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

Manas Patnaik
19 Mar 201807:24

Summary

TLDRIn 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.

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Related Tags
EngineeringMechanicsCentroidI-SectionProblem SolvingTutorialGeometryEngineering LecturesLearningMath Calculations