Breif description of Post 2a-inertia.

2a- X bar for a right angle-case-1-using vertical strip.

X bar for a right angle-case-1-using vertical strip.

For more information about the difference between case-1 and case-2, please refer to post-2.

Using a vertical strip to get x bar for a right angle case-1.

Fo another approach to get X bar for a right angle-case-1 by using a vertical strip to get the value of the X bar or the Cg horizontal distance to the y-axis.


We have X and Y axes respectively and the base of the triangle. We have line AB with the length of b, the rise of the triangle is=h, and the inclined portion AC, equation: y =mx+C m which is a slope is equal to -h/b *x, and the intersection with y-axis =h.

You can click on any picture to enlarge, then press the small arrow at the right to review all the other images as a slide show.

Derive the expression for the first moment of area for a right angle using a vertical strip.

The area of the strip is the product of (y*dx), which is the area of the hatched strip.

The width of strip =dx and its height=y.dA=y*dx, since we are integrating into the x-direction we will omit the expression of y, by substituting its value in terms of x. the value of y can be expressed as equal to (-h*X/b)+h. The procedure is shown in the next image picture.

The area of a right-angle triangle using a vertical strip.

The area=0.50*b*h, which is the same result obtained earlier by using the horizontal strip.

Perform integration for the vertical strip to get the first-moment area about the Y-axis.

to get the X bar for a right angle-case-1, using a vertical strip. Start using a vertical strip for which, the expression of the dA*x-strip will be represented by the first moment of area about the y-axis, where the x-strip is the horizontal distance from the Cg of the strip to the y-axis.

The expression of dA*x-strip is shown in the next slide image and integration will be carried out in the horizontal direction from x=0 to x=b.

The detailed process of integration can be found in the next slide image. The final A*x bar represents the product of total area * the horizontal CG distance from the y-axis will be found as= in our case=b^2*h/6, where b is the triangle base while h is the height.

Derive the expression for the first moment of area for a right angle – case-1 by using a vertical strip.

The area=0.50*b*h, which is the same result obtained earlier by using the horizontal strip.

X bar for a right angle final step.

X bar for a right angle-case-1. The value of X bar value will be obtained by simply dividing the first moment of area /Area. the first moment of Area can be found as equal to (b^2*h/6). We will get an x bar for a right angle=b/3 or one-third of the base width.

X bar for a right angle-case-1

The next slide image shows the value of the X-bar.

This is the link to view or download the pdf used for the illustration of this post.

For a good external reference, please refer to the following link.
The next post is How to determine y bar for a right angle-case-1?

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