom Structures : A single degree of freedom (SDOF) structure can generally be defined by a single reference point. In this case the large mass (or weight) at the top of the structure is the critical point with the threaded rods providing the lateral stiffness resisting the motion. Recall that the period of an oscillating system is the time it takes for the oscillator to complete one full cycle of displacement (usually measured in seconds). The frequency is the number of displacement cycles that occur per unit of time (usually measured cycles per second, or Hz). Note that the frequency is the inverse of the period. The Frequency of Vibration, f n , and the Period of Vibration, T n , are fundamental properties of a specific SDOF system that are determined by the mass, m , and the equivalent lateral stiffness, k , of the system. Equation 1 and 2 provide these relationships. 𝑓 ? = 1 2𝜋 √ 𝑘 ? Equation 1 𝑇 ? = 2𝜋√ ? 𝑘 Equation 2 Procedure for Shake Table Testing : The procedure for testing will be as follows: 1. Assemble three four-legged towers on the shake table. The height of the three towers are 12 in., 18 in., and 24 in. from the top of the table to the top of the square plate. Each tower supports the same weight (14.2 lb). 2. Excite the towers using the following five simple sinusoidal functions. Run each function twice — or more if necessary for everyone to watch the experiment. For each of the five excitation functions, observe the response of each of the three towers. Note the apparent period and fundamental frequency of vibration for each tower. a) Frequency: 2 Hz, Amplitude: 1 mm, Number of Cycles: 10 b) Frequency: 4 Hz, Amplitude: 1 mm, Number of Cycles: 10

CIVL 3610 Laboratory p. 2 of 4 Spring 2024 Roueche c) Frequency: 6 Hz, Amplitude: 1 mm, Number of Cycles: 10 d) Frequency: 8 Hz, Amplitude: 1 mm, Number of Cycles: 10 e) Frequency: 10 Hz, Amplitude: 1 mm, Number of Cycles: 10 3. Excite the towers using the following two programmed functions. Run each function twice, or more if necessary for everyone to watch the experiment. For the two different excitation functions, observe the response of each of the three towers. a) Frequency Sweep: Frequency Range: 0.2 – 10 Hz, Amplitude: 1 mm b) Kobe Earthquake (1995) Record, 100% Shake Table Testing Post-Exercise Requirements : 1. Qualitatively discuss how each tower behaved when vibrated in response to each of the different excitations (sinusoidal and programmed)? 2. Report the apparent fundamental frequency and period of vibration that you observed for each tower (based on its response to the five sinusoidal excitation functions). 3. Using the apparent fundamental frequency of vibration that you observed in the tests, determine the equivalent lateral stiffness of each tower, knowing that the weight is 14.2 lbs. (Remember that the acceleration of gravity is 386.4 in/s 2 .) Is there a relationship between the lateral stiffness of each tower and the length of the tower legs? 4. Briefly discuss how changing the variables would affect the natural frequency of the system. (What if we used a bigger cube? Or changed the heights of the tower?) C. Write a single, abbreviated lab report presenting the results for Exercise 25. The lab report should contain a Title Page, Introduction, Results and Discussion, References (if needed), and Appendix X (see below). Make sure that your report includes the results and observations requested for each test in the Procedure section of Exercise 25. Submit a single PDF file of your report ( username03.docx ) via Canvas prior to the deadline. D. Include as Appendix X your solution to the four application problems given below. Comply with CIVL 3610 homework guidelines. You do not need to refer to these problems in the body of your report. 1) Compute the weight per lineal foot of a reinforced concrete beam with the cross section shown at right. The beam is constructed with a normal-weight concrete (unit weight = 150 pcf). 18 in. 18 in. 8 in. 16 in. 4 in.

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