Chapter 8.3, Problem 22WE

To determine

To check and calculate: whether the given truss is stable; and determine the values of $x$ and $y$ .

Answer to Problem 22WE

The given truss is stable and the values of $x$ and $y$ are $12\text{ cm,}$ each.

Explanation of Solution

Given information:

In the truss, there are 9 segments and 6 joints.

Formula used:

If suppose the truss is stable, then −

  

Calculation:

Since,

  $\begin{array}{l}s=9\text{ and }j=6,\\ \Rightarrow \text{ 2j-3,}\\ \Rightarrow \text{ 2(6)-3,}\\ \Rightarrow \text{ 12-3,}\\ \Rightarrow \text{ 9}\text{.}\end{array}$

Thus, $s=2j-3$ and for given $j=6$ , is satisfied.

Hence, the given truss is stable.

Again, by properties of triangles and equating the ratios of sides, we have −

  $\frac{12}{y}=\frac{5}{5}$

  $\Rightarrow$ $y=12\text{ cm}$ .

And,

  $\frac{12}{x}=\frac{13}{13}$

  $\Rightarrow$ $x=12\text{ cm}$ .

Hence, the values of $x$ and $y$ for a stable truss is $12\text{ cm,}$ each.