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Problem 10.8 - A beam is built up from two standard rolled-steel mỹímýmỹmm mỹmmmmjumm mmg mỹmýjumumỹınğınğıným channels and a cover plate. Locate the centroid of the section and determine the moments of inertia about the centroidal x- and y- axes. 40 mm 254 mm 100 mm 100 mm majjum 127 mm. A nümm 127 mm Centroid of channel A3780 mm 15.3 mm 32,6 mm gm Thần Bàn Bàn Bàn Thần Bàn Bàn Bàn ným

Problem 10.8 - A beam is built up from two standard rolled-steel mỹímýmỹmm mỹmmmmjumm mmg mỹmýjumumỹınğınğıným channels and a cover plate. Locate the centroid of the section and determine the moments of inertia about the centroidal x- and y- axes. 40 mm 254 mm 100 mm 100 mm majjum 127 mm. A nümm 127 mm Centroid of channel A3780 mm 15.3 mm 32,6 mm gm Thần Bàn Bàn Bàn Thần Bàn Bàn Bàn ným

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Problem 10.8**: A beam is built up from two standard rolled-steel channels and a cover plate. Locate the centroid of the section and determine the moments of inertia about the centroidal \( x' \)- and \( y' \)- axes. ### Diagram Explanation **Beam Configuration:** - The beam consists of a horizontal cover plate and two vertical channels. - The cover plate is 100 mm wide on either side of the center, making it a total of 200 mm wide. - The thickness of the cover plate is 40 mm. **Vertical Channels:** - Each channel is 127.7 mm tall. - The overall height from the bottom of the lower channel to the top of the cover plate is 254 mm. **Dimensions and Calculations:** - The horizontal distance separating the centroids of the channels is shown as 153 mm. - The sectional view of one channel is provided, indicating: - Cross-sectional area \( A = 3780 \, \text{mm}^2 \). - \( I_x = 32.6 \times 10^6 \, \text{mm}^4 \) and \( I_y = 1.44 \times 10^6 \, \text{mm}^4 \). - The centroid of each channel is positioned at point \( C \). ### Instructions To solve this problem: 1. Calculate the centroid location of the entire composite section. 2. Compute the moments of inertia about the centroidal \( x' \)- and \( y' \)-axes for the beam. This involves using parallel axis theorem and taking into account each component's area, centroidal location, and individual moment of inertia.
Transcribed Image Text:**Problem 10.8**: A beam is built up from two standard rolled-steel channels and a cover plate. Locate the centroid of the section and determine the moments of inertia about the centroidal \( x' \)- and \( y' \)- axes. ### Diagram Explanation **Beam Configuration:** - The beam consists of a horizontal cover plate and two vertical channels. - The cover plate is 100 mm wide on either side of the center, making it a total of 200 mm wide. - The thickness of the cover plate is 40 mm. **Vertical Channels:** - Each channel is 127.7 mm tall. - The overall height from the bottom of the lower channel to the top of the cover plate is 254 mm. **Dimensions and Calculations:** - The horizontal distance separating the centroids of the channels is shown as 153 mm. - The sectional view of one channel is provided, indicating: - Cross-sectional area \( A = 3780 \, \text{mm}^2 \). - \( I_x = 32.6 \times 10^6 \, \text{mm}^4 \) and \( I_y = 1.44 \times 10^6 \, \text{mm}^4 \). - The centroid of each channel is positioned at point \( C \). ### Instructions To solve this problem: 1. Calculate the centroid location of the entire composite section. 2. Compute the moments of inertia about the centroidal \( x' \)- and \( y' \)-axes for the beam. This involves using parallel axis theorem and taking into account each component's area, centroidal location, and individual moment of inertia.
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