Last Updated on September 10, 2026 by Maged kamel
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.
Another approach to get the x-bar for a right-angle case 1 is to use a vertical strip to find 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.
The Area of the strip is the Product of (y*dx), which is the Area of the hatched strip.
The strip has width dx and height y. dA = y*dx. Since we are integrating in the x-direction, we omit y by substituting its value in terms of x. The value of y can be expressed as (-h*x/b)+h. The next image shows the procedure. The Area is 0.50bh, the same result obtained earlier using the horizontal strip.
Perform integration for the vertical strip to get the first-moment Area about the Y-axis.
To get X-bar for right-angle case 1 using a vertical strip. Start using a vertical strip for which the Expression of dA*x-strip will be represented by the first Moment of Area about the y-axis, where 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 integration process is shown in the next slide image. The final A*x bar represents the Product of the total Area and the horizontal CG distance from the y-axis, which will be found as: in our case=b^2*h/6, where b is the Triangle base. At the same Time, h is the height—the Area = 0.50bh, which is the same result obtained earlier 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 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 get x-bar for a right angle as b/3, or one-third of the base width. The next slide image shows the value of the X-bar.
You can view or download the PDF for this post and the previous 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?