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<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 />",/'. ,."'" <br />;' <br />,," ",. <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 />:::; <br />o <br />:::; <br />t'J <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 />