Chapter 4.4, Problem 27E

To determine

To find: the weight if the vertical deflection is 0.8 feet?.

Answer to Problem 27E

The weight could be 100 feet or dead center.

According to the graph, it could also be 161.8 feet.

Explanation of Solution

Given information: Construction: A steel beam is supported by two pilings 200 feet apart. If a weight is placed x feet from the piling on the left, a vertical deflection dequals $0.0000008x^2\left(200-x\right)$ .

  

Calculation:

Given

  $d=0.0000008x^2\left(200-x\right)$

Let d = 0.8

Replace d

  $\begin{array}{l}0.0000008x^2\left(200-x\right)=0.8\\ 0.00016x^2-0.0000008x^3-0.8=0\end{array}$

Bring terms to one side, multiply both sides by − 10,000,000

  $8x^3-1600x^2+8,000,000=0$

Divide both sides by 8

  $x^3-200x^2+1,000,000=0$

  

  

Graphing the function you can see there are 2 places.

The weight could be 100 feet or dead center.

According to the graph, it could also be 161.8 feet.