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02-02ChapGere.0005 - d 5 d d 5 4 W p d 2 EL L y dy 5 2 WL p...

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Problem 2.3-13 A long, slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight (see figure). The weight of the cone is W and the modulus of elasticity of the material is E . Derive a formula for the increase d in the length of the bar due to its own weight. (Assume that the angle of taper of the cone is small.) Solution 2.3-13 Conical bar hanging vertically 84 CHAPTER 2 Axially Loaded Members d L E LEMENT OF BAR W 5 weight of cone E LONGATION OF ELEMENT dy E LONGATION OF CONICAL BAR
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Unformatted text preview: d 5 # d d 5 4 W p d 2 EL # L y dy 5 2 WL p d 2 E d d 5 N y dy E A y 5 Wy dy E A B L 5 4 W p d 2 EL y dy d y L dy dy N y N y T ERMINOLOGY N y 5 axial force acting on element dy A y 5 cross-sectional area at element dy A B 5 cross-sectional area at base of cone V 5 volume of cone V y 5 volume of cone below element dy W y 5 weight of cone below element dy N y 5 W y 5 V y V ( W ) 5 A y yW A B L 5 1 3 A y y 5 1 3 A B L 5 p d 2 4 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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