CALCS BAS017
SECTION SHEAR FLOW by flat plate stiffness method

NOTATION

constrained nodesingle freedom of fe model (not implemented)
NODEidentity, number between 1 to 50
z ycoordinate position vectors, in plane of section
ELEMENTshear flow model element
1stNnode, 1st end point at element mid thickness
2ndN2nd element node, calculated- mid point between 1stN & 3rdN
3rdNnode, 3rd end point at element mid thickness
tthickness, element, constant
Casecombined load case, transverse loading
Pzforce, parallel to z axis, thru shear centre
Pyforce, parallel to y axis, thru shear centre
Mxmoment, parallel to longitudinal axis
ez eyshear centre position coordinate vectors
sumPz sumPyforce, total shear acting in section parallel to z & y axes
etb propssee bas008
fs(2N)stress, shear, average at element 2nd node
Psforce, shear, average thru element
Ps1 Ps2force, shear, average thru element parallel to 1 & 2 axes

APPLICATION

Bending sections subject to significant transverse loading for which determination of the shear centre and shear flow distribution is required.
Maximum numbers of: Nodes 50, Elements 50, Cases 10.

OUTPUT

General engineer's theory of bending properties. Shear centre position.
Shear flow data for unit orthogonal shear forces applied at shear