# 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 .

### Mechanics of Materials (MindTap Co...

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

### 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.

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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