The actual weight of the Rectangular Aluminum Beam (used in Task 3) is 25 grams,

Question

The actual weight of the Rectangular Aluminum Beam (used in Task 3) is 25 grams, while the actual weight of the Square Aluminum Box Beam is only 5 grams.
But under the maximum applied force (500 grams), the deflection of the Rectangular Beam was greater than the deflection of the Square (Open) Box Beam, as shown in the table below:
Aluminum Beams Weight of Beam Maximum deflection (at 500 grams)
Rectangular Solid Beam 25 grams ~ 0.250"
Square (Open) Box Beam 5 grams ~ 0.170"

Discuss and explain this apparent contradiction

Explanation / Answer

The most important factor to resist or reduce the deflections or stresses is the moment of inertia of cross section, - The weight of (Rec. - sec.) greater than weight of (Square Box - sec.); because the cross sectional area of (Rec. - sec.) > (Square Box - sec.) - (Square Box - sec.) stronger than (Rec. - sec.) to resist the applied loads on the beam (reducing stresses and deflections); because the moment of inertia of (Square Box - sec.) grater than moment of inertia of (Rec. - sec.) You can prove that by assuming two cross sections and compare the cross sectional areas and inertia of the assumed sections.

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