The beams, one having square cross-section and another circular

The beams, one having square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then

1. maximum bending stress developed in both the beams is the same
2. the circular beam experience more bending stress than the square one
3. the square beam experiences more bending stress than the circular one
4. as the material is same both beams will experience same deformation

Since cross-sectional area of square and circular cross-sections are equal
Let d = diameter of circular cross-section
a² = side of square

∴	π	d² = a²
	4

Now, σ for circular cross section

=	M.C.
	I

σ for square cross section

=	M.C.	= M	(a / 2)	=	6M
	I		(a⁴ / 12)		a³

=	32M	×	a³
	πd³		6M

Since , a =	π	d² = 7
	4

σ for circular cross-section > σ for square cross section.