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A circular shaft has a diameter d [m] that varies with axial position x [m] according to d = 0.02(1/x²)/e*;0

A circular shaft has a diameter d [m] that varies with axial position x [m] according to d = 0.02(1/x²)/e*;0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. SIMPSON’S 1/3 RULE (? → ? + 2ℎ)
2. PRECISE RULE (? → ? + 4ℎ)
3. % R. E. = [(PRECISE RULE−SIMPSON′S RULE)/PRECISE RULE]× 100 

A circular shaft has a diameter d [m] that varies with axial position x [m] I. according to d = 0.02(1/x²)/e*;0 < x < 3m An axial load P of 30000 N is applied to one end of the shaft whose modulus of elasticity E is 2 × 1011N/m². The axial elongation of the shaft is Ax [m] and is given Ax (P / E) (1/ A)dx ; A = cross-sectional area = nd?/4 Estimate Ax by 1. SIMPSON'S RULE (a → a + 2h) 2. PRECISE RULE (a → a + 4h) PRECISE RULE-SIMPSON'S RULE 3. % R. E. = × 100 PRECISE RULE
Transcribed Image Text:A circular shaft has a diameter d [m] that varies with axial position x [m] I. according to d = 0.02(1/x²)/e*;0 < x < 3m An axial load P of 30000 N is applied to one end of the shaft whose modulus of elasticity E is 2 × 1011N/m². The axial elongation of the shaft is Ax [m] and is given Ax (P / E) (1/ A)dx ; A = cross-sectional area = nd?/4 Estimate Ax by 1. SIMPSON'S RULE (a → a + 2h) 2. PRECISE RULE (a → a + 4h) PRECISE RULE-SIMPSON'S RULE 3. % R. E. = × 100 PRECISE RULE
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