mws_civ_nle_txt_newton_examples

mws_civ_nle_txt_newton_examples - Chapter 03.04...

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Chapter 03.04 Newton-Raphson 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 a 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 Newton-Rapshon 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
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mws_civ_nle_txt_newton_examples - Chapter 03.04...

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