Last Updated on September 10, 2026 by Maged kamel
Y-bar for a right-angle-case-1, using a vertical strip.
For more information about the difference between case 1 and case 2, please refer to post-2.
The following explanation clarifies how to calculate the y-bar for a right-angle case 1 effectively.
Using a vertical strip to get the y-bar for a right-angle case 1.
For another approach, use a vertical strip to find the value of y-bar, or the Cg vertical distance to the X-axis.
We have X and Y axes, respectively, and a width equal to b. We have line AB with length b; the triangle’s rise is h, and the inclined portion AC has the equation y = mx + C, where m is the slope, equal to -h/b, and the y-intercept is h. The Area of the strip is the Product of (y*dx).
The width of the strip =dx, and its height is equal to Y. The strip Area is dA = y*dx.
Since we are integrating in the x-direction, we omit y by substituting its value in terms of x. The next image shows the procedure—the aareais t0.50*b*h, he same result obtained earlier bsing the horizontal strip.
Perform integration for the vertical strip to get the Area about the X-axis.
The Expression of dA*y-strip will be represented by the first Moment of Area about the x-axis, where y-strip is the horizontal distance from the Cg of the strip to the x-axis. The Expression of dA*y-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 next slide shows the integration details.
Integrate the vertical strip to find the first moment of Area about the X-axis.
For the Y-bar in the right-angle case (Case 1) using a vertical strip, the first Moment of Area for the small strip about the x-axis is dA*y, where dA = y*dx. We use the equation of line CB: y = -b/c*x + h.
The final A*y bar represents the Product of the total Area and the vertical CG distance from the x-axis, which, in this case, is b*h^2/6 = b*h^2/6, where b is the triangle base and h is the height.
Y-bar for a right-angle triangle: final step.
The y-bar value for a right-angle triangle will be obtained by simply dividing the first Moment of Area by Area of the right-angle triangle. For a right triangle, we can find that y-bar = h/3, or one-third of the opposite side height. The next slide shows the value of y-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 shows X bar for right-angle case 2.