Last Updated on October 17, 2026 by Maged kamel
Y-bar for a right-angle-case-1, using a vertical strip.
For more information on the difference between case 1 and case 2, see Post 2.
The following explanation clarifies how to calculate y-bar for a right-angle case 1.
Using a vertical strip to get the y-bar for a right-angle case 1.
For another approach, use a vertical strip to find y-bar, or the Cg vertical distance to the X-axis.
We have the X and Y axes, respectively, and a width of b. Line AB has length b; the Triangle’s rise is h, and the inclined portion AC has the equation y = mx + C, where m = -h/b and the y-intercept is h. The Area of the strip is the Product of (y*dx).
The strip has width dx and height y. The strip Area is dA = y*dx. We are integrating from x=0 to x=b.
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 Area is 0.50*b*h, he same result obtained earlier using 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 slope is negative, and the intercept equals h, the Triangle height.
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, where b is the Triangle base, and h is the height. To find the y-bar Value, please refer to the following slide.
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 height of the opposite side. The next slide shows the Value of y-bar. The value of Y-bar is similar to the Value obtained by using a horizontal strip.
You can view or download the PDF for this Post and the previous Post.
For an external reference, please see the following Link.
The next Post shows X bar for the right-angle case 2.