An electric overhead traveling crane, consisting of a girder, trolley, and wire rope, is shown in Fig. 5.28. The girder has a flexural rigidity \((E I)\) of \(17 \times 10^{9} \mathrm{~N}-\mathrm{m}^{2}\) and a span \((L)\) of \(10 \mathrm{~m}\). The rope is made of steel and has a length \((l)\) of \(7 \mathrm{~m}\). The masses of the trolley and the load lifted are \(4000 \mathrm{~kg}\) and \(1000 \mathrm{~kg}\), respectively. Find the area of cross section of the rope such that the fundamental natural frequency is greater than \(20 \mathrm{~Hz}\).

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Girder; kg, E, I Trolley m1 Wire k rope 0000 m1 Load lifted m2 k m2 (b) (a) FIGURE 5.28 Overhead traveling crane.