Core of section

Another thing related to the statics – basic info guide is, of course, the guide flat figures. Very often, when the lecturers hand out projects, the core of the given cross-section and the eccentric action of forces are to be determined, and this is due to the connection of these things with each other. A person who will understand this problem well and make a few examples, without calculations, can determine what the core will look like for the given cross-section. Let’s explain what is the core of the cross-section?

The cross-sectional core is the cross-sectional area in which the applied normal force causes the same sign (+ or -) in the entire cross-section. We will now learn the formulas needed to determine the core and show what the core of the cross-section should look like on the example of the I-beam 140.

Before proceeding to the calculations, a contour on the characteristic points should be drawn. In this case, a rectangle will come out.

For example, let’s see the outline of a figure made of I-beam 140 and C-section 140. The C-section bar lies on a I-section beam.

The outline is no longer a simple figure. Let’s return to our I-section 140. Starting calculations, we have to designate the main rays of inertia. We make these calculations using the following formula.

i_{x}^{2}= \frac{J_{1}}{A}            i_{y}^{2}=\frac{J_{2}}{A}

where:

J_{1}\; \; and\; \; J_{2} – the main central moments of inertia
A – cross-section area

Having the designated main inertia rays, we can set the core in the given cross-section. To do this we will use the following formulas.

X_{0}=-\frac{i_{y}^2}{X_{n}}          Y_{o}=-\frac{i_{x}^2}{Y_{n}}

where:

X_{0} – coordinate which should be set on the X axis
Y_{0} – coordinate which should be set on the Y axis
i_{x}^{2}\; \; and \; \; i_{y}^{2} – the main rays of inertia
X_{n}\; \; and \; \; Y_{n} – coordinates of the point at which force is applied

In our case, the above two formulas should be used for four points A, B, C and D.
With the results already on the X axis, measure the calculated coordinate and mark with a dot, then on the Y axis also measure the calculated coordinate and mark with a dot, and then combine them. The above steps are repeated for each calculated point.
I recommend using a different colors for each point to make it transparent. It should look like this:

Warning!
The core area can’t go beyond the area of the drawn circuit!

It is best to make a 1: 1 scale drawing to be sure that we have calculated the core well.
I hope that you can handle your projects with great success, good luck!