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ENME361 Quiz 10 Solution

# ENME361 Quiz 10 Solution - ENME 361 Fall 2008 Solution for...

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ENME 361 Fall 2008 Solution for Quiz #10 (November 25, 2008; Duration: 20 minutes) 1) Three springs composed of a cantilever beam, a beam hinged at both ends, and a coil spring are attached as shown in Figure 1. When a force is applied to the system at the midpoint of the hinged beam as shown in the figure, determine the equivalent spring constant of the system. E 1 , I 1 , L 1 E 2 , I 2 , L 2 k 3 Midpoint F Fixed end Figure 1 Solution: In the given arrangement, the three different springs are in parallel with the equivalent beam stiffness forms determined by using the given table as follows: i) stiffness of the cantilever beam 3 1 1 1 1 3 L I E k = and ii) stiffness of the hinged-hinged beam 2 2 2 3 2 48 E I k L = . Then, the equivalent spring stiffness of the system is 1 k + 2 k + 3 k = 3 1 1 1 3 L I E + 2 2 3 2 48 E I L + 3 k Some formulae Beam stiffness Cantilever beam a F , x L 3 3 ; 0 EI k a L a = < Pinned-pinned beam (Hinged, simply supported) a b F , x 2 2 ) ( 3 b a b a EI k + = 2) What is an inertial reference frame?

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ENME361 Quiz 10 Solution - ENME 361 Fall 2008 Solution for...

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