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If shear force V= 5000 N, The shear stress at joint b is: [I(x)=8.62*10^6 mm^4 and tow=VQ/lb) 100 mm

If shear force V= 5000 N, The shear stress at joint b is: [I(x)=8.62*10^6 mm^4 and tow=VQ/lb) 100 mm

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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# Shear Stress in Beams ## Problem Statement: Given a beam with a specific configuration and dimensions, we are tasked to determine the shear stress at a particular joint when subjected to a shear force. ### Details: - **Shear Force, V:** 5000 N - **Moment of Inertia, I(x):** 8.62 × 10^6 mm^4 - **Shear Stress Formula:** τ = VQ/Ib ## Beam Diagram: The beam has the following characteristics: - The top flange is 100 mm wide and 20 mm thick. - The web of the beam is 80 mm high and 20 mm thick. - The bottom flange mirrors the top flange, being 60 mm wide and 20 mm thick. ## Key Points: - There are two joints labeled in the diagram: - **Joint a** is located at the top flange. - **Joint b** is specifically marked at 68.3 mm from some reference line across the height of the beam. ### Explanation: This setup describes a typical I-beam used in structural contexts. The shear stress at a given point in the beam can be calculated using the formula provided. Here, specific values of dimensions and properties of the beam are provided to compute the shear stress at joint b, utilizing the central web and dimensions of the different beam parts. To solve this problem, one must: 1. Understand the location of the centroid and neutral axis for determining Q. 2. Calculate the product Vy/Ib, considering the respective web thickness and other parameters as detailed in structural mechanics for stress computations.
Transcribed Image Text:# Shear Stress in Beams ## Problem Statement: Given a beam with a specific configuration and dimensions, we are tasked to determine the shear stress at a particular joint when subjected to a shear force. ### Details: - **Shear Force, V:** 5000 N - **Moment of Inertia, I(x):** 8.62 × 10^6 mm^4 - **Shear Stress Formula:** τ = VQ/Ib ## Beam Diagram: The beam has the following characteristics: - The top flange is 100 mm wide and 20 mm thick. - The web of the beam is 80 mm high and 20 mm thick. - The bottom flange mirrors the top flange, being 60 mm wide and 20 mm thick. ## Key Points: - There are two joints labeled in the diagram: - **Joint a** is located at the top flange. - **Joint b** is specifically marked at 68.3 mm from some reference line across the height of the beam. ### Explanation: This setup describes a typical I-beam used in structural contexts. The shear stress at a given point in the beam can be calculated using the formula provided. Here, specific values of dimensions and properties of the beam are provided to compute the shear stress at joint b, utilizing the central web and dimensions of the different beam parts. To solve this problem, one must: 1. Understand the location of the centroid and neutral axis for determining Q. 2. Calculate the product Vy/Ib, considering the respective web thickness and other parameters as detailed in structural mechanics for stress computations.
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