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Problem 10.7 - A composite beam is constructed from three plates and four standard rolled-steel angles. Locate the centroid of the section and determine the moment of inertia about the centroidal x-axis. 110 mm 110 mm, TR 140 mm 140 mm 10 mm -10 mm -10 16.2 mm mmčim 6 A=877 mm² Ixc0.202 x 10 mmª

Problem 10.7 - A composite beam is constructed from three plates and four standard rolled-steel angles. Locate the centroid of the section and determine the moment of inertia about the centroidal x-axis. 110 mm 110 mm, TR 140 mm 140 mm 10 mm -10 mm -10 16.2 mm mmčim 6 A=877 mm² Ixc0.202 x 10 mmª

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 10.7**: A composite beam is constructed from three plates and four standard rolled-steel angles. Locate the centroid of the section and determine the moment of inertia about the centroidal x-axis. --- ### Diagram Explanation The diagram presents a detailed layout of a composite beam cross-section, constructed using three plates and four standard rolled-steel angles. The section includes specific measurements and details relevant for structural analysis: 1. **Dimensions:** - The top and bottom plates are each 110 mm in width and 10 mm in thickness. - The vertical plate, or web, is 140 mm in height and 10 mm in thickness. - The angles are each placed on the top and bottom, measuring 16.2 mm from the edge to the centroid, as noted by the small inset diagram. - The overall height from the bottom to the top plate, including the web, is 140 mm. 2. **Centroid Location:** - The diagram indicates the y-axis as the vertical axis and the x-axis as the horizontal axis through the centroid. - The distance from the base of the section to the centroid is marked as "C." 3. **Properties of the Angle Section (as per the inset diagram):** - Area, \( A = 877 \, \text{mm}^2 \) - Moment of inertia about its centroidal x-axis, \( I_{xc} = 0.262 \times 10^6 \, \text{mm}^4 \) This composite beam structure requires determining the precise location of the centroid and computing the moment of inertia about the centroidal x-axis, essential for analyzing the beam's resistance to bending.
Transcribed Image Text:**Problem 10.7**: A composite beam is constructed from three plates and four standard rolled-steel angles. Locate the centroid of the section and determine the moment of inertia about the centroidal x-axis. --- ### Diagram Explanation The diagram presents a detailed layout of a composite beam cross-section, constructed using three plates and four standard rolled-steel angles. The section includes specific measurements and details relevant for structural analysis: 1. **Dimensions:** - The top and bottom plates are each 110 mm in width and 10 mm in thickness. - The vertical plate, or web, is 140 mm in height and 10 mm in thickness. - The angles are each placed on the top and bottom, measuring 16.2 mm from the edge to the centroid, as noted by the small inset diagram. - The overall height from the bottom to the top plate, including the web, is 140 mm. 2. **Centroid Location:** - The diagram indicates the y-axis as the vertical axis and the x-axis as the horizontal axis through the centroid. - The distance from the base of the section to the centroid is marked as "C." 3. **Properties of the Angle Section (as per the inset diagram):** - Area, \( A = 877 \, \text{mm}^2 \) - Moment of inertia about its centroidal x-axis, \( I_{xc} = 0.262 \times 10^6 \, \text{mm}^4 \) This composite beam structure requires determining the precise location of the centroid and computing the moment of inertia about the centroidal x-axis, essential for analyzing the beam's resistance to bending.
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