## Related questions with answers

Hoover Dam (is the highest arch-gravity type of dam in the United States. A plan view and cross section of the dam are shown in Fig. The walls of the canyon in which the dam is located are sloped, ream of the dam the vertical plane shown in Fig. is imately represents the cross section of the wate Use this vertical cross section to estime zontal force of the water on the dam. force acts.

Solution

Verified$\textbf{Given}$- width of top of dam(B) = 880 ft width of base of dam(b)= 290 ft Area of section 1

$\begin{align*} A_{1} &= \dfrac{1}{2}(\dfrac{B-b}{2})\cdot h\\ &= \dfrac{1}{2}(\dfrac{880-290}{2})\cdot 215\\ &=105461.56\text{ft}^{2}\\ \end{align*}$

Since beam is symmetric, the area of section 1 and 3 are equal $A_{1} = A_{3}$ = $105461.56\text{ft}^{2}$ Calculating area of section 2 $A_{2} =b\cdot h$ = $290\cdot 715$ = $207350 \text{ft}^{2}$ Calculate the centroid at section 1 and 3

$\begin{align*} y_{1}= y_{3} &=\dfrac{1}{3}h\\ y_{1}= y_{3} &=238.3 ft\\ \end{align*}$

calculate centroid at section 2

$\begin{align*} y_{2} &= \dfrac{h}{2}\\ y_{2} &= \dfrac{715}{2}\\ &= 357.5 ft\\ \end{align*}$

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