<br />the end of the report). Because of logistical con-
<br />straints, such as protruding branches, however, the
<br />dynamometer was not always placed at this posi-
<br />tion on the vegetation. The relation of bending
<br />moment to height of vegetation was determined for
<br />each vegetation type (fig. 3). Additionally, equa-
<br />tions were developed by regression techniques of
<br />the bending moment with height for each of the
<br />four vegetation types (table 3).
<br />
<br />Table 3. Regression equations relating bending
<br />moment to vegetation height for saltcedar, willow,
<br />mesquite, and palo verde
<br />
<br />(BM, bending moment in foot pounds; H, height of vegetation in feet]
<br />
<br />Vegetation type
<br />
<br />Equation
<br />
<br />Coefficient of
<br />determination
<br />(r2)
<br />
<br />Saltcedar............... BM = lOo.I02H +0.880 0.87
<br />Willow.................. BM = IOO.122H+O.S81 .98
<br />Mesquite............... BM = JOO. I 24H +0.935 .88
<br />Palo verde............. BM = lOo.17IH+o.848 .86
<br />
<br />The bending moment (also referred to as
<br />flexural strength or stiffness) of the vegetation at
<br />varying heights can be estimated from the
<br />equations in table 3. For example, a flexural
<br />
<br />2,500
<br />2,000
<br />
<br />strength of 63.2 ft-Ib is estimated for a IO-foot-tall
<br />willow; whereas, a flexural strength of 361 ft-Ib is
<br />estimated for a IO-foot-tall palo verde. The
<br />assumption, therefore, is that a lone palo verde in
<br />midchannel, is thought to be substantially more
<br />likely to resist bending when it is subjected to a
<br />similar magnitude of stream power and similar
<br />degree of submergence as a lone willow tree in
<br />midchannel.
<br />
<br />Although uncertainties are associated with this
<br />simplified approach, data collected during this
<br />investigation seem to support these assumptions.
<br />For example, figure 4 shows a lone willow about
<br />15 ft tall that was laid over during a flow of
<br />6,590 ft3/S; whereas, figure 5 shows a lone
<br />16-foot-tall palo verde that remained erect
<br />throughout a flow of 9,760 ft3/S. Duration of flow
<br />for the events was about equal. The magnitude of
<br />stream power that affected the palo verde was
<br />20.2 ft-Ib/s/ft'; whereas, the magnitude of stream
<br />power to which the willow was subjected is equal
<br />to 12.9 ft-lb/s/ft2 (table I). These data indicate that
<br />the large flexural strength of the palo verde enabled
<br />it to resist the stream power that was substantially
<br />larger than the computed stream power that altered
<br />or laid over a willow with similar dimensions. The
<br />
<br />
<br />" .
<br />" . ".
<br />" ;'
<br />J-""-' ,~,,,,,';"
<br />
<br />",/'. ,."'"
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<br />" ..,,-
<br />"k" ,.."" .
<br />" .. ..,."
<br />" ;
<br />; ;'
<br />,,/.. ;-"""
<br />'" ..".'
<br />,,". ."
<br />; ,;
<br />... / ./
<br />" ,;
<br />'" .,;,; .
<br />....."Z ,,/"
<br />,/ ,;' .
<br />; .
<br />,," .'';
<br />~;;~,;
<br />
<br /><JJ
<br />o
<br />Z
<br />:::J
<br />o
<br />a.
<br />..:.
<br />o
<br />o
<br />u..
<br />~
<br />,.:
<br />z
<br />w
<br />:::;
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<br />:::;
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<br />Z
<br />is
<br />z
<br />w
<br />'"
<br />
<br />1,000
<br />
<br />700
<br />500
<br />400
<br />300
<br />
<br />200
<br />
<br />...
<br />
<br />
<br />100
<br />
<br />70
<br />
<br />50
<br />40
<br />30
<br />
<br />20
<br />
<br />.'
<br />...........
<br />
<br />.......... .
<br />..' .
<br />.~.,.
<br />.....
<br />., ...-
<br />..........
<br />. .....
<br />...,.....
<br />......
<br />.'
<br />~..,
<br />
<br />
<br />... PALO VERDE
<br />
<br />. MESQUITE
<br />. SAL TCEDAR
<br />., WILLOW
<br />
<br />4
<br />
<br />8
<br />
<br />
<br />14
<br />
<br />10
<br />
<br />16
<br />
<br />20
<br />
<br />...
<br />
<br />
<br />10
<br />
<br />6
<br />
<br />18
<br />
<br />12
<br />
<br />VEGETATION HEIGHT, IN FEET
<br />
<br />Figure 3. Bending-moment values for four types of vegetation in central Arizona.
<br />
<br />10 Melhod to Estimate Effects of Flow-Induced Vegetation Changes on Channel Conveyances of Streams In Central Arizona
<br />
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