   Chapter 8, Problem 8.63P ### International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
ISBN: 9781305501607
Textbook Problem

# Using the method of composite surfaces, locate the centroid of the surface. To determine

Centroidal coordinates of composite surface.

Explanation

Given Information:

The following composite surface in given,

Calculation:

For the calculation of x¯i, axis x is to be considered and similarly for y¯i ,y axis is considered. For calculating z¯i, z axis is considered.

The above figure has been divided into simple geometrical shapes and these shapes have been numbered to find the individual area and centroidal distances from the reference axes.

The area of the simple geometrical shapes can be calculated as follows

1. Rectangle = A=b×d
2. Triangle = A=12×b×h

The centroidal distance of the geometries lies at

1. Rectangle (marked as 1, 2 and 4) = Centroid lies at the midpoint of the dimension in consideration. If the centroid lies on the axis considered, the centroidal distance is considered zero. There are total 3 rectangles in the above figure.
2. For the rectangle marked as 2, the area can be calculated by calculating the length AC,

AC2=AE2+EC2AC2=9002+(360150)2AC2=854100AC=854100AC=924.175

3. Triangle (marked as 3) = Centroid lies at the distance of h3 of the dimension in consideration. There are 2 triangular plates.

Consider the following figure,

Let us prepare the table for area and centroidal distances.

 i Part Ai x¯i y¯i z¯i 1 Rectangular Plate 2×(900×100)=180000 0.00 9002=450 0.00 2 Rectangular Plate 2×(924.175×150)=277252.59 0.00 9002=450 1502=75 3 Triangular Plate 2×12×(900×(360−150))=189000 0.00 23×900=600 150+( 360−150)3 =220 4 Rectangular Plate (300×900)=270000 0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

## Additional Engineering Solutions

#### What does WCS stand for?

Precision Machining Technology (MindTap Course List)

#### What e input masksâ€� What are validation rules? Why are they important?

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

#### What is a Tier I ERP software vendor?

Principles of Information Systems (MindTap Course List)

#### Same as Problem 9.8-3, but use ASD.

Steel Design (Activate Learning with these NEW titles from Engineering!) 