$8\mathrm{.}7-1$ Assuming that the deflected shape of a beam with immovable supports $($see Fig. $8-20$b$)$ is given by the equation $v=sin\frac{x}{L},$ where $$ is the deflection at the middle of the beam, determine the horizontal force $H$ at the ends. If the beam is made of aluminium with $E=70$GPA, calculate the axial tensile stress $$ when the ratio of the deflection $$ to the length $L$ is $\frac{1}{300}.$

Fig. $8-20($a$)$ Horizontal displacement of the end of a beam and $($b$)$ horizontal reactions for a beam with immovable supports