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A channel shape is used to support the loads shown on the beam. The dimensions of the shape are also shown. Assume LAB 3 ft, LBc-9 ft, P=2300 lb, w=1100 lb/ft, b=16 in., d=10 in., t=0.500 in. Consider the entire 12-ft length of the beam and determine (a) the maximum tension bending stress at any location along the beam, and (b) the maximum compression bending stress at any location along the beam. LAB B W LBC Break the cross-sectional area into three areas: (1) Top horizontal flange with rectangular cross-section 16 in. x 0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x 9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x 9.5 in. b Find the areas and the centroid locations in the y-direction for each part. Enter the centroid locations, V₁, V2, and y3, as measured with respect to a reference axis at the bottom of the cross-section. In other words, let y = 0 at the bottom edge of the vertical stems.

A channel shape is used to support the loads shown on the beam. The dimensions of the shape are also shown. Assume LAB 3 ft, LBc-9 ft, P=2300 lb, w=1100 lb/ft, b=16 in., d=10 in., t=0.500 in. Consider the entire 12-ft length of the beam and determine (a) the maximum tension bending stress at any location along the beam, and (b) the maximum compression bending stress at any location along the beam. LAB B W LBC Break the cross-sectional area into three areas: (1) Top horizontal flange with rectangular cross-section 16 in. x 0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x 9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x 9.5 in. b Find the areas and the centroid locations in the y-direction for each part. Enter the centroid locations, V₁, V2, and y3, as measured with respect to a reference axis at the bottom of the cross-section. In other words, let y = 0 at the bottom edge of the vertical stems.

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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A channel shape is used to support the loads shown on the beam. The dimensions of the shape are also shown. Assume LAB-3 ft, LBc-9 ft, P=2300 lb, w=1100 lb/ft, b=16 in., d=10 in., t=0.500 in. Consider the entire 12-ft length of the beam and determine (a) the maximum tension bending stress at any location along the beam, and (b) the maximum compression bending stress at any location along the beam. A LAB Answers: A1 = Break the cross-sectional area into three areas: (1) Top horizontal flange with rectangular cross-section 16 in. x 0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x 9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x 9.5 in. A₂ = A3 = Find the areas and the centroid locations in the y-direction for each part. Enter the centroid locations, y₁, y2, and y3, as measured with respect to a reference axis at the bottom of the cross-section. In other words, let y = 0 at the bottom edge of the vertical stems. i B i W i LBC in.² Y₁ = in.² Y₂ = in.² y3 = i i t i b y in. in. in.
Transcribed Image Text:A channel shape is used to support the loads shown on the beam. The dimensions of the shape are also shown. Assume LAB-3 ft, LBc-9 ft, P=2300 lb, w=1100 lb/ft, b=16 in., d=10 in., t=0.500 in. Consider the entire 12-ft length of the beam and determine (a) the maximum tension bending stress at any location along the beam, and (b) the maximum compression bending stress at any location along the beam. A LAB Answers: A1 = Break the cross-sectional area into three areas: (1) Top horizontal flange with rectangular cross-section 16 in. x 0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x 9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x 9.5 in. A₂ = A3 = Find the areas and the centroid locations in the y-direction for each part. Enter the centroid locations, y₁, y2, and y3, as measured with respect to a reference axis at the bottom of the cross-section. In other words, let y = 0 at the bottom edge of the vertical stems. i B i W i LBC in.² Y₁ = in.² Y₂ = in.² y3 = i i t i b y in. in. in.
Determine the centroid location in the y direction for the entire beam cross-section with respect to the reference axis at the bottom of the cross-section. Answer: y = i e Textbook and Media Save for Later Part 3 Consider again the cross-section broken into three area, as in Step 1: (1) Top horizontal flange with rectangular cross-section 16 in. x0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x9.5 in. Determine the moment of inertia for each area about its own centroid and the distance from the centroid of each area to the centroid of the entire cross-section. For example, Ic₁ is the moment of inertia for area (1) about its own centroid, and d₁ is the distance from the centroid of area (1) to the centroid of the entire cross-section, y. Enter the distances d₁, d₂, and d3 as positive values here, regardless of whether the centroid for an area is above or below y. Answers: Ic1= Ic2= 3 Ic3 = i in. i i in.² d₁= in.² d₂= in.4 d3= i i i in. in. in.
Transcribed Image Text:Determine the centroid location in the y direction for the entire beam cross-section with respect to the reference axis at the bottom of the cross-section. Answer: y = i e Textbook and Media Save for Later Part 3 Consider again the cross-section broken into three area, as in Step 1: (1) Top horizontal flange with rectangular cross-section 16 in. x0.500 in. (2) Left vertical stem with rectangular cross-section 0.500 in. x9.5 in. (3) Right vertical stem with rectangular cross-section 0.500 in. x9.5 in. Determine the moment of inertia for each area about its own centroid and the distance from the centroid of each area to the centroid of the entire cross-section. For example, Ic₁ is the moment of inertia for area (1) about its own centroid, and d₁ is the distance from the centroid of area (1) to the centroid of the entire cross-section, y. Enter the distances d₁, d₂, and d3 as positive values here, regardless of whether the centroid for an area is above or below y. Answers: Ic1= Ic2= 3 Ic3 = i in. i i in.² d₁= in.² d₂= in.4 d3= i i i in. in. in.
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