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01-02ChapGere.0029 - CHAPTER 1 Tension Compression and...

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Problem 1.8-15 Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle can be varied by moving support A vertically and changing the length of bar AC to correspond with the new position of support A . The allowable stresses in the bars are the same in tension and compression. We observe that when the angle is reduced, bar AC becomes shorter but the cross-sectional areas of both bars increase (because the axial forces are larger). The opposite effects occur if the angle is increased. Thus, we see that the weight of the structure (which is proportional to the volume) depends upon the angle . Determine the angle so that the structure has minimum weight without exceeding the allowable stresses in the bars. ( Note : The weights of the bars are very small compared to the force
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Unformatted text preview: CHAPTER 1 Tension, Compression, and Shear L P A B C θ Solution 1.8-15 Two bars supporting a load P T 5 tensile force in bar AC C 5 compressive force in bar BC A REAS OF BARS L ENGTHS OF BARS L AC 5 L cos u Ê L BC 5 L A BC 5 C s allow 5 C s allow tan u A AC 5 T s allow 5 P s allow sin u © F horiz 5 Ê C 5 P tan u © F vert 5 Ê T 5 P sin u W EIGHT OF TRUSS g 5 weight density of material W 5 g ( A AC L AC 1 A BC L BC ) Eq. (1) g , P , L , and s allow are constants W varies only with u Let Eq. (2) G RAPH OF E Q . (2): W k 5 1 1 cos 2 u sin u cos u (Nondimensional) k 5 g PL s allow ( k has units of force) 5 g PL s allow ¢ 1 1 cos 2 u sin u cos u ≤ 5 g PL s allow ¢ 1 sin u cos u 1 1 tan u ≤ L P A B C P T C C Joint C 3 6 9 12 30 ° 60 ° 90 ° u W k A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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