# Changes for page Calculations of the geometrical properties

From empty
To version 29.1
edited by StruSoft Developers
on 2019/05/16 14:45
Change comment: There is no comment for this version

## Details

Page properties
Title
 ... ... @@ -1,0 +1,1 @@ 1 +Calculations of the geometrical properties
Parent
 ... ... @@ -1,0 +1,1 @@ 1 +Manuals.Theory Manual.WebHome
Author
 ... ... @@ -1,1 +1,1 @@ 1 -XWiki.XWikiGuest 1 +XWiki.StruSoft
Content
 ... ... @@ -1,0 +1,36 @@ 1 +(% style="text-align: justify;" %) 2 +Beam finite elements of arbitrary cross sections are important members of finite element models for a variety of practical applications. In the effective use of such elements, at the modelling stage, the user is faced with the time consuming problem of accurate determination of beam cross sectional properties. 3 + 4 +(% style="text-align: justify;" %) 5 +In the analysis of beams, the following local coordinate systems and notations are used (see Fig. below): 6 + 7 +* **N** node of finite element mesh, 8 +* **G** centroid, 9 +* **S** shear centre, 10 +* **x, y, z** local coordinates, where x is passing through element nodes, 11 +* **x', y', z'** central axes, parallel to x, y, z (i.e. x' is the beam axis), 12 +* **y,,G,,, z,,G,,** coordinates of **G** centroid, relative to N node,Fig. below 13 +* **y,,S,,, z,,S,,** coordinates of **S** shear (torsion) centre, relative to G centroid, 14 +* **e,,xmax,,, e,,xmin,,, e,,ymax,,, e,,ymin,,, e,,1max,,, e,,1min,,, e,,2max,,, e,,2min,,** distances of extreme fibres. 15 + 16 +(% style="text-align: justify;" %) 17 +[[image:1558007716236-122.png||height="514" width="553"]] 18 +The cross sectional properties are related to internal forces, namely tension, bending, torsion (free or constrained) and shear. The general solution of elastic beam problems can be found in many textbooks, for example in references (% style="color:#e74c3c" %)[3](%%) and (% style="color:#e74c3c" %)[4](%%), only the definitions and final results will be presented. 19 + 20 +(% style="text-align: justify;" %) 21 += Tension, bending = 22 + 23 + 24 +The well known formula calculating the normal stress distribution due to tension and bending: 25 + 26 +(% style="text-align: justify;" %) 27 +[[image:1558007957069-112.png||height="60" width="364"]] 28 + 29 +(% style="text-align: justify;" %) 30 +The cross sectional properties appearing here are: 31 + 32 +(% style="text-align: justify;" %) 33 +area: 34 + 35 +(% style="text-align: justify;" %) 36 +
1558007712531-479.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558007716236-122.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558007957069-112.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008053789-726.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008063210-994.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008074293-163.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008113792-834.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008140147-438.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008160287-773.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008190437-802.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008213998-836.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008225233-584.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558008319356-824.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010005100-497.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010036032-488.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010087669-335.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010164363-236.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010181872-975.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010207323-183.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010239259-976.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010262462-720.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010328103-313.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010351120-148.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010375065-938.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010455816-103.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010502782-757.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content
1558010643831-424.png
Author
 ... ... @@ -1,0 +1,1 @@ 1 +XWiki.StruSoft
Size
 ... ... @@ -1,0 +1,1 @@ 1 +0 bytes
Content