The Minimum Moment of Inertia Calculation for a Steel Beam

The steel beam shown supports a masonry wall. Local codes limit the masonry deflection to L/360. What is most nearly the minimum moment of inertia for the beam?

Minimum Moment of Inertia Calculation

The minimum moment of inertia depends on the length of the beam, load, and material properties. Calculating the minimum moment of inertia requires use of the local code's L/360 limit and the beam's length. An explicit numerical calculation requires more specific information about the beam and load.

Explanation

To solve this problem, we need to recall Moments of Inertia, defined as the measure of an object's resistance to changes in its rotation rate. In the construction industry, it plays a crucial role in designing structural elements, such as the steel beam in this problem.

Local codes pointing out a limit of L/360 implies that the maximum allowable deflection for the beam is its length divided by 360. However, without the values for length of the beam, the actual load and material properties, we can't provide a numerical value for the minimum moment of inertia. Usually the moment of inertia can be found by integrating the square of the distance to the axis of rotation over the object's volume.

Each choice in your question (A) 57in^4, (B) 85 in^4, (C) 132 in ^4, and (D) 176in ^4 can be the actual answer, depending on various factors, so additional information is needed to accurately determine the minimum moment of inertia for the steel beam.