How to find Centroid of an I - Section | Problem 1 |

Summary

In this engineering mechanics lecture, the tutor explains how to calculate the centroid of an unequal I-section. The section is broken down into three rectangles, and their areas, x-coordinates, and y-coordinates are calculated step-by-step. The x-coordinate remains constant, while the y-coordinate is derived for each rectangle. The tutor then uses a formula to compute the centroid's coordinates. The session ends with the centroid values for the I-section. This tutorial is part of a series on centroid calculations involving various geometric sections like L, T, and S sections.

Takeaways

• 📐 The session covers centroid calculations in engineering mechanics, focusing on an unequal I-section.
• 🟦 The I-section is composed of three rectangles, and the instructor labels them as 1, 2, and 3 for easy reference.
• 🔀 The I-section is symmetrical along the vertical Y-axis, meaning the centroid will lie on this axis.
• 📊 A table is used to calculate the areas and coordinates of the centroids for each rectangle in the section.
• 📝 Areas of the three rectangles are calculated: 150 cm² for the first, 75 cm² for the second, and 100 cm² for the third.
• 📏 Since the rectangles are symmetrical, all x-coordinates of the centroids are the same at 15 cm.
• 📍 The y-coordinates for the centroids are calculated as 2.5 cm for rectangle 1, 12.5 cm for rectangle 2, and 22.5 cm for rectangle 3.
• 🔢 The formula to calculate the x and y coordinates of the overall centroid is shown and applied.
• 📐 The x-coordinate (Xc) of the centroid is 15 cm, and the y-coordinate (Yc) is 10.96 cm.
• 🎥 The instructor encourages viewers to ask questions and subscribe for more content on engineering mechanics.

Q & A

What is the main focus of the video lecture?

The video lecture focuses on solving problems related to centroid calculations, particularly with an unequal I-section.

How is the I-section described in the lecture?

The I-section is described as symmetrical about the Y-axis and is made up of three rectangles.

Why are the x-coordinates of the centroids of the rectangles the same?

The x-coordinates of the centroids of all three rectangles are the same because the I-section is symmetrical about the Y-axis.

How are the areas of the three rectangles calculated?

The areas of the three rectangles are calculated by multiplying their lengths and widths. For example, the area of the first rectangle is 30 x 5 = 150 cm².

What is the formula used to calculate the x-coordinate of the centroid?

The formula to calculate the x-coordinate of the centroid is: x_c = (A₁x₁ + A₂x₂ + A₃x₃) / (A₁ + A₂ + A₃).

How is the y-coordinate of the centroid calculated?

The y-coordinate of the centroid is calculated using the formula: y_c = (A₁y₁ + A₂y₂ + A₃y₃) / (A₁ + A₂ + A₃).

What are the final x and y coordinates of the centroid for the unequal I-section?

The final x-coordinate of the centroid is 15 cm, and the y-coordinate is approximately 10.96 cm.

What is the purpose of dividing the I-section into three rectangles?

Dividing the I-section into three rectangles simplifies the process of calculating the centroid by breaking the complex shape into simpler components.

How are the y-coordinates for each rectangle’s centroid calculated?

The y-coordinates are calculated based on the height and half-height of each rectangle. For example, y₁ is half of the height of the bottom rectangle, y₂ includes the height of the bottom rectangle plus half of the middle rectangle's height.

What should the viewer do if they have questions about the lecture?

The viewer is encouraged to write down any doubts or queries in the comment section below the video, and the instructor will respond.