. The strength of materials; a text-book for engineers and architects. resses in any practicalcase somewhat uncertain, so that many designers do not usethis type of beam. All the above objections can be obviatedby cutting the beam through at the points of contraflexureand resting the centre portion on the two end portions. Thisis the principle of the cantilever girder construction and for FIXED AND CONTINUOUS BEAMS 435 large spans is very economical. This is shown diagrammatic-ally in Fig. 204, in which a fixed beam a b is shown dividedat the points of inflexion c and d and the centre portion
. The strength of materials; a text-book for engineers and architects. resses in any practicalcase somewhat uncertain, so that many designers do not usethis type of beam. All the above objections can be obviatedby cutting the beam through at the points of contraflexureand resting the centre portion on the two end portions. Thisis the principle of the cantilever girder construction and for FIXED AND CONTINUOUS BEAMS 435 large spans is very economical. This is shown diagrammatic-ally in Fig. 204, in which a fixed beam a b is shown dividedat the points of inflexion c and d and the centre portion isrepresented as hanging from the end portions. The inthe centre portion will be the same as for a freely supportedbeam of span I loaded in the given manner. The forthe cantilever portions will be the same as for cantilevers ofspan Zj loaded with the given loading and also with loads atthe ends equal to the reactions at the ends of the centreportions. In the figure, uniform loading is shown, and in such case these reactions are each equal to -^. It will be. Fig. 204. found that the resulting and shear curves obtained inthis way will be the same as shown in Fig. 198. The deflec-tions can also be found by adding together the deflections atthe centre of the centre portion and at the end of one of thecantilever portions. Fixed Beam with Ends not at same Level.—Supposethat a fixed beam a b. Fig. 205, has its ends at a differentlevel, then apart from the loading on the beam, the deflectedform of the beam will be as shown in the figure, the point ofcontraflexure being at the centre point c. The deflection 6 e of the portion a c, assuming the beamdivided at c, will be equivalent to that due to a weight Phanging downwards at c, but for a cantilever with load at end WZ3 8 = 3 EI 436 THE STRENGTH OF MATERIALS In this case we have eh =. P - Z\3 3EI24 EI X eb P12^1 X cf 12EI X <Z
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