$11\mathrm{.}53$ A beam with a rectangular cross section is made of Man$-$Ten steel and has dimensions, as defined in Fig. $8\mathrm{.}13,$ of $\backslash ($ b$=40\backslash )$ and $\backslash ($ t$=20\backslash$mathrm$\{$~mm$\}\backslash ).$ Assume that a through$-$thickness, inspection$-$size crack of length $\backslash ($ a$\_\{$d$\}=1\mathrm{.}00\backslash$mathrm$\{$~mm$\}\backslash )$ is initially present. How many repetitions of the bending moment history shown in Fig. P$11\mathrm{.}53$ are required to grow the crack to failure?