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A wood beam supports the loads shown. The cross-sectional dimensions of the beam are shown in the second figure. Assume LAB = 3.7 m, Lec= 1 m, Lcp = 1.8 m, w = 12.1 kN/m, P = 14.5 kN, b₁ = 10 mm, b₂ = 95 mm, d₁ = 100 mm, and d₂ = 240 mm. Determine the magnitude of: (a) the maximum horizontal shear stress Tmax in the beam. (b) the maximum tension bending stress max (and location x) in the beam.

A wood beam supports the loads shown. The cross-sectional dimensions of the beam are shown in the second figure. Assume LAB = 3.7 m, Lec= 1 m, Lcp = 1.8 m, w = 12.1 kN/m, P = 14.5 kN, b₁ = 10 mm, b₂ = 95 mm, d₁ = 100 mm, and d₂ = 240 mm. Determine the magnitude of: (a) the maximum horizontal shear stress Tmax in the beam. (b) the maximum tension bending stress max (and location x) in the beam.

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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**Wood Beam Analysis** A wood beam supports the loads shown in the diagram. The cross-sectional dimensions of the beam are depicted in the second figure. Here are the given parameters for the analysis: - **L\_AB** = 3.7 m - **L\_BC** = 1 m - **L\_CD** = 1.8 m - **w** = 12.1 kN/m - **P** = 14.5 kN - **b1** = 10 mm - **b2** = 95 mm - **d1** = 100 mm - **d2** = 240 mm **Objective:** Determine: (a) The maximum horizontal shear stress (τ\_max) in the beam. (b) The maximum tension bending stress (σ\_max) and its location (x) in the beam. **Parameters to be calculated:** - **τ\_max** (kPa) - **σ\_max** (kPa) - Location of **σ\_max** (x-coordinate in meters) **Diagrams Explanation:** 1. **Beam Diagram:** - The beam is supported at point A and has distributed loads labeled as "w" over section AB. - A point load "P" is applied at the midpoint of section CD. - The beam is divided into sections AB, BC, and CD with their respective lengths. 2. **Cross-sectional View:** - Shows a rectangular beam section. - Dimensions: - **b1** (width of the top and bottom flanges) = 10 mm - **b2** (width of the central web) = 95 mm - **d1** (height of the central web) = 100 mm - **d2** (overall height) = 240 mm **Answers Section:** - The maximum horizontal shear stress (τ\_max) in kPa is to be calculated. - The maximum bending stress (σ\_max) in kPa and its location along the x-axis in meters are to be identified.
Transcribed Image Text:**Wood Beam Analysis** A wood beam supports the loads shown in the diagram. The cross-sectional dimensions of the beam are depicted in the second figure. Here are the given parameters for the analysis: - **L\_AB** = 3.7 m - **L\_BC** = 1 m - **L\_CD** = 1.8 m - **w** = 12.1 kN/m - **P** = 14.5 kN - **b1** = 10 mm - **b2** = 95 mm - **d1** = 100 mm - **d2** = 240 mm **Objective:** Determine: (a) The maximum horizontal shear stress (τ\_max) in the beam. (b) The maximum tension bending stress (σ\_max) and its location (x) in the beam. **Parameters to be calculated:** - **τ\_max** (kPa) - **σ\_max** (kPa) - Location of **σ\_max** (x-coordinate in meters) **Diagrams Explanation:** 1. **Beam Diagram:** - The beam is supported at point A and has distributed loads labeled as "w" over section AB. - A point load "P" is applied at the midpoint of section CD. - The beam is divided into sections AB, BC, and CD with their respective lengths. 2. **Cross-sectional View:** - Shows a rectangular beam section. - Dimensions: - **b1** (width of the top and bottom flanges) = 10 mm - **b2** (width of the central web) = 95 mm - **d1** (height of the central web) = 100 mm - **d2** (overall height) = 240 mm **Answers Section:** - The maximum horizontal shear stress (τ\_max) in kPa is to be calculated. - The maximum bending stress (σ\_max) in kPa and its location along the x-axis in meters are to be identified.
Expert Solution
Step 1: Determine the given Variables

Given 

LAB=3.7 m

LBC=1 m

LCD=1.8 m

w=12.1 kN/m

P=14.5kN

b1=10 mm

b2=95 mm

d1=100 mm

d2=240 mm

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