questions 15&18. step by step solutions. 15. A steel joist has a span of 6 m and the ends are simply supported. Thejoist has a mass of 52 kg/m and the second moment of area of the cross-sectionis 120 x 10-6 m². A load of 3 t is carried at a point 2-4 m from one support.Find from first principles the frequency of the natural transverse vibrationsof the joist, if the effect of its own mass is neglected. Then find the approximatefrequency when the mass of the joist is taken into account. (I. Mech. E.)(Ans. 7.01 Hz; 6-82 Hz [8 = 5.09 mm; A = 0.3585 mm])16. A beam with second moment of area of cross-section 8 x 10-6 m andof mass 18 kg/m is simply supported at the end of a 3.6 m span and it carries abody of mass 250 kg at the centre. Find the frequency of transverse vibrations.(I. Mech. E.)(Ans.: 12.2 Hz [8: 1.49 mm; A = 0.241 mm])=17. Two parallel steel beams span an opening of 6 m and jointly supporta central load of 3 t. Each beam has a mass of 45 kg/m run and the momentof inertia of the section is 86 x 10-6 m¹. Assuming the beams are simplysupported at the ends, calculate the natural frequency of the transverse vibra-tions. (U. Lond.) (Ans.: 7-72 Hz [8= 3-85 mm; A = 0.433 mm])18. A small, imperfectly balanced machine is mounted on a rigid horizontalplate, supported on four vertical legs each 28 mm outside diameter, 25 mminside diameter and 0.9 m long, rigidly welded to the plate but having theirother extremities always position fixed but direction fixed or not at will. Ifthe effective mass of the assembly is 45 kg, find the five lowest machine speedswhich would give resonance corresponding to the five different conditions ofthe legs. (U. Lond.)(Ans. 9.06, 8-16, 7-17, 5-99, 4-53 Hz)

To determine:a) The natural transverse vibrations of the joist when mass is neglected.b) Frequency…

15. A steel joist has a span of 6 m and the ends are simply supported. The joist has a mass of 52 kg/m and the second moment of area of the cross-section is 120 x 10-6 m4. A load of 3 t is carried at a point 2-4 m from one support. Find from first principles the frequency of the natural transverse vibrations of the joist, if the effect of its own mass is neglected. Then find the approximate frequency when the mass of the joist is taken into account. (I. Mech. E.) (Ans: 7-01 Hz: 6.82 Hz [8= 5.09 mm: A 0-3585 mm])

15. A steel joist has a span of 6 m and the ends are simply supported. The joist has a mass of 52 kg/m and the second moment of area of the cross-section is 120 x 10-6 m4. A load of 3 t is carried at a point 2-4 m from one support. Find from first principles the frequency of the natural transverse vibrations of the joist, if the effect of its own mass is neglected. Then find the approximate frequency when the mass of the joist is taken into account. (I. Mech. E.) (Ans: 7-01 Hz: 6.82 Hz [8= 5.09 mm: A 0-3585 mm])

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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