What are the requirements for an underwater structure to maintain its structural integrity?

The results table for Figure 8 may be found in Results for thickness and maximum depth for HSLA.

The table of results for the subsequent Figure can be found in. Results for Acrylic Thickness and Maximum Force. In order to calculate the pressure acting on the structure, i.e. P = \(F \over A\), the surface area must also be measured. In Fusion 360, the surface area is specified.

Another important aspect of this inquiry is finding out how the thickness of a material would affect its strength and the depth at which it can be placed. The most significant force required to achieve a safety factor of 1.0 for each thickness will be calculated to determine this. The trend will then be chosen by plotting the graph. The two equations provided in the essay's "Background information" section will determine each thickness's height. The findings will be planned, and a correlation between size and consistency will be noted.

 

Figure 5 provides a picture of the experiment, and Figure 6 illustrates how the material's thickness will be altered.

Figure 8 shows that the depth to which the HSLA can be submerged exponentially increases with increasing thickness; for 0.2 m thickness, the depth was approximately 175 m, and for 0.4 m thickness, it was around 750 m.

 

The maximum thickness for an underwater construction would be 0.3 metres since, as previously stated, the regular room height cannot be less than 2.40 metres. This is because 3.0 - 0.6 = 2.40 metres. The thickness had to be substituted into the line of the best-fit equation to determine the maximum depth of the water at which the construction may be placed. The maximum depth to which a structure with a thickness of 0.3 metres can be lowered without losing structural integrity is determined by the equation y = 24.9e^8.06x, where x = 0.3 is substituted into y to obtain the value of 279.5m.

 

The depth for acrylic must be computed in the same way as it was for HSLA. Figure 9 depicts a piece of acrylic with dimensions 4.88 m x 2.40 m. This site was selected because it allows the acrylic to fit in the semi-hollow structural shape with a thickness of 0.3 metres, which is the size necessary for the acrylic to work as the hotel room window.

A two-dimensional ball on the ocean floor is seen in Figure 1. The black arrows show the direction of the forces being applied to the surfaces by the pressure of the water. Underwater, the water's pressure exerts itself perpendicular to the surface in all directions around the ball, constantly acting in its path. The yellow arrow with the designation W shows the weight of the object. The red arrow, FB, indicates the buoyancy force. This is a simple model of how an object and the forces acting on it interact underwater. Because no net staff is working on the ball, it does not deform. The ball is balanced at this moment. This ball is depicted at a modest scale and would weigh less than an undersea hotel.

 

The pressure acting on the item must also be known to determine whether the construction retains its structural integrity. The equations used to determine the pressure exerted on the object are.

 

P = \(\pmb{F \over A}\)

 

P – Pressure (Pa)

 

F — Force (N)

 

A — Area (m²)

 

Note that stress, defined as the force per unit area, is also calculated using this equation. On the other hand, the pressure only acts at a 90-degree angle to the surface, whereas stress can also act parallel to the surface. Both have the same units.

 

𝐏 = 𝛒 ∗ 𝐠 ∗ 𝐡

 

For the derivation of this equation, refer to the Derivation of the pressure equation.

 

P = Pressure (Pa)

 

ρ — density of the fluid (kg/m³)

 

g — gravitational acceleration (ms-²)

 

h — height from the surface of the water to the object (m)

 

The hydrostatic pressure, or the pressure caused by water at various depths, is determined by this equation, as should be noted. This study will employ water with a density of 1027 kg/m³, as stated by the National Earth Science Teachers Association (2001). There will be a gravitational acceleration of 9.81ms^-2 (Henderson, n.d.)

 

This equation will be used to find the total pressure acting in a particular area.

 

P_total = P_atm + ρgh

 

P_total — Total Pressure (Pa)

 

P_atm — Atmospheric pressure (Pa)

 

It should be noted that atmospheric pressure is regarded as constant, and its value is 1.01×10⁵ Pa (Khan, 2014).

The maximum force required to maintain the safety factor increases with increasing acrylic thickness, as shown in Figure 10, where the entire staff for Acrylic with a 0.1 m thickness is approximately 6.0 x 10⁸N and for Acrylic with a 0.2 m thickness is 7.5 x 10⁸N.

 

The formulas P = \(F \over A\) and P = ρgh were used to determine the maximum depth of water for acrylic at each thickness. Below is a calculation example.

 

For 0.1m

 

P = \(F \over A\)

 

𝑃 = \(6.0∗10^8 \over 13.168\) = 4.5565 x 10⁷ Pa

 

Ptotal = patm + ρgh

 

4.5565 x 10⁷ = 1.1 x 10⁵ + 1027(9.81h)

 

2.41196 x 10⁷ = 1.1 x 10⁵ + 10074.87h

 

h = 4511.72 m

 

The calculations shown above were repeated with the different forces and surface areas. Refer to Calculations for maximum depth for Acrylic for the rest of the estimates for the different thicknesses.

The strength of the materials must be looked into to identify the best ones for an underwater structure. To do this, it will be necessary to compare the materials' safety factors. A system's safety factor demonstrates its reliability under the predicted load. The following formula can be used to determine safety factors.

 

Safety factor = Strength of material / Stress_max

 

A system is twice as vital for the anticipated load if it has a safety factor. For a structure to maintain its structural integrity, the maximum stress must always be less than the material's stress, or the safety factor must not drop below the 1.0 level.

