Chapter 2, Problem 22P

To determine

Calculate the hydrodynamic load applied at floor level on the wall IJKL due to outflow for load cases 2 and 3.

Calculate the hydrostatic loading on the adjacent outside walls due to water retained by the floor and the debris impact load applied to the free standing column CD.

Answer to Problem 22P

The hydrodynamic load applied at floor level on the wall IJKL due to outflow for load case 2 is $\underset{\_}{F_{dK}=8,624\text{kips}}$.

The hydrodynamic load applied at floor level on the wall IJKL at J due to outflow for load case 3 is $\underset{\_}{F_{dJ}=616.6\text{kips}}$.

The hydrodynamic load applied at floor level on the wall IJKL at K due to outflow for load case 3 is $\underset{\_}{F_{dK}=1,096.2\text{kips}}$.

The hydrostatic loading on the adjacent outside walls due to water retained by the floor is $\underset{\_}{F_h=11.1\text{kips}}$.

Explanation of Solution

Given information:

The width of the building (B) is 35 ft.

The maximum inundation height $\left(h_{\max }\right)$ is 33 ft.

The flow velocity $\left(u_{\max }\right)$ is $20\text{ft}/\text{sec}$.

Assume $I_{tsu}=1.0$ and $C_d=1.25$.

Calculation:

For load case 2:

Calculate the height of the water applicable to the structure $\left(h_{des}\right)$ as shown below.

$\begin{array}{c}{h}_{des}=\frac{2}{3}{h}_{\max }\\ =\frac{2}{3}\times 33\\ =22\text{ft}\end{array}$

Calculate the velocity of flow applicable to the structure $\left(u_{des}\right)$ as shown below.

$\begin{array}{c}{u}_{des}=u_{\max }\\ =20\text{ft}/\sec \end{array}$

Sketch the load applied at floor level on the wall IJKL due to outflow for load case 2 as shown in Figure 1.

Refer to Figure 1.

Calculate the height of the water applicable to the structure for K as shown below.

$\begin{array}{c}{h}_{des,K}=\text{Tributory}\text{height of point }K\\ =8+6\\ =\text{14}\text{ft}\end{array}$

Consider the specific weight density of sea water $\left({\gamma }_s\right)$ is $70.4\text{lb}/{\text{ft}}^3$.

Calculate the hydrodynamic load applied at floor level on the wall IJKL $\left(F_{dK}\right)$ due to outflow for load case 2 as shown below.

$\begin{array}{c}{F}_{dK}=\frac{1}{2}{\gamma }_s{I}_{tsu}{C}_d{C}_{cx}B{h}_{des,K}{u}_{des}^2\\ =\frac{1}{2}\times \left(70.4\text{lb}/{\text{ft}}^{\text{3}}\right)\times 1\times 1.25\times 1\times \left(35\text{ft}\right)\times \left(14\text{ft}\right)\times {\left(20\text{ft}/\text{sec}\right)}^2\times \frac{1\text{kip}}{1,000\text{lb}}\\ =8,624\text{kips}\end{array}$

Hence, the hydrodynamic load applied at floor level on the wall IJKL due to outflow for load case 2 is $\underset{\_}{F_{dK}=8,624\text{kips}}$.

For load case 3:

Calculate the height of the water applicable to the structure $\left(h_{des}\right)$ as shown below.

$\begin{array}{c}{h}_{des}=h_{\max }\\ =33\text{ft}\end{array}$

Calculate the velocity of flow applicable to the structure $\left(u_{des}\right)$ as shown below.

$\begin{array}{c}{u}_{des}=\frac{1}{3}{u}_{\max }\\ =\frac{20}{3}\\ =6.67\text{ft}/\sec \end{array}$

Sketch the load applied at floor level on the wall IJKL due to outflow for load case 3 as shown in Figure 2.

Refer to Figure 2.

Calculate the height of the water applicable to the structure for J as shown below.

$\begin{array}{c}{h}_{des,J}=\text{Tributory}\text{height of point }J\\ =8+1\\ =9\text{ft}\end{array}$

Calculate the hydrodynamic load applied at floor level on the wall IJKL at J $\left(F_{dJ}\right)$ due to outflow for load case 3 as shown below.

$\begin{array}{c}{F}_{dJ}=\frac{1}{2}{\gamma }_s{I}_{tsu}{C}_d{C}_{cx}B{h}_{des,J}{u}_{des}^2\\ =\frac{1}{2}\times \left(70.4\text{lb}/{\text{ft}}^{\text{3}}\right)\times 1\times 1.25\times 1\times \left(35\text{ft}\right)\times \left(9\text{ft}\right)\times {\left(6.67\text{ft}/\text{sec}\right)}^2\times \frac{1\text{kip}}{1,000\text{lb}}\\ =616.6\text{kips}\end{array}$

Hence, the hydrodynamic load applied at floor level on the wall IJKL at J due to outflow for load case 3 is $\underset{\_}{F_{dJ}=616.6\text{kips}}$.

Calculate the height of the water applicable to the structure for K as shown below.

$\begin{array}{c}{h}_{des,K}=\text{Tributory}\text{height of point }K\\ =8+8\\ =16\text{ft}\end{array}$

Calculate the hydrodynamic load applied at floor level on the wall IJKL at K $\left(F_{dK}\right)$ due to outflow for load case 3 as shown below.

$\begin{array}{c}{F}_{dK}=\frac{1}{2}{\gamma }_s{I}_{tsu}{C}_d{C}_{cx}B{h}_{des,K}{u}_{des}^2\\ =\frac{1}{2}\times \left(70.4\text{lb}/{\text{ft}}^{\text{3}}\right)\times 1\times 1.25\times 1\times \left(35\text{ft}\right)\times \left(16\text{ft}\right)\times {\left(6.67\text{ft}/\text{sec}\right)}^2\times \frac{1\text{kip}}{1,000\text{lb}}\\ =1,096.2\text{kips}\end{array}$

Hence, the hydrodynamic load applied at floor level on the wall IJKL at K due to outflow for load case 3 is $\underset{\_}{F_{dK}=1,096.2\text{kips}}$.

Sketch the hydrostatic loading on the adjacent outside walls due to water retained by the floor as shown in Figure 3.

Refer to Figure 3.

Calculate the height of the water applicable to the structure $\left(h_{des}\right)$ as shown below.

$h_{des}=3\text{ft}$

Calculate the hydrostatic loading on the adjacent outside walls due to water retained by the floor as shown below.

$\begin{array}{c}{F}_h=\frac{1}{2}{\gamma }_{s}B{h}_{des}^2\\ =\frac{1}{2}\times \left(70.4\text{lb}/{\text{ft}}^{\text{3}}\right)\times \left(35\text{ft}\right)\times {\left(3\text{ft}\right)}^2\times \frac{1\text{kip}}{1,000\text{lb}}\\ =11.1\text{kips}\end{array}$

Hence, the hydrostatic loading on the adjacent outside walls due to water retained by the floor is $\underset{\_}{F_h=11.1\text{kips}}$.

Consider the orientation coefficient $\left(C_o\right)$ as 0.65.

Calculate the debris impact load applied to the free standing column CD as shown below.

$\begin{array}{c}{F}_i=330C_o{I}_{tsu}\\ =330\times 0.65\times 1\\ =214.5\text{kips}\end{array}$

Therefore, the debris impact load applied to the free standing column CD is $\underset{\_}{F_i=214.5\text{kips}}$.