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.

Explosion Formula

Skyscraper's are noted to be 100 to 150 meters in height, though using a median, I'm using 125 meters.

W = (125m)^3*((27136*1.37895+8649)^(1/2)/13568-93/13568)^2

W = 156.9696009738101485 Tons of TNT or 6.5676081047442163e11 Joules, City Distrct 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.

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.