User:Eas4200c.f08.carbon.orear/HW2/Pb1.7

Problem
Make a comparison of the ability to bear loads of the two beams shown below using bending rigidity.

Solution


To find the value of R1, equate the areas of the two beams.

A1 = πRo2 = π m

A2 = 2tRo + 2πR12 = (.002 + 2πR12)m

→ R1 ≈ .06842m

Moments of Interia

Iy,1 = πRo^4/4 = (2.5*10-5)

Iy,2 = bh3/12 + 2[πR14/4 + πR12*d], where d = Ro + R1/2 ≈ .003983m

The moment of inertia of case 2 about the y-axis is much larger than that of case 2 indicating that the second beam has a larger load-bearing capability.