Per code, steel I-beams used in the supporting structure of a stadium sunshade should have the moment of inertia equal to 2.64 in⁴ or more.

The engineer would like to evaluate if the weight of the structure can be reduced by replacing steel with aluminum.

Aluminum alloys are a favored material in modern construction due to their lighter weight, fairly high strength-to-weight ratio, and resistance to corrosion.

Next Steps:

1. Search for the material properties of steel and aluminum
2. Calculate moment of inertia, section area, and nominal weight of both steel and aluminum
3. Compare the properties to determine if aluminum is an acceptable substitute for steel

Searching for Properties of Steel and Aluminum in Knovel

The engineer starts by searching for 'material selection'

(Click to run search)

and open Chapter 11, Selection of Material and Shape of the Materials Selection in Mechanical Design (3rd Edition).

In the bookmark, select Section 11.5 Exploring and Comparing Structural Sections and navigate to Figure 11.12 on page 306.

Using the Interactive Graph in Figure 11.12, find the typical properties of modulus of elasticity and density of steel and aluminum alloys.

Finding Nominal Weight of a Steel Beam

Taking into account that 2.64 in⁴ = 1.1×10^-6 m⁴ and using the “Shape” portion of the Interactive graph, he finds that the typical section area for a steel section is 5.6×10^-4 – 1.6×10^-3 m² (.00056 – .0016 m²).

Using the 7,905 kg/m³ density value for steel found earlier, and Knovel's Unit Converter, this beam's nominal weight is between 4.4 kg/m and12.6 kg/m (or 3.0 and 8.5 lb/ft).

Calculating Moment of Inertia for Aluminum

Since the beam stiffness has to be the same for both steel and aluminum, I_s×E_s = I_a×E_a, the moment of inertia of aluminum alloy beam is I_a = I_s × E_s/E_a.

Thus, I_a = 3.15×10⁶ m⁴ (.0000011 x 203/71).

The same result could be obtained using the "Constraint" portion of the chart:

Determining Aluminum Section Area

Returning to the "Shape" portion of the chart, determine the range of section areas for this I_a. It is between 1.2×10^-3 and 3.7×10^-3 m².

Nominal Weight of Aluminum

Using the 2,640 kg/m³ density value for aluminum found earlier, the nominal weight of the required aluminum beam is then between 3.2 and 9.8 kg/m (or 2.2–6.6 lb/ft).

In one quick search, and use of Knovel's interactive tools, the engineer was able to determine that aluminum could indeed replace the steel structure.

The expected reduction of the weight of the beam resulting from steel being replaced with aluminum is 1.2–2.8 kg/m. It will be 22–27% of the original weight.

The stress on concrete foundation will decrease due to the lower weight of the structure, resulting in a longer lifespan. Additionally, the structure made from aluminum will last longer and require less maintenance compared to steel, due to reduced corrosion.

We want to hear from you! We are constantly looking to develop use cases that are helpful to engineers. We'd like to learn about how Knovel has helped you solve a problem. Please share your experience with us and if your story is selected, you will be awarded a new iPad.

TELL US YOUR KNOVEL STORY then...

489 5th Ave, 9th Floor, NY, NY 10017
Contact Us