Why the rectangular beam is more efficient than circular beam?
Answers
Answer:
The answer provided by HeroUjaan is spot on, I’ll just add the mathematical equations involved that show exactly how the moment of inertia is the contributing factor to decide which cross-sectional shape will better perform against the same bending moment:
In structural mechanics, “more efficient” against bending usually means the particular cross-section will develop lower bending stress (σ) under the action of the same bending moment (M). The formula for determining the bending stress in a beam under simple bending is:
σ=My/I ; (Ref.)
Where I = moment of inertia of the particular cross-section,
y = distance of a horizontal plane on the cross-section from the neutral axis plane (usually the centroidal axis plane)
Therefore, for the same M and same y in the above formula, lowering the bending stress (σ) will require the moment of inertia (I) to be higher. Now, let’s check whether the circular section or the square section has the higher value of I:
The area (A) of a square section with side h is A=h2 and its I=h4/12
The area (A) of a circular section with radius r is A=πr2 and its I=πr4/4
Given that the two areas are equal: h2=πr2 or, r=h/π−−√
Plugging this value of r into the circular I=πr4/4 will give: I=h4/4π=h4/12.57 which is smaller than the I for square section: I=h4/12
Therefore, the higher value of I for the square section means the bending stress will be lower at any point on the square cross-section compared to the circular section and the square section will be more efficient.
Answer:
Explanation:
circular