Tiagojoseferreira: Tiagojoseferreira moved page Draft Ferreira 761749235 to Ferreira 2019a

2019-07-01T17:55:57Z

Tiagojoseferreira moved page Draft Ferreira 761749235 to Ferreira 2019a

Scipediacontent at 07:44, 17 June 2019

2019-06-17T07:44:45Z

Scipediacontent at 07:40, 17 June 2019

2019-06-17T07:40:31Z

Show changes

Tiagojoseferreira: Created page with " '''Numerical Analysis of Axisymmetric Solids by the Finite Element Method: Use in Concrete, Steel and Mixed Steel-Concrete Elements'''
2019-06-13T13:45:13Z

Created page with " <big>'''Numerical Analysis of Axisymmetric Solids by the Finite Element Method: Use in Concrete, Steel and Mixed Steel-Concrete Elements'''</big> <span style="text-align: c..."
Show changes

@@ Line 590: / Line 590: @@
 In this section, the applications of the present study are shown. Four examples were analyzed, namely: a hollow sphere subjected to uniformly distributed radial load; a tube subjected to internal radial pressure; a concrete pile subjected to thrust along its shank and to nodal loading  transferred from the foundation block to its top; and finally, a mixed steel-concrete pillar without steel armor subjected to  surface load. The results obtained are compared to literature results and also with those determined using the ANSYS 17 (2) software.
-<span id='_Toc478406639'></span><span style="text-align: center; font-size: 75%;">'''3.1 Hollow sphere subjected to Uniformly Distributed Radial Load '''</span>
+'''3.1 Hollow sphere subjected to Uniformly Distributed Radial Load '''
 The hollow sphere considered in this application had an internal radius of 1m and an external radius of 2m, and was subjected to a negative unit pressure P inside, as shown in Figure 6.
@@ Line 736: / Line 736: @@
 It should be noted that the hollow sphere stresses were analyzed at the centroids of the discretized elements.
-<span id='_Toc478406640'></span><span style="text-align: center; font-size: 75%;">'''3.2 Hollow Cylinder Subjected to Internal Radial Pressure '''</span>
+'''3.2 Hollow Cylinder Subjected to Internal Radial Pressure '''
 This example presents the results corresponding to an empty cylinder, previously analyzed  by Timoshenko and Goodier (6), with E=20.77x103kN/cm², ð=0.3, internal diameter 5.08cm and external diameter 10.16cm, length equal to 10.16cm and subjected to an internal pressure p=0.616kN/cm², as shown in Figure 11. In this application, the values of the maximum displacements in the piece were assessed and the values of the radial and the tangential stresses at the nodes of the finite elements at the points of maximum displacement were also calculated.
@@ Line 749: / Line 749: @@
 <span style="text-align: center; font-size: 75%;">.</span></div>
-<span style="text-align: center; font-size: 75%;">Figure 12 presents the structured mesh, composed by 40 finite elements and 33 nodes, as well as the contour conditions adopted to obtain the responses by Progaxisymmetric</span>. It must be emphasized that this is the same finite element mesh presented in the literature.
+Figure 12 presents the structured mesh, composed by 40 finite elements and 33 nodes, as well as the contour conditions adopted to obtain the responses by Progaxisymmetric. It must be emphasized that this is the same finite element mesh presented in the literature.
 {| style="width: 65%;"
@@ Line 798: / Line 798: @@
 In this application, the graphs of displacements and stresses at the nodes of the elements show an excellent approximation between the numerical results obtained in this study and the theoretical values found in literature.
-<span id='_Toc478406642'></span><span style="text-align: center; font-size: 75%;">'''3.3 Concrete pile'''</span>
+'''3.3 Concrete pile'''
 This example shows the results of the modeling of a concrete pile as shown in Figure 16.
@@ Line 810: / Line 809: @@
 <span style="text-align: center; font-size: 75%;">'''Figure 16'''</span>''':'''<span style="text-align: center; font-size: 75%;"> Piles used in deep foundations</span></div>
-<span style="text-align: center; font-size: 75%;">The concrete pile had</span>  <math display="inline">\mbox{f}_{\mbox{ck}}\mbox{=}\mbox{ }\mbox{25MPa}</math> , <span style="text-align: center; font-size: 75%;">Poisson</span> coefficient  <math display="inline">\mbox{ν}\mbox{ }\mbox{=}\mbox{ }\mbox{ }\mbox{0,2}</math> and the concrete elasticity modulus was calculated with the equation  <math display="inline">\mbox{E}_\mbox{c}\mbox{=}\mbox{ }\mbox{5600}\sqrt{\mbox{f}_{\mbox{ck}}}</math> .
+The concrete pile had  <math display="inline">\mbox{f}_{\mbox{ck}}\mbox{=}\mbox{ }\mbox{25MPa}</math> , Poisson coefficient  <math display="inline">\mbox{ν}\mbox{ }\mbox{=}\mbox{ }\mbox{ }\mbox{0,2}</math> and the concrete elasticity modulus was calculated with the equation  <math display="inline">\mbox{E}_\mbox{c}\mbox{=}\mbox{ }\mbox{5600}\sqrt{\mbox{f}_{\mbox{ck}}}</math> .
