Chapter 8, Problem 18P

Figure P8.18a shows a uniform beam subject to a linearly increasing distributed load. The equation for the resulting elastic curve is (see Fig. P8.18b)

$y=\frac{w_0}{120EIL}\left(-x^5+2L^2{x}^3-L^{4}x\right)\left(\text{P8}\text{.18}\text{.1}\right)$

Use bisection to determine the point of maximum deflection (that is, the value of $x\text{ where }dy/dx=0$). Then substitute this value into Eq. $\left(\text{P8}\text{.18}\text{.1}\right)$ to determine the value of the maximum deflection. Use the following parameter values in your computation: $L=450\text{cm, }E=50,000\text{kN}/{\text{cm}}^2,I=30,000{\text{ cm}}^4,\text{ and }{w}_0=1.75\text{kN}/\text{cm}$.

FIGURE P8.18