Lecture 28 Built-Up Sections Example Problem

Lecture 28
Example Problem

Built-Up Sections

Given:
the following cross sections
Determine:
Ix of each section considering its component parts.
built-up sections

Solution:
The top shape can either be treated as two smaller rectangles or one large rectangle. It CANNOT be treated as four small rectangles using the rectangle formula because that formula gives the moment about the axis through the centroid of the area only. Therefore, the centroidal axis of the small areas must be the same as the centroidal axis of the larger area. Later a formula will be given which makes it possible to transfer moments from one centroidal axis to another, but that is not possible at this t ime.

I_xx as two small rectangles:

I_xx = (2)(1/12)(2in)(6in)³ = 72 in⁴

I_xx as one large rectangle:

I_xx = 1/12(4in)(6in)³ = 72 in⁴

The trick to the second shape is to find the moment of inertia of the large shape as if it were a solid rectangle and then subtract the moment of inertia of the smaller rectangular shape of the hole. The remainder will be the moment of inertia of the rin g. This is possible because the two shapes have the same centroidal axis.

I_xx = 1/12(12in)(16in)³ - 1/12(6in)(8in)³

4096 in⁴ - 256 in⁴

3840 in⁴

Lecture 28 Example Problem

Lecture 28
Example Problem