-<span style="text-align: center; font-size: 75%;">The soil considered in this example had specific weight </span> <math display="inline">{\mbox{γ}}_{\mbox{solo}}\mbox{=}\mbox{ }\mbox{18}\mbox{ }\mbox{kN}/\mbox{m}^\mbox{3}</math> , friction angle <math>\phi ={30}^{\circ }</math> and<span style="text-align: center; font-size: 75%;">the coefficient of  active soil thrust </span> <math>\mbox{k}_\mbox{a}\mbox{=}\mbox{ }{\mbox{tg}}^\mbox{2}\left({\mbox{45}}^\mbox{o}-\right. </math><math>\left. \frac{\phi }{\mbox{2}}\right)</math> , that is,  <math display="inline">\mbox{k}_\mbox{a}\mbox{=0,333}</math> .
+The soil considered in this example had specific weight <math display="inline">{\mbox{γ}}_{\mbox{solo}}\mbox{=}\mbox{ }\mbox{18}\mbox{ }\mbox{kN}/\mbox{m}^\mbox{3}</math> , friction angle <math>\phi ={30}^{\circ }</math> and the coefficient of  active soil thrust  <math>\mbox{k}_\mbox{a}\mbox{=}\mbox{ }{\mbox{tg}}^\mbox{2}\left({\mbox{45}}^\mbox{o}-\right. </math><math>\left. \frac{\phi }{\mbox{2}}\right)</math> , that is,  <math display="inline">\mbox{k}_\mbox{a}\mbox{=0,333}</math> .
-<span style="text-align: center; font-size: 75%;">The block had a height of 2m and the pile had 10m length, that is, the height of the soil massif was  h=12m. Pile diameter was 2m and the axial load to which it was subjected was q=3000kN. Acting pressures on the edges of the pile were calculated by equation </span> <math display="inline">\mbox{p}\mbox{ }\mbox{=}\mbox{ }\mbox{k}_\mbox{a}\mbox{ }{\mbox{γ}}_{\mbox{solo}}\mbox{ }\mbox{h}</math> .
+The block had a height of 2m and the pile had 10m length, that is, the height of the soil massif was  h=12m. Pile diameter was 2m and the axial load to which it was subjected was q=3000kN. Acting pressures on the edges of the pile were calculated by equation <math display="inline">\mbox{p}\mbox{ }\mbox{=}\mbox{ }\mbox{k}_\mbox{a}\mbox{ }{\mbox{γ}}_{\mbox{solo}}\mbox{ }\mbox{h}</math> .
 The structure was discretized with 126 nodes and  200 elements, as shown in Figure 17. It is worth emphasizing that the same finite element mesh was used in the analyses by Progaxisymmetric  and       ANSYS (2).
@@ Line 1,072: / Line 1,071: @@
 In this application, when the stresses at the centroid of the element determined by the implemented code were compared with  the results obtained through ANSYS 17 (2) software a maximum percent              difference of 0.08% was obtained.
-<span id='_Toc478406643'></span><span style="text-align: center; font-size: 75%;">'''3.4 Mixed Steel-Concrete Pillar '''</span>
+'''3.4 Mixed Steel-Concrete Pillar '''
-<span style="text-align: center; font-size: 75%;">This example presents the numerical results of the analysis of a mixed steel-concrete pillar subjected to a designed axial load </span> <math display="inline">\mbox{P}_\mbox{d}=1200\mbox{ }\mbox{kN}</math> . The length of the pillar was <span style="text-align: center; font-size: 75%;">2m and the dimensions of the steel tube were 35.56cmx33.06cmx1.25mm. The tube was filled with concrete whose characteristic strength after 28 days was </span> <math display="inline">\mbox{f}_{\mbox{ck}}\mbox{=30MPa}</math> , the elasticity modulus of concrete was calculated with the equation  <math display="inline">\mbox{E}_\mbox{c}\mbox{=}\mbox{ }\mbox{5600}\sqrt{\mbox{f}_{\mbox{ck}}}</math> , Poisson coefficient for the steel tube was considered  <math display="inline">\mbox{ν}=0,3</math> and for the confined concrete Poison coefficient was equal to  <math display="inline">\mbox{ν}=0,2</math> .
+This example presents the numerical results of the analysis of a mixed steel-concrete pillar subjected to a designed axial load <math display="inline">\mbox{P}_\mbox{d}=1200\mbox{ }\mbox{kN}</math> . The length of the pillar was 2m and the dimensions of the steel tube were 35.56cmx33.06cmx1.25mm. The tube was filled with concrete whose characteristic strength after 28 days was <math display="inline">\mbox{f}_{\mbox{ck}}\mbox{=30MPa}</math> , the elasticity modulus of concrete was calculated with the equation  <math display="inline">\mbox{E}_\mbox{c}\mbox{=}\mbox{ }\mbox{5600}\sqrt{\mbox{f}_{\mbox{ck}}}</math> , Poisson coefficient for the steel tube was considered  <math display="inline">\mbox{ν}=0,3</math> and for the confined concrete Poison coefficient was equal to  <math display="inline">\mbox{ν}=0,2</math> .
 The objective of the analysis was to calculate lateral displacements and radial, axial, tangential and circumferential stresses at different points of the structure and, aiming to validate the results obtained by the computer program developed in the present research, the structure was also modeled through  ANSYS 17 (2) software.

← Older revision	Revision as of 17:55, 1 July 2019
(No difference)

Ferreira 2019a - Revision history

Tiagojoseferreira: Tiagojoseferreira moved page Draft Ferreira 761749235 to Ferreira 2019a

Scipediacontent at 07:44, 17 June 2019

Scipediacontent at 07:40, 17 June 2019