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A small dam of a height h = 6 ft is constructed of vertical wood beams AB, as shown in the figure. The wood beams, which have a thickness I = 2.5 in., are simply supported by horizontal steel beams at A and Ä Construct a graph showing the maximum bending stress tram in the wood beams versus the depth d of the water above the lower support at B. Plot the stress0 m a s (psi) as the ordinate and the depth d (ft) as the abscissa. Note: The weight density y of water equals 62.4 lb/ft 3 .

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

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BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 5, Problem 5.5.27P
Textbook Problem
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A small dam of a height h = 6 ft is constructed of vertical wood beams AB, as shown in the figure. The wood beams, which have a thickness I = 2.5 in., are simply supported by horizontal steel beams at A and Ä Construct a graph showing the maximum bending stress tram in the wood beams versus the depth d of the water above the lower support at B. Plot the stress0mas(psi) as the ordinate and the depth d(ft) as the abscissa. Note: The weight density y of water equals 62.4 lb/ft3.

  Chapter 5, Problem 5.5.27P, A small dam of a height h = 6 ft is constructed of vertical wood beams AB, as shown in the figure.

To determine

Graph showing the maximum bending stress in the wood beam and graph of the stress as the ordinate and the depth as the abscissa.

Explanation of Solution

Given information:

  

  h=6ftt=2.5inγwater=62.4lb/ft3

Formula used:

  qo=γbdMoment(M)=F×D

  σmax=MmaxS

Calculation:

Let b be the width of beam and qo as the intensity of load at depth d.

We know that, qo=γbd ;

  L=h=6ft

Now we will find the reaction at point A;

  RA=qod26L

And now the reaction at B;

  RB=qod6(3dL)

  xo=dd3L

  

Calculate the moment at C;

  MC=RA(Ld)

  qod26(1dL)

The section modulus will be;

  S=16bt2

We know the formula for the maximum stress, i.e

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