Second Moment of Area Example 4 (I beam)

The video tutorial demonstrates how to calculate the second moment of area for an I-beam about the X-axis at the centroid. The instructor advises against using calculus due to the complexity of the shape and instead recommends using formulas for rectangles and the parallel axis theorem. The I-beam is deconstructed into three rectangles, and the second moment of area is calculated for each, then summed to find the total. The final result is presented in millimeters to the fourth power.

What is the main reason the instructor advises against using calculus for this problem?

• The shape is complex and not friendly for calculus.

• The instructor prefers using calculus for simpler shapes.

• Calculus is not accurate for this problem.

• The shape is too simple for calculus.

Which formula is used to calculate the second moment of area for a rectangle at its centroid?

• Base times height squared

• One on twelve base times height cubed

• Base times height cubed

• One on twelve base times height squared

What does the parallel axis theorem help to determine?

• The second moment of area about a parallel axis

• The centroid of a shape

• The area of a rectangle

• The distance between two axes

How is the I-beam deconstructed for the calculation?

• Into one large square

• Into four circles

• Into three rectangles

• Into two triangles

Why is the parallel axis theorem not needed for the blue rectangle?

• The blue rectangle is symmetrical.

• The axis of the blue rectangle is already at the centroid.

• The blue rectangle is not part of the I-beam.

• The blue rectangle is too small.

What is the final result of the second moment of area for the I-beam?

• 4.52 * 10^8 millimeters to the power of four

• 5.42 * 10^8 millimeters to the power of four

• 5.42 * 10^6 millimeters to the power of four

• 4.52 * 10^6 millimeters to the power of four

What is the purpose of summing the second moments of area for the three rectangles?

• To find the height of the I-beam

• To calculate the total second moment of area for the I-beam

• To determine the weight of the I-beam

• To find the total area of the I-beam