Zhang et al 2017a - Revision history

Scipediacontent at 10:42, 26 June 2017

2017-06-26T10:42:20Z

Rimni: Rimni moved page Draft Samper 373521087 to Zhang et al 2017a

2017-06-23T11:48:05Z

Rimni moved page Draft Samper 373521087 to Zhang et al 2017a

Rimni at 11:51, 20 June 2017

2017-06-20T11:51:32Z

Rimni at 10:27, 15 June 2017

2017-06-15T10:27:24Z

Rimni at 10:26, 15 June 2017

2017-06-15T10:26:10Z

Rimni at 10:14, 15 June 2017

2017-06-15T10:14:40Z

Rimni at 10:13, 15 June 2017

2017-06-15T10:13:14Z

Rimni at 10:08, 15 June 2017

2017-06-15T10:08:54Z

Rimni at 10:08, 15 June 2017

2017-06-15T10:08:04Z

Rimni at 13:58, 13 June 2017

2017-06-13T13:58:36Z

← Older revision		Revision as of 10:42, 26 June 2017
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−	~~Submitted: 10/01/2017~~
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−	~~Accepted: 06/06/2017~~
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	==Abstract==		==Abstract==

← Older revision		Revision as of 11:51, 20 June 2017
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		+	Submitted: 10/01/2017
		+
		+	Accepted: 06/06/2017
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		+
	==Abstract==		==Abstract==

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 {| style="text-align: center; margin:auto;"
 |-
-| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta + \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B1}{\gamma }^2\left(3\beta + 2\gamma \right)}{6\left(\beta +\gamma \right)}+ {\omega }_{AC2}\left(1-x_{AC2}/\beta +\gamma \right)-</math>
+| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta + \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B1}{\gamma }^2\left(3\beta + 2\gamma \right)}{6\left(\beta +\gamma \right)}+ </math>
-<math>\frac{R_{A2}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B2}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
+<math>{\omega }_{AC2}\left(1-x_{AC2}/\beta +\gamma \right)-\frac{R_{A2}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B2}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (40)

@@ Line 445: / Line 445: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta +\right. </math><math>\left. \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-</math><math>\frac{R_{B1}{\gamma }^2\left(3\beta +</math>
+| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta + \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B1}{\gamma }^2\left(3\beta + 2\gamma \right)}{6\left(\beta +\gamma \right)}+ {\omega }_{AC2}\left(1-x_{AC2}/\beta +\gamma \right)-</math>
-<math>2\gamma \right)}{6\left(\beta +\gamma \right)}+ {\omega }_{AC2}\left(1-x_{AC2}/\beta +\gamma \right)-</math><math>\frac{R_{A2}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B2}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
+<math>\frac{R_{A2}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B2}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (40)

@@ Line 445: / Line 445: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta +\right. </math><math>\left. \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-</math><math>\frac{R_{B1}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}+</math><math>{\omega }_{AC2}\left(1-x_{AC2}/\beta +\gamma \right)-</math><math>\frac{R_{A2}{\left(\beta +\gamma \right)}^2}{3}-\frac{R_{B2}{\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
+| <math>EI{\theta }_C={\omega }_{AC1}\left(1-x_{AC1}/\beta +\right. </math><math>\left. \gamma \right)-\frac{R_{A1}{\left(\beta +\gamma \right)}^2}{3}-</math><math>\frac{R_{B1}{\gamma }^2\left(3\beta +</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (40)
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 {| style='margin:auto;width: 100%; text-align:center;'
 |-
-| <math>\beta \left({\omega }_{AB1}+{\omega }_{AB2}\right)-</math><math>\left({\omega }_{AB1}x_{AB1}+{\omega }_{AB2}x_{AB2}\right)-</math><math>\left({\omega }_{BC1}x_{BC1}+{\omega }_{BC2}x_{BC2}\right)=</math><math>\frac{\left(R_{A1}+R_{A2}\right)\left[2{\beta }^3-{\gamma }^2\left(3\beta +\gamma \right)\right]}{6}-</math><math>\frac{\left(R_{B1}+R_{B2}\right){\gamma }^3}{6}</math>
+| <math>\beta \left({\omega }_{AB1}+{\omega }_{AB2}\right)-</math><math>\left({\omega }_{AB1}x_{AB1}+{\omega }_{AB2}x_{AB2}\right)-</math><math>\left({\omega }_{BC1}x_{BC1}+{\omega }_{BC2}x_{BC2}\right)=</math>
 |}
 | style='width: 5px;text-align: right;white-space: nowrap;' | (42)
@@ Line 474: / Line 476: @@
 {| style='margin:auto;width: 100%; text-align:center;'
 |-
-| <math>\left({\omega }_{AC1}+{\omega }_{AC2}\right)-\frac{\left({\omega }_{AC1}x_{AC1}+{\omega }_{AC2}x_{AC2}\right)}{\left(\beta +\gamma \right)}=</math><math>\frac{\left(R_{A1}+R_{A2}\right){\left(\beta +\gamma \right)}^2}{6}+</math><math>\frac{\left(R_{B1}+R_{B2}\right){\gamma }^2\left(3\beta +2\gamma \right)}{6\left(\beta +\gamma \right)}</math>
+| <math>\left({\omega }_{AC1}+{\omega }_{AC2}\right)-\frac{\left({\omega }_{AC1}x_{AC1}+{\omega }_{AC2}x_{AC2}\right)}{\left(\beta +\gamma \right)}=</math><math>\frac{\left(R_{A1}+R_{A2}\right){\left(\beta +\gamma \right)}^2}{6}+</math>
 |}
 | style='width: 5px;text-align: right;white-space: nowrap;' | (43)