 

First, a size that is adequate for the building must be used. The average hotel room in the US is 325 square feet or around square metres. Thus, a semi-hollow cube with dimensions 5.48 m x 5.48 m x 3.00 m and a thickness of 0.25 m was generated in Fusion 360. This cube will remain constant, but the essay will later analyze the link between thickness, strength, and depth. The height of 3.00m was picked since it was the most accessible quantity to use, and online research revealed that the usual room height is between 2.4m and 3.0m (Constructor, n.d.). The force applied to the object would then be raised until it reached a safety factor below 1.0. A specific amount would reduce the pressure after determining the maximum power, and the structure's safety factors would be noted. Following that, the graphs for each material were plotted. Six materials were used in this process: glass, acrylic, steel, wood, and mild steel. HSLA stands for High Strength Low Alloy. Results for Materials' Strength contains a table of values for each material.

 

The picture of the simulation is shown in Figure 2.

The results table for the subsequent graph can be found in. Results for Thickness and Force for HSLA. In order to calculate the pressure acting on the structure, i.e. P = \(F \over A\), the surface area must also be measured. In Fusion 360, the surface area is specified.

Refer to Results for Materials' Strength to view the results table. Figure 2 depicts the safety factor against force graph for all materials.

According to Figure 7, the relationship between thickness and maximum force is inversely proportional. For example, for a 0.2 m thickness, the maximum force is roughly 7.00 x 107 N, while for a 0.4 m thickness, the maximum force is roughly 6.0 x 108 N. As thickness increases, this relationship between maximum force and safety factor increases exponentially. The formula P = \(F \over A\) and P = ρgh was used to calculate the maximum depth of water for the HSLA for each thickness after determining the maximum force for each thickness. The calculating example is displayed below.

 

For 0.1m.

 

P = \(F \over A\)

 

𝑃 = \(2.5∗10^7 \over 77.6944\) = 321774 Pa

 

Ptotal = Patm + ρgh

 

321774 = 1.1 x 10⁵ + 1027(9.81h)

 

321774 = 1.1 x 10⁵ + 10074.87h

 

h = 21.02 m

 

The calculations depicted above were carried out again using various forces and surface areas. For the remaining calculations for the various thicknesses, see Calculations for Maximum Depth for HSLA.

When the data are plotted on the graph in Figure 3, it can be seen that HSLA is the strongest material and glass is the weakest one. This is because the highest force that HSLA could withstand before deforming was about 3.50 x 108 N, as reported in the results table. It would be attractive if consumers had windows to observe the underwater views, however acrylic or glass must be taken into consideration in the structure. According to the graph, acrylic is more durable than glass since glass can withstand 1.9 x 107 N for a safety value of 1.29, whereas acrylic can withstand around 1.6 x 107 N for the same safety factor. Thus, it can be inferred from this that HSLA and acrylic are the two materials that ought to be employed in underwater construction. Because HSLA is an alloy, which means it is composed of two or more different metals, it is extreme. Carbon, vanadium, copper, nickel, titanium, and niobium are the main ingredients in HSLA.

Anything that has been built by assembling parts is considered a structure. This essay will only discuss submerged buildings, such as hotels, restaurants, and tunnels, which are continually being constructed around the globe, from Dubai to London. However, it might also be built to lessen the effects of congestion on land, which could be a potential future solution to the exponential growth of the world's population. The primary goal of developing underwater structures is to enhance tourism owing to the ocean vistas. In comparison to land-based structures, underwater structures are considerably different. When building an underwater structure, several other aspects must be considered, including the depth of the water, the material, the strength and thickness of the material, and the structure's shape to the pressure of the water. In this extended essay, we'll try to find out what it takes for underwater structures to be structurally sound. The ability of a structure to remain stable and maintain its shape without distorting is known as structural integrity. All of the previously listed criteria will need to be tested using a simulation to provide an answer to the research question.

 

This subject merits discussion since one potential future answer to the overpopulation problem is undersea development. Additionally, as a student who aspires to major in Civil Engineering at university, knowing the physics behind underwater structures would help me become more engaged with the subject, and I will better comprehend the fundamental concepts of this engineering branch through experimentation.

 

The primary goal of this essay is to build a model with adequate dimensions that will be used to simulate everything. Then, a material that is appropriate for the structure and will allow it to preserve its structural integrity will be discovered. The structure's maximum depth before collapsing or deforming owing to underwater pressure would be determined together with an acceptable thickness utilizing the ideal material. The construction will next be given a suitable shape to bear the strain. The research will be finished by stating the precise guidelines for any undersea structure to retain structural integrity.

 

Fusion 360, an integrated 3D CAD (Computer-Aided Design), CAM (Computer-Aided Manufacturing), and CAE (Computer-Aided Engineering) program for modelling, simulating, and analyzing buildings, will be used for this inquiry.

Figure 5 depicts a schematic of an alloy with atoms from two different metals of various sizes. Alloys are the most vital sort of metal because the variable-sized particles in the combined metals cause the atomic layers to be less regular, which prevents them from sliding as quickly. Other than HSLA, several other alloys, such as carbon steel, have characteristics similar to HSLA and would be suitable for underwater buildings due to their strength.

 

According to additional research, high-strength alloy steel is also employed to construct bridges and other strong constructions. This demonstrates why HSLA steel is a good material for underwater structures. Additionally, acrylic is less dense than glass when compared to drink, so it is a suitable material to utilize. According to this simulation, glass has a 2.18 x 106 kg/mm³, but acrylic density is 1.19 x 106 kg/mm³. Even while acrylic and glass have around 90% light transmission (Genzo Shimadzu, n.d.), glass damages with an average energy need of 1.08 ft-lb, which may be converted to 4.06 J for acrylic and 1.08 J for glass, respectively (Ghose, n.d.). As a result, acrylic is nearly four times more durable. Acrylic is a suitable material for underwater buildings because it is also utilized for submarine windows.

Understanding the fundamental physics underlying underwater structures is essential before beginning the investigation.