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02-02ChapGere.0001 - 80 A-PDF Axially Loaded Members...

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Solution 2.3-8 Bar with a hole 80 CHAPTER 2 Axially Loaded Members d 2 d 1 L 4 P P L 4 L 2 d d diameter of hole S HORTENING OF THE BAR (Eq. 1) N UMERICAL VALUES ( DATA ): maximum allowable shortening of the bar 8.0 mm PL E ¢ 1 d 1 2 d 2 1 d 1 2 2 d 2 2 P E C L 4 4 ( d 1 2 d 2 ) L 4 4 d 1 2 L 2 4 d 2 2 S a N i L i E i A i P E a L i A i P 110 kN L 1.2 m E 4.0 GPa d 1 100 mm d max maximum allowable diameter of the hole d 2 60 mm S UBSTITUTE NUMERICAL VALUES INTO E Q . (1) FOR AND SOLVE FOR d d max : U NITS : Newtons and meters d max 23.9 mm d 0.02387 m d 2 569.81 10 6 m 2 761.598 100 555.556 106.042 1 0.01 d 2 761.598 1 0.01 d 2 1 0.01 2 0.0036 B 1 (0.1) 2 d 2 1 (0.1) 2 2 (0.06) 2 R 0.008 (110,000)(1.2) (4.0 10 9 ) Problem 2.3-9 A wood pile, driven into the earth, supports a load P entirely by friction along its sides (see figure). The friction force f per unit length of pile is assumed to be uniformly distributed over the surface of the pile. The pile has length L , cross-sectional area A , and modulus of elasticity E . (a) Derive a formula for the shortening of the pile in terms of P , L , E , and A . (b) Draw a diagram showing how the compressive stress
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