mws_civ_nle_txt_bisection_examples

mws_civ_nle_txt_bisection_examples - Chapter 03.03...

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Bisection Method of Solving a Nonlinear Equation- More Examples Civil Engineering Example 1 You are making a bookshelf to carry books that range from 8½" to 11" in height and would take up 29" of space along the length. The material is wood having a Young’s Modulus of , thickness of 3/8" and width of 12". You want to find the maximum vertical deflection of the bookshelf. The vertical deflection of the shelf is given by Msi 667 . 3 x x x x x v 018507 . 0 10 66722 . 0 10 13533 . 0 10 42493 . 0 ) ( 4 6 5 8 3 4 where x is the position along the length of the beam. Hence to find the maximum deflection we need to find where 0 ) ( dx dv x f and conduct the second derivative test. x Books Bookshelf Figure 1 A loaded bookshelf. The equation that gives the position x where the deflection is maximum is given by 0 018507 . 0 10 12748 . 0 10 26689 . 0 10 67665 . 0 2 3 3 5 4 8 x x x Use the bisection method of finding roots of equations to find the position x where the deflection is maximum. Conduct three iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration. 03.03.1
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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mws_civ_nle_txt_bisection_examples - Chapter 03.03...

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