00049___80fc81efc2c2f419d3f183d4f26b9292 - determine the...

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28 INTRODUCTION Chap. 1 1.5. A circular ring of uniform linear elastic material and uniform cross section is loaded by a pair of equal and opposite forces at the ends of a diameter (Fig. P1.5). Find the change of diameters aa and bb. Note: This is a statically indeterminate problem. You have to determine the bending moment distribution in the ring. 1.6. Compare the changes in diameters aa, bb, and cc when a circular ring of uniform linear elastic material and uniform cross section is subjected to a pair of bending moments at the ends of a diameter (Fig. P1.6). 1.7. Begg's Defonneter: G. E. Beggs used an experimental model to de- termine the reactions of a statically indeterminate structure. For example, to
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Unformatted text preview: determine the horizontal reaction H at the right-hand support b of an elastic arch under the load P, he imposes at b a small displacement 6 in the horizontal b b P1.5 P1.6 direction and measures at P the deflection 6' in the direction corresponding with P, while preventing the vertical displacement and rotation of the end b, Fig. P1.7. Show that H = -P6'/6. (Use the reciprocal theorem.) [G. E. Beggs, J. Franklin Institute, 203 (1927), pp. 375-386.1 P1.7 P1.8 1.8. A simply supported, thin elastic beam of variable cross section with bending rigidity E I ( z ) rests on an elastic foundation with spring constant k and...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.

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