02-02ChapGere.0011

# 02-02ChapGere.0011 - (4 S OLUTION OF THE EQUATIONS Solve...

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Problem 2.4-3 Three prismatic bars, two of material A and one of material B , transmit a tensile load P (see figure). The two outer bars (material A ) are identical. The cross-sectional area of the middle bar (material B ) is 50% larger than the cross-sectional area of one of the outer bars. Also, the modulus of elasticity of material A is twice that of material B . (a) What fraction of the load P is transmitted by the middle bar? (b) What is the ratio of the stress in the middle bar to the stress in the outer bars? (c) What is the ratio of the strain in the middle bar to the strain in the outer bars? Solution 2.4-3 Prismatic bars in tension 90 CHAPTER 2 Axially Loaded Members A A B P A A B P F REE - BODY DIAGRAM OF END PLATE E QUATION OF EQUILIBRIUM © F horiz 5 0 P A 1 P B 2 P 5 0 (1) E QUATION OF COMPATIBILITY d A 5 d B (2) F ORCE - DISPLACEMENT RELATIONS A A 5 total area of both outer bars (3) Substitute into Eq. (2):
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Unformatted text preview: (4) S OLUTION OF THE EQUATIONS Solve simultaneously Eqs. (1) and (4): (5) Substitute into Eq. (3): (6) d 5 d A 5 d B 5 PL E A A A 1 E B A B P A 5 E A A A P E A A A 1 E B A B Ê P B 5 E B A B P E A A A 1 E B A B P A L E A A A 5 P B L E B A B d A 5 P A L E A A A Ê d B 5 P B L E B A B S TRESSES : (7) (a) L OAD IN MIDDLE BAR (b) R ATIO OF STRESSES (c) R ATIO OF STRAINS All bars have the same strain Ratio 5 1 s B s A 5 E B E A 5 1 2 ∴ P B P 5 1 ¢ E A E B ≤ ¢ A A A B ≤ 1 1 5 1 8 3 1 1 5 3 11 Given: E A E B 5 2 Ê A A A B 5 1 1 1 1.5 5 4 3 P B P 5 E B A B E A A A 1 E B A B 5 1 E A A A E B A B 1 1 s B 5 P B A B 5 E B P E A A A 1 E B A B s A 5 P A A A 5 E A P E A A A 1 E B A B P P A 2 P B P A 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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