← Older revision	Revision as of 11:48, 23 June 2017
(No difference)

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 {| style='margin:auto;width: 100%; text-align:center;'
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-| <math>\begin{array}{l} {EI\theta _{B} =\omega _{AB1} \frac{\beta -x_{AB1} }{\left(\beta +\gamma \right)} -\omega _{BC1} \frac{x_{BC1} }{\left(\beta +\gamma \right)} -\frac{R_{A1} \beta ^{3} }{3\left(\beta +\gamma \right)} +\frac{R_{A1} \gamma ^{2} \left(\beta +\gamma /  3 \right)}{2\left(\beta +\gamma \right)} +\frac{R_{B1} \gamma ^{3} }{6\left(\beta +\gamma \right)} } \\ {+\omega _{AB2} \frac{\beta -x_{AB2} }{\left(\beta +\gamma \right)} -\omega _{BC2} \frac{x_{BC2} }{\left(\beta +\gamma \right)} -\frac{R_{A2} \beta ^{3} }{3\left(\beta +\gamma \right)} +\frac{R_{A2} \gamma ^{2} \left(\beta +{\gamma / 3} \right)}{2\left(\beta +\gamma \right)} +\frac{R_{B2} \gamma ^{3} }{6\left(\beta +\gamma \right)} } \end{array}</math>
+| <math>{EI\theta _{B} =\omega _{AB1} \frac{\beta -x_{AB1} }{\left(\beta +\gamma \right)} -\omega _{BC1} \frac{x_{BC1} }{\left(\beta +\gamma \right)} -\frac{R_{A1} \beta ^{3} }{3\left(\beta +\gamma \right)} +\frac{R_{A1} \gamma ^{2} \left(\beta +\gamma /  3 \right)}{2\left(\beta +\gamma \right)} +\frac{R_{B1} \gamma ^{3} }{6\left(\beta +\gamma \right)} } </math>
 |}
 | style='width: 5px;text-align: right;white-space: nowrap;' | (39)

@@ Line 63: / Line 63: @@
-Assuming that flexural rigidity (''EI'') of vertical girder is constant. To simplify calculation, length of girder is regarded as 1. Length coefficient of upper , middle and lower section of vertical girder is  <math>\alpha ,\beta ,\gamma </math> respectively, that is the point of intersection of the strut and girder can be determined. then:
+Assuming that flexural rigidity (''EI'') of vertical girder is constant. To simplify calculation, length of girder is regarded as 1. Length coefficient of upper , middle and lower section of vertical girder is  <math>\alpha ,\beta ,\gamma </math> respectively, that is the point of intersection of the strut and girder can be determined. Then:
 {| class='formulaSCP' style='width: 100%;'
 |-

← Older revision		Revision as of 10:08, 15 June 2017
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	The overall stability of hydraulic tainter steel gate decrease seriously, and they are caused by improper structure layout of the two-way eccentric compression of struts. Chinese and American specification method, structural mechanics method and finite element method are respectively used to study rational structural layout of strut arms in vertical frame. First of all, a unified method for rational layout of struts of tainter gate in vertical frame is deduced by using structural mechanics method that simplifies curve girder as straight girder on the basis of zero rotation in vertical girder. Second, rational layouts of struts were researched by utilizing spatial finite element method according to zero rotation in vertical girder. The 756 groups rational layout results of the above three methods with different water heads, different number of struts and different unit stiffness ratios were researched. The differences of struts stress and material dosages of various rational layout methods were evaluated. From the point of view of the forces of tainter gate struts in vertical frame, as the results shown, the layouts of struts by Chinese and American specification method, straight beam method and finite element method are large eccentric compression, small eccentric compression and axial compression respectively. The layout of struts with specification method in lower head is quite different from straight beam method and finite element method, and the layouts of deep water head with straight beam method and finite element method are tend to be consistent. Unit stiffness ratio between vertical girder and strut has little effect on layout of tainter gate struts, but has a great influence on material dosages of tainter gate. Compared with specification method, layout of tainter gate with two struts and three struts by using straight beam method and finite element method can improve stability of struts and save materials of overall tainter gate structure, and the material saving rates of tainter gate with two struts and three struts with finite element method are respectively [32.63, 47.58] (%) and [21.61, 30.01] (%). Rational layout concise charts of tainter gate with two struts and three struts by specification method, straight beam method and finite element method are given, which can be used directly for projects designs. Compared with specification method, the layout of struts of straight beam method and finite element method is not only security and economy, but also method and mechanics concept are simple, which can provide the theoretical basis for specification revision of Chinese and American.		The overall stability of hydraulic tainter steel gate decrease seriously, and they are caused by improper structure layout of the two-way eccentric compression of struts. Chinese and American specification method, structural mechanics method and finite element method are respectively used to study rational structural layout of strut arms in vertical frame. First of all, a unified method for rational layout of struts of tainter gate in vertical frame is deduced by using structural mechanics method that simplifies curve girder as straight girder on the basis of zero rotation in vertical girder. Second, rational layouts of struts were researched by utilizing spatial finite element method according to zero rotation in vertical girder. The 756 groups rational layout results of the above three methods with different water heads, different number of struts and different unit stiffness ratios were researched. The differences of struts stress and material dosages of various rational layout methods were evaluated. From the point of view of the forces of tainter gate struts in vertical frame, as the results shown, the layouts of struts by Chinese and American specification method, straight beam method and finite element method are large eccentric compression, small eccentric compression and axial compression respectively. The layout of struts with specification method in lower head is quite different from straight beam method and finite element method, and the layouts of deep water head with straight beam method and finite element method are tend to be consistent. Unit stiffness ratio between vertical girder and strut has little effect on layout of tainter gate struts, but has a great influence on material dosages of tainter gate. Compared with specification method, layout of tainter gate with two struts and three struts by using straight beam method and finite element method can improve stability of struts and save materials of overall tainter gate structure, and the material saving rates of tainter gate with two struts and three struts with finite element method are respectively [32.63, 47.58] (%) and [21.61, 30.01] (%). Rational layout concise charts of tainter gate with two struts and three struts by specification method, straight beam method and finite element method are given, which can be used directly for projects designs. Compared with specification method, the layout of struts of straight beam method and finite element method is not only security and economy, but also method and mechanics concept are simple, which can provide the theoretical basis for specification revision of Chinese and American.
−

	==Introduction==		==Introduction==

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 ==3 Layout of finite element method==
-<span id='OLE_LINK273'></span><span id='OLE_LINK274'></span>Finite element models of vertical frame structure of tainter gate were established by using the ''APDL'' language programming in three-dimensional finite element software. The detailed analysis procedures were as follows: 1) Beam188 element was selected [13,14], and the cross section of struts is box section and vertical girder is I-shaped section. Finite element models of two struts and three struts with vertical girder were established [15,16] as shown in Figures 5 and 6. 2) Material properties were determined: Elastic modulus and Poisson's ratio are 2.06 x 10<sup>5</sup>''MPa'' and 0.3 respectively. 3) Constraints were imposed: trunnion of tainter gate is hinged joint, and vertical upward constraint at the bottom of the girder; 4) Loads were applied: hydrostatic loads were applied to the skin plate of the tainter gate, and the density of water is 9.8''KN/m<sup>3</sup>''; 5) Results were solved and analyzed. Taking a hydropower station with radius of skin plate is 32 ''m'' and normal storage level is 23.8 ''m'' as an example, and the layout results of 21 groups different water heads of two struts and 21 groups different water heads of three struts respectively under the conditions of 756 groups of different unit stiffness ratio between girder and strut by using the above steps. Regarding layout results of the Chinese and American specification as the initial value and the point of intersection of the strut and girder as variable, ''APDL'' language of ''ANSYS14.0'' calculation program was utilized. The bending moment at the end of the strut was extracted, and stop calculation when the values of bending moment is zero(that is zero rotation in vertical girder). Then the arrangement results of the strut are the rational arrangement results of finite element method.
+<span id='OLE_LINK273'></span><span id='OLE_LINK274'></span>Finite element models of vertical frame structure of tainter gate were established by using the ''APDL'' language programming in three-dimensional finite element software. The detailed analysis procedures were as follows: 1) Beam188 element was selected [13,14], and the cross section of struts is box section and vertical girder is I-shaped section. Finite element models of two struts and three struts with vertical girder were established [15,16] as shown in Figures 5 and 6; 2) Material properties were determined: Elastic modulus and Poisson's ratio are 2.06 x 10<sup>5</sup>''MPa'' and 0.3 respectively; 3) Constraints were imposed: trunnion of tainter gate is hinged joint, and vertical upward constraint at the bottom of the girder; 4) Loads were applied: hydrostatic loads were applied to the skin plate of the tainter gate, and the density of water is 9.8''KN/m<sup>3</sup>''; 5) Results were solved and analyzed. Taking a hydropower station with radius of skin plate is 32 ''m'' and normal storage level is 23.8 ''m'' as an example, and the layout results of 21 groups different water heads of two struts and 21 groups different water heads of three struts respectively under the conditions of 756 groups of different unit stiffness ratio between girder and strut by using the above steps. Regarding layout results of the Chinese and American specification as the initial value and the point of intersection of the strut and girder as variable, ''APDL'' language of ''ANSYS14.0'' calculation program was utilized. The bending moment at the end of the strut was extracted, and stop calculation when the values of bending moment is zero(that is zero rotation in vertical girder). Then the arrangement results of the strut are the rational arrangement results of finite element method.
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