hw1 - P x gage 1 gage 2 x 1 x 2 MASSACHUSETTS INSTITUTE OF...

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Unformatted text preview: P x gage 1 gage 2 x 1 x 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS AND MATERIALS II HOMEWORK NO. 1 Distributed : Wednesday, February 11, 2004 Due : Wednesday, February 18, 2004 Problem 1 ( 35 points ) A cantilever beam has been constructed from a steel having Young’s modulus E = 208 GP a , Poisson ratio ν = 0 . 29, and tensile yield strength σ y = 410 M P a . The length of the beam, from its base to its tip, is L = 1 m , and the uniform cross-section is rectangular, h = 5 mm thick and b = 30 mm wide. Two axially-mounted strain gages have been mounted on the top surface ( y = h/ 2). The precise absolute axial position “ x ” is not known for either gage; however, it is known that the two gages are spaced an axial distance of = 200 mm apart along the length of the beam. A tip load of magnitude ‘ P ’ is applied to the cantilever, acting in a direction parallel to the y-axis, causing the two gages (#1, which is nearer the base of the cantilever, and #2, which is nearer its tip) to register the following strain values: Figure 1: Schematic of tip-loaded cantilever showing positions of strain gages numbers 1 and 2. 1 Gage no. axial coordinate strain 1 x 1 =? 1200 × 10 − 6 2 x 2 = x 1 + 200 mm 900 × 10 − 6 • (20 points) Evaluate the load P . • (15 points) Using the (now-known) value of P , find the axial locations ( x 1 and x 2 ) of both gages. 2 Problem 2. ( 25 points ) There is current interest in the use of microfabricated cantilever beams in detecting the presence of bacteria in a liquid solution. Following fabrication of the cantilever, its surface is coated with an antibody that is specific to the presence of the bacterium of interest, and the free vibration characteristics of the cantilever (its first-mo de natural frequency, ω ) is recorded experimentally. Then the coated cantilever is exposed to a liquid medium. If the sought-for bacteria are present in solution, they will preferentially attach themselves to the antibody coating on the surface of the cantilever, in the process increasing the vibrating mass of the cantilever by an...
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.002 taught by Professor Davidparks during the Spring '04 term at MIT.

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hw1 - P x gage 1 gage 2 x 1 x 2 MASSACHUSETTS INSTITUTE OF...

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