Chapter 5, Problem 2PP

(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula:

$d=\frac{w{x}^2}{24EI}(x^2+6l^2-4lx)$

d is the deflection at location x (ft).

$\begin{array}{l}xisthedistancefromthesecuredend\left(ft\right).\hfill \\ wistheweightplacedattheendofthebeam\left(lbs/ft\right).\hfill \\ listhebeamlength\left(ft\right).\hfill \end{array}$

$\begin{array}{l}Eisthemodulesofelasticity\left(lbs/f{t}^2\right).\hfill \\ Iisthesecondmomentofinertia\left(f{t}^4\right).\hfill \end{array}$

For the beam shown in Figure 5.15, the second moment of inertia is determined as follows:

$l=\frac{b\times h^3}{12}$

b is the beam’s base.

h is the beam’s height.

Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data:

$\begin{array}{l}w=200lbs/ft\hfill \\ l=3ft\hfill \\ E=187.2\times 106lb/f{t}^2\hfill \\ b=.2ft\hfill \\ h=.3ft\hfill \end{array}$