By C. B. Smith, N. Hiller and G. E. Walker (Auth.)
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In this book, only loads which are normal or perpendicular to the axis of the beam will be considered. Typical examples of beams are the wooden joists supporting the floor in a house, the steel joists forming a bridge and the reinforced concrete beams in modern building construction. Other examples include the crank to which a bicycle pedal is fixed, the brake lever of a car and the wings of an aeroplane. The most simple types of beam are the simply supported beam which merely rests on two supports and the cantilever which is rigidly built in at one end and projects into space to carry various loads.
When carrying these loads? F. max. ] 5. D. load of 2 cwt/ft. F. M. diagrams. State the max. F. M. and where these occur. [Reactions. Vertical force of 16 cwtf. Fixing moment 64 cwtf ft. F. max. M. max. ] 6. A beam 30 ft long is simply supported at 4 ft from each end. D. load of i tonf/ft between the supports. F. M. diagrams. Find the max. F. M. stating where each occurs. F. max. 4 tonf overhanging end. M. max. ] 52 APPLIED MECHANICS FOR ENGINEERS 7. D. load of 560 lbf/ft for 18 ft from one end.
The beam carries point loads of 3, 5 and 4 tonf at 5, 12 and 18 ft, from the supported end. Find the reactions at the supports. Referring to Fig. 1, let Rx and R2 be the reactions at the supports (1) and (2). Taking moments about support 1, 3 x 5 + 5 x 12 + 4 x 18 = 15 + 60 + 72 = 147 = 1 5 i ^ 2 t o n f ft. Λ R2 = 147/15 = 9-8 tonf. Taking moments about support 2, 3 x 10 + 5 x 3 - 4 x 3 = 3 0 + 1 5 - 1 2 = 33 = 1 5 ^ tonf ft. Λ Rx = 33/15 = 2-2 tonf. Resolving normal to the beam, 3 + 5 + 4 = 12 tonf = RT+R2 = 2-2 + 9-8 = 12 tonf.
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