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.ALABAnswers: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 measuredwith respect to a reference axis at the bottom of the cross-section. In other words, let y = 0 at the bottom edge of the verticalstems.iBiWiLBCin.²Y₁ =in.² Y₂ =in.² y3 =iitibyin.in.in. Determine the centroid location in the y direction for the entire beam cross-section with respect to the reference axis at thebottom of the cross-section.Answer: y = ie Textbook and MediaSave for LaterPart 3Consider 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 thecentroid of the entire cross-section. For example, Ic₁ is the moment of inertia for area (1) about its own centroid, and d₁ is thedistance from the centroid of area (1) to the centroid of the entire cross-section, y. Enter the distances d₁, d₂, and d3 as positivevalues here, regardless of whether the centroid for an area is above or below y.Answers:Ic1=Ic2=3Ic3 =iin.iiin.² d₁=in.² d₂=in.4 d3=iiiin.in.in.

Answered: Image /qna-images/answer/0152e9e3-d3bc-4c54-807b-0fb91d8adbbb.jpg

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

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

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.

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Step 1: Introducing given data

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Step 2: Calculate centroid

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Step 3: Calculate moment of inertia

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Step 4: Calculate reactions

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Step 5: Calculate shear force & bending moment

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Step 6: Draw shear force & bending moment diagram

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Step 7: Calculate bending stress at max +ve moment

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Step 8: Calculate bending stress at max -ve moment

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