Chapter 6.4, Problem 24ES

As shown in the accompanying figure, a horizontal beam with dimensions $2\text{ in}\times \text{6 in}\times \text{16 ft}$ is fixed at both ends and is subjected to a uniformly distributed load of $120\text{ lb/ft}$ . As a result of the load, the centerline of the beam undergoes a deflection that is described by

$y=-1.67\times {10}^{-8}\left(x^4-2L{x}^3+L^2{x}^2\right)$

$\left(0\le x\le 192\right)$ , where $L=192$ in is the length of the unloaded beam, $x$ is the horizontal distance along the beam measured in inches from the left end, and $y$ is the deflected of the centerline in inches.

(a) Graph $y$ versus $x$ for $0\le x\le 192$ .

(b) Find the maximum deflection of the centerline.

(c) Use a CAS or a calculator with a numerical integration capability to find the length of the centerline of the loaded beam. Round your answer to two decimal places.