Richard Morris, Joe Kardos, Josh Hanke, Jenny Folinusz
Cranford High School

Tall Buildings Project: "The Lava Lamp"

Through the partnership of Kean University and Cranford High School's University Program, high school students were presented with the idea of designing what could be the tallest building in the world. Instituted by Dr. Charles H. Murphy, Executive Director at the New Jersey Center for Science and Technology Education, we were presented with specific specifications to propose a 120-story skyscraper. Although we had specifications, we did not factor considerations (to a large extent) such as building materials, cost, the environment, and the overall impact on its surroundings. We were asked to design a tall building by calculating the building properties and determining the I-Beam column requirements. Our building required:

• 120 Floors
• Floor to Floor Height = 12.5
• Dead Load per floor = 45 lbs/sq ft
• Live Load per floor = 53 lbs/sq ft
• Total Floor space= 3.5 to 4.8 million sq ft

In the development of our building, we had control over two variables:

• Building Profile (sq ft per floor)
• Column Spacing

In our considerations for the aesthetics of the building, we decided to design our building like most others, big at the bottom and small at the top. However, we took a different approach to the design in which it moved from big to small. Instead of having sharp corners and right angles, we decided to institute diagonal- and curve-like features into the profile. From our design, we had to determine many facets:

• Determine the sq ft of area per floor, especially since the design requires a different measurement for each floor
• Calculate the total floor load
• Determine the load per column
• Add the total column weight to floor
• Decide the column spacing
• Determine column types
• Establish a suitable I-Beam Column for every 10 floors (See Determining Suitable I-Beam Column)

To calculate the area per floor, we designed our building and measured the width of the building at every design change, which is set at a floor of 10 or 5. Setting the area of Floor 120 to be 7,000 sq ft, we, using proportions, determined the area of every 10th floor and the 5th floor for Floor 15. In the end, our math proved correct in each step, since Floor 1 had an area of 61,000, which was 8 5/7ths wider than the first floor.

To determine the suitable I-Beam Columns for every 10 floors (as was required by Dr. Murphy), we had to take into account that each floor (or every 10 floors) must support the allowable load. In selecting our I-Beams, we had to factor in certain criteria:

• Length (effective length)
• Cross Sectional Area
• Radius of Gyration
• Safety Factors
• Slenderness Ratio (also critical value)
• Allowable Stress
• Allowable Load
• Properties of Steel:
• Young's Modulus (30 * 106 psi)
• Yield Stress (3.4 * 104 psi)

In picking an I-Beam Column, we followed these 9 steps:

1. 1. Determine the required load RL in pounds that the column must support, let us use 186,863 lbs.
2. 2. Assume an initial safety factor of FS=1.667
3. 3. The yield stress for steel is 34,000 psi, so calculate the allowable stress AS by dividing the yield stress by the safety factor. AS=34,000/1.667 = 20395 lbs/sq in
4. 4. Determine the minimum cross sectional area A of the I-beam as the required load divided by the allowable stress. A=RL/AS = 186,863/20,395 = 9.16 sq in
5. 5. Pick the I-beam from the table that has a cross sectional area that is larger than found in 4. (W10x39, A=9.71 R=1.94)
6. 6. We use a factor called the critical slenderness ratio C=132. Calculate the slenderness ratio SL for your beam, use the radius of gyration R from the table and the length of the beam L (i.e. the floor to floor distance of your building, we will use 12.5 feet = 150 inches) as: SR=0.7*L(inches)/R(inches) = 0.7*150/1.94 = 54.124
7. 7. Now find the allowable stress for this beam from: AS = (34,000/1.9)(1-0.5(SR/132)^2) = (34,000/1.9)(1-0.5(54.124/132)^2) = 17188.28 lbs/sq in
8. 8. Determine allowable load AL for this beam from: AL=AS*(cross sectional area of beam) = 17188.28*9.71 = 166898. 23 lbs
9. 9. If AL is less than required load, as is shown, go back to 5 and pick next largest area.

Note: The table used can be found at:
http://physics.uwstout.edu/StatStr/Statics/tables/ibd.htm

In our investigation, we were successful in designing a building according to the specifications given. We learned much of the terminology that concerns the construction of a building, such as dead load (weight of structure), live load (weight of building contents), column (vertical support between floors), Beam (horizontal supports for floors), and I-Beam (steel beam with I-cross section). We also learned how to calculate the various measurements that are required for developing the building.

All in all, our group was extremely motivated to be successful in designing the tallest building in the world. Although we only took into account a minimized portion of specifications and concerns, we obtained a working idea of what goes into the development and overall design of a building.