Area moments — square about its base State whether the following is true or false: “The second moment of area (area moment of inertia) of a square of side a about its base is a^4 / 3.”

Introduction / Context:Area moments of inertia are essential in bending stress and deflection calculations. Recognizing standard formulas helps engineers set up beam problems quickly and accurately.

Given Data / Assumptions:

• Plane area: square cross-section of side a.
• Axis: the base line of the square (edge) lying in the plane of the area.
• Use standard area-moment formulas.

Concept / Approach:For a rectangle of breadth b and height h, the area moment about its base is I_base = b * h^3 / 3. A square is a special rectangle with b = a and h = a, so I_base = a * a^3 / 3 = a^4 / 3.

Step-by-Step Solution:

Verification / Alternative check:Using centroidal value I_centroid = b * h^3 / 12 = a^4 / 12 and the parallel-axis theorem to the base at distance a/2: I_base = I_centroid + A * (a/2)^2 = a^4/12 + a^2 * a^2 / 4 = a^4/12 + a^4/4 = a^4/3.

Why Other Options Are Wrong:

• False / mass moment only / centroidal axis: Confuse area vs mass moments or axes; the given base-axis formula is correct.

Common Pitfalls:Mixing up centroidal vs base axes and area moments vs mass moments. Always specify the reference axis.

Final Answer:True