Key And Supplement to Elementary Mechanics

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99 To find AE '; in the right-angled triangle DAB we have A D tang B = = i = 0-666 + ; . -. B = 33 41'. Then AE = AB sin B = 3-327 + inches.
Substituting above gives 24 x 20 2. Taking the origin of moments at D we have P ^ ~ 20 x 24 10A . , : - = 120 Ibs.
3. Taking the origin of moments at B we have W. BC^F. AB, or PAGE 116.
4. If t = TF, we have 100 KEY AND SUPPLEMENT or = AC.
From the right-angled triangle AEB we have sin 45 C substituting, AC 5. Taking the origin of moments at A we have t x
...AC= BE x W. But from the example DB=2AB, 6 = 45, TF= Ibs. From the figure BE- AB sin 45 = $V2 AB = 0-7071AB.
BE AB sin 45 . -. 9> = 20 42' 17". To find A C we have from the figure AC=AB&\nABC = J# sin (0 - cp) TO ELEMENTARY MECHANICS. 101 = AB sin 24 17' 43" = 04115 AB.
Substituting in the first equation above gives Q. 7071 x 50 04115 = 85-97 + Ibs.
To get the compression on the bar, take the origin of moments at D, in which case the moment of the tension will be zero. The perpendicular from D upon AB prolonged will be AD sin #, and from D perpendicular upon the vertical through B will equal BE = AB sin 6 ; hence we have calling c the compression c.


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