By William Elwood Byerly
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Extra resources for An introduction to generalized coordinates in mechanics and physics
E s muß also gelten h 1 - z0 = acosh Xo, a l-x0 h 2 - z0 = a cosh - a- (2) (3) Man beachte, daß sie für homogene Seile konstanten Querschnittes nur für einen flachen Durchhang (dx RJ ds) näherungsweise konstant ist ! 1 3* I. Kräfte, Spannungen und Gleichgewichtsbedingungen 36 und unter Beachtung von (1) J l L= X=O fl+z' 2 dx=[asinhX-Xo]l x~o a . 0 +sinh~) =a(sinhl-x a a 2x0 - l 2a l 2a (4) = 2asmh--cosh---. Aus (2) und (3) erhält man 2x0 - l l. • l-x0 ) X0 (5) h 1 - h 2 = a (cosh - - cosh - - = 2a smh- smh - - · - .
0 bzw. 1) aus Q(x0 ) = 0 zu x 0 = 4,24 m und damit das größte Feldmoment zu max M = M(x0) = 2300 kpm. Die Abb. 2 zeigt die graphische Darstellung aller ermittelten Schnittlasten. 54 II. Elementare Spannungs- und Deformationstheorie des Balken s A 3. Stützlinie einer Dreigelenkbogenbrücke. Welche Form z = z (x) muß die durch die gleichförmig verteilte Belastung q0 beanspruchte Dreigelenkbogenbrücke (Abb. 1) haben, damit der Bogen biegemomentenfrei ist ? Man ermittle für diesen Fall den Verlauf der Querund Normalkräfte.
3) [Q a cos cp- G (b + c) cos
An introduction to generalized coordinates in mechanics and physics by William Elwood Byerly