User:GiverOfThePeace/Standard Calculation for Destroying a Skyscraper

Introduction

There's a couple of times where skyscraper destruction is done in series and for a bit it was assumed to be large building but after this calculation we'll see how legitimate that is.

Exploding a Skyscraper

Assume a typical high-rise building has a height of 100 meters.

W = (100m)^3*((27136*1.37895+8649)^(1/2)/13568-93/13568)^2

W = 80.368435698590796 Tons of TNT or 3.3626153496290393e11 Joules, City Block level.

Toppling a Skyscraper

We'll be using Gravitational Potential Energy for this one.

U=m g h

Where
U = gravitational energy m = mass g = gravitational field h = height

Step I: Mass of the Building
Assume a typical high-rise building has a height of 100 meters and a base area of 40 meters by 40 meters. The volume of the building can be calculated as: Volume = Height × Base Area = 100m × 40m × 40m = 160,000m³

Assume the building is made of reinforced concrete and steel, with the following densities:

Reinforced Concrete Density: 2400 kg/m³ Steel Density: 7850 kg/m³ Assume the building is composed of 80% concrete and 20% steel by volume. The mass of the concrete and steel in the building can be calculated as:

Mass of Concrete = 160,000m³ × 0.8 ×2400kg/m³ = 307,200,000 kg Mass of Steel= 160,000m³ × 0.2 × 7850kg/m<sup3 = 251,200,000 kg

Total Mass = 307,200,000 kg + 251,200,000 kg

Total Mass = 558,400,000 kg

Step II: Gravitational Field
This one is easy, acceleration due to gravity on Earth is 9.8 m/s².

Step III: Height
Assume a typical high-rise building has a height of 100 meters.

Step IV: Formula U=m g h

U = (558,400,000 kg) * (9.8 m/s²) * (100 m)

U = 5.47232e11 Joules or 130.791586998088 Tons of TNT, 8-A.

Cutting a Skyscraper

For cutting a skyscraper, we must find the following:

Step I: Mass of the Building
Assume a typical high-rise building has a height of 100 meters and a base area of 40 meters by 40 meters. The volume of the building can be calculated as: Volume = Height × Base Area = 100m × 40m × 40m = 160,000m³

Assume the building is made of reinforced concrete and steel, with the following densities:

Reinforced Concrete Density: 2400 kg/m³ Steel Density: 7850 kg/m³ Assume the building is composed of 80% concrete and 20% steel by volume. The mass of the concrete and steel in the building can be calculated as:

Mass of Concrete = 160,000m³ × 0.8 ×2400kg/m³ = 307,200,000 kg Mass of Steel= 160,000m³ × 0.2 × 7850kg/m<sup3 = 251,200,000 kg

Total Mass = 307,200,000 kg + 251,200,000 kg

Total Mass = 558,400,000 kg

Step II: Energy Required to Cut Steel
I couldn't find much on it beyond some sources saying that, so I'll have to do a calculation within a calculation.

Cutting force is

F= Tensile Strength * Area

Mild Steel's MPA value is 620.

1 MPa = 1×10⁶ N/m²

So 6.2e+8 N/m²

Assuming the height and width of a skyscraper is being cut for this case, we get:

100 m * 40m = 4000 m²

F = 6.2e+8 N/m² * 4000 m²

F = 2.48e12 N

Now we need to find convert this to energy, but we can't covert Newtons to Joules conventionally, it needs to be Newtons * Meters to convert to joules, luckily we have one more piece we left out, the other 40 meters.

J = Newtons * meters

J = 2.48e12 N * 40 m

J = 9.92e13 Joules

Now we use the volume of the skyscraper and divide it, since that's what's being cut.

Energy Density = (9.92e13 Joules)/(1.6e+11 cc)

Energy required to cut steel = 620 J/cc

Alright, jesus that's done, now then.

Step III: Getting the results
Now we convert 620 J/cc to J/m³

Which gets us 620000000J/m³

Energy Required = Volume × Specific Energy

Energy Required = (160,000m³) * (620000000J/m³)

E = 9.92e13 Joules or 23.709369024856596 Kilotons of TNT, Town level

Pulverizing a Skyscaper

To estimate the energy required to pulverize entire high-rise buildings, we'll break down the problem into several steps. Step 1: Size of the Building
Assume a typical high-rise building has a height of 100 meters and a base area of 40 meters by 40 meters. The volume of the building can be calculated as: Volume = Height × Base Area = 100m × 40m × 40m = 160,000m³

Step 2: Material and Mass
Assume the building is made of reinforced concrete and steel, with the following densities:

Reinforced Concrete Density: 2400 kg/m³ Steel Density: 7850 kg/m³ Assume the building is composed of 80% concrete and 20% steel by volume. The mass of the concrete and steel in the building can be calculated as:

Mass of Concrete = 160,000m³ × 0.8 ×2400kg/m³ = 307,200,000 kg Mass of Steel= 160,000m³ × 0.2 × 7850kg/m<sup3 = 251,200,000 kg

Step 3: Energy Required to Pulverize
The specific energy required to pulverize the materials is:

Concrete Pulverization Energy: 10⁶J/m³ ("Concrete and Masonry Databook" by Christine Beall and "Recycling of Demolished Concrete and Masonry" edited by T.C. Hansen both list energy requirements for crushing concrete, falling within the range of 1 to 10 MJ/m³)

Steel Pulverization Energy: 10⁸J/m³ (Steel is significantly harder to pulverize compared to concrete, requiring much higher energy due to its tensile strength and ductility. The value of ~10^8 J/m³ can be estimated based on the energy required for high-intensity processes like ball milling or other forms of mechanical alloying, where steel is broken down into fine particles. "Introduction to the Mechanical Behavior of Steel" by G. Krauss and "Mechanical Alloying And Milling" by C. Suryanarayana go further into this)

Step 4: Total Energy
The total energy required to pulverize the concrete and steel can be calculated as:

Energy for Concrete = 307,200,000 kg × 10⁶J/m³ = 3.072×10¹⁴J

Energy for Steel = 251,200,000 kg × 10⁸J/m³ = 2.512×10¹⁶J

Adding these together gives the total energy required:

Total Energy = 3.072×10¹⁴J + 2.512×10¹⁶J = 2.54272×10¹⁶J or 6.0772466539196940971 Megatons of TNT, 7-B.