Tom Algie Thesis Excerpts

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<ul><li><p>8/10/2019 Tom Algie Thesis Excerpts</p><p> 1/5</p><p>Chapter4 ExperimentalResults</p><p>- 102 -</p><p>Figure 4.27 The pull back moment-rotation curves from all the snaps in test 7</p><p>Figure 4.28 The pull back moment-rotation curves from all the snaps in test 9</p><p>0 5 10 15 20 25 300</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>Rotation (millirads)</p><p>Moment(kNm)</p><p>Snap 1</p><p>Snap 2</p><p>Snap 3</p><p>Snap 4</p><p>Snap 5Snap 6</p><p>Snap 7</p><p>Snap 8</p><p>Snap 9</p><p>0 5 10 15 200</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>Rotation (millirads)</p><p>Moment(kNm)</p><p>Snap 1</p><p>Snap 2</p><p>Snap 3</p><p>Snap 4</p><p>Snap 5</p><p>Snap 6</p><p>Snap 7</p><p>Snap 8</p><p>Snap 9</p></li><li><p>8/10/2019 Tom Algie Thesis Excerpts</p><p> 2/5</p><p>4.3 SnapBackTestResults</p><p>- 103 -</p><p>Figure 4.29 Dynamic moment-rotation for test 7 snap back 4</p><p>Figure 4.30 Dynamic moment-rotation for test 7 snap back 5</p><p>-15 -10 -5 0 5 10 15 20 25-80</p><p>-60</p><p>-40</p><p>-20</p><p>0</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>120</p><p>Rotation (millirads)</p><p>Moment(kNm)</p><p>-15 -10 -5 0 5 10 15 20 25-80</p><p>-60</p><p>-40</p><p>-20</p><p>0</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>120</p><p>Rotation (millirads)</p><p>Moment(kNm)</p></li><li><p>8/10/2019 Tom Algie Thesis Excerpts</p><p> 3/5</p><p>Chapter4 ExperimentalResults</p><p>- 104 -</p><p>4.3.13.3</p><p>Curve Fitting</p><p>The static moment-rotation curves were fitted with curves using Matlabs nonlinear</p><p>regression function that enables an equation to be fitted to an arbitrary curve</p><p>(MathWorks 2009). Producing equations that represent the static moment rotation</p><p>curves given in Figures 4.27 and 4.28 would allow a designer to choose a rotational</p><p>stiffness based on what rotations are expected, and thus proceed with designing for</p><p>rocking foundations. Sullivan et al. (2010) say this particular topic needs to be</p><p>researched further, and the results from the static moment rotation curves gives us an</p><p>insight into how much stiffness degradation takes place during rocking.</p><p>Kondner (1963) gives an equation for a hyperbolic stress strain relationship for cohesive</p><p>soils, and describes the factors contributing to the curve. The form of the stress strain</p><p>curve is:</p><p>baQ</p><p> (4.7)</p><p>where Q= shear stress; = axial strain; and aand bare parameters for the hyperbolic</p><p>curve, given below.</p><p>Figure 4.31 The stress strain curves that give the parameters a and b. Actual curve left, transformed curve to estimate parameters for stress strain behaviour right</p></li><li><p>8/10/2019 Tom Algie Thesis Excerpts</p><p> 4/5</p><p>4.3 SnapBackTestResults</p><p>- 105 -</p><p>Although these parameters are for stress-strain behaviour they can be applied to</p><p>moment-rotation behaviour as well. The parameter that gives the initial slope of the line,</p><p>a, is related to the initial stiffness of the system, and the parameter that specifies the</p><p>horizontal asymptote, b, relates to the moment capacity of the system.</p><p>Figure 4.32 gives the static moment-rotation curves from test 7 (same as Figure 4.27)</p><p>along with upper and lower bounds from the curve fitting. Figure 4.33 gives a close up</p><p>of those upper and lower bounds compared with snap-backs 1 and 9 respectively. The</p><p>curves were created by having an initial part that was elastic, and then applying the</p><p>nonlinear regression at some defined moment the point where initial nonlinearity</p><p>occurs. As is evident the curve functions can capture the static moment rotation</p><p>distribution that was recorded in the experiments. The initial elastic part of the curve</p><p>was calculated as around 60% of the Gazetas formula for the upper bound and around</p><p>20% for the lower bound. Subsequently the ultimate moment capacities for each were</p><p>110 kNm for the upper bound and around 85 kNm for the lower bound.</p><p>Figure 4.32 The upper and lower bound of the fitted curves, with the 9 snap-backs oftest 7 plotted in grey.</p><p>0 5 10 15 20 25 30 35 400</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>120</p><p>Rotation (millirads)</p><p>Moment(kNm)</p></li><li><p>8/10/2019 Tom Algie Thesis Excerpts</p><p> 5/5</p><p>Chapter4 ExperimentalResults</p><p>- 106 -</p><p>Figure 4.33 A close up with of the upper (left) and lower (right) bound fitted curves</p><p>for test 7</p><p>Figure 4.34 The upper and lower bound of the fitted curves, with the 9 snap-backs oftest 9 plotted in grey.</p><p>Figure 4.34 gives the upper and lower bounds to the curve fitting for test 9 along with</p><p>all the snap-backs of that test. Again it shows that the nonlinear behaviour can be</p><p>captured by the equation. The upper bound had an initial stiffness of around 80% of the</p><p>Gazetas value and a moment capacity of 110 kNm the same as what was found for test</p><p>0 5 10 15 20 25 30 35 400</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>120</p><p>Rotation (millirads)</p><p>Moment(k</p><p>Nm)</p><p>Upper Bound</p><p>Lower Bound</p></li></ul>