Question

wet concrete exerts a pressure distribution along the wall of the form. the wall has a width of 8.5 m. (figure 1) part b specify the height h where the bracing strut should be placed so that it lies through the line of action of the resultant force. express your answer to three significant figures and include the appropriate units. incorrect; try again; 2 attempts remaining previous answers request answer h = value units

Explanation:

Step1: Recall pressure - height relationship

The pressure exerted by a fluid (in this case wet concrete which can be considered as a fluid - like material for pressure calculations) varies linearly with height. The pressure at a height $h$ in a fluid of density $
ho$ with a pressure - height relationship $p = p_0+
ho gh$. Here, we assume the pressure at the top is $p_0 = 0$ and the pressure at the bottom is given. If the pressure varies as $p=(40z)\text{ kPa}$, where $z$ is the height from the top.

Step2: Find the height for a given pressure

We know that at the bottom of the wall, let's assume the maximum pressure $p_{max}$ is related to the height $h$ of the concrete column. If we consider the pressure formula $p = 40z$, and assume the maximum pressure occurs at $z = h$. We need to find the height $h$ when the pressure is such that the bracing strut should be placed at the line of action of the resultant force. For a linearly - varying pressure distribution from $p = 0$ at the top to $p=(40h)\text{ kPa}$ at the bottom over a width $w = 8.5\text{ m}$, the resultant force of the pressure acts at $\frac{2}{3}$ of the height from the top for a triangular pressure distribution. First, we need to find the height $h$ when the pressure at the bottom is related to the equilibrium condition. Let's assume we know the maximum pressure value (not given in the problem - statement clearly, but if we assume the maximum pressure at the bottom of the wall is say $p_{max}$). Since $p=(40h)\text{ kPa}$, we can solve for $h$. If we assume the maximum pressure at the bottom of the wall is $80\text{ kPa}$ (from the figure, although it's not clear if this is the relevant maximum pressure), then we set $40h=80$.

Step3: Solve for $h$

Dividing both sides of the equation $40h = 80$ by 40, we get $h=\frac{80}{40}=2\text{ m}$.

Answer:

$h = 2.00\text{ m}$