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ME260HW#1 Solutions

# ME260HW#1 Solutions - ME 260 Homework#1 MEASUREMENT...

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ME 260 Homework #1 MEASUREMENT TECHNIQUES Due on February 8, 2007 Dr. B. Zhang (Instructor) Office Hours 8:00-10:00 (Mon &Wed) UTE Building, Room 384 and by appointment Phone: 486-2072 [email protected] 1. A strain gage having a nominal resistance of 350 , and a gauge factor of 1.8 is mounted in an equal-arm bridge, which is balanced at a zero applied strain condition. The gauge is mounted on a 1-cm 2 aluminum rod, having E m =70 GPa. The gauge senses axial strain. The bridge output is 1 mV for a bridge input of 5 V. What is the applied load, assuming the rod is in uni-axial tension? KNOWN : A strain gage has a nominal resistance of 350 , and GF =1.8, and senses axial strain. The gage is mounted on a 1 cm 2 aluminum rod ( E m =70 GPa), δ E o =1 mV, E i =5 V. FIND : Applied load, assuming uniaxial tension. SOLUTION : For an equal arm bridge, as the following parameters are known: 4 / R R E E i o δ δ = × × = 28 . 0 5 001 . 0 350 4 4 i o E E R R δ δ Since we have ( 29 GF R R ε δ = and m E σ ε = and C N A F = σ where 2 4 2 m 10 1 cm 1 - × = = C A Then ( 29 N GF R R E A F m C N 3111 8 . 1 350 28 . 0 10 70 10 1 9 4 = × × × × × = = - δ 2. Consider a structural member subject to loads that produce both axial and bending stresses, as shown in Fig. 1a. Two strain gauges are to be mounted on the member and connected in a Wheatstone bridge (Fig. 1b) in such a way that the bridge output indicates the axial component of strain only (the installation is bending compensated). Show that the installation of the gauges shown in Fig. 1a will not be sensitive to bending.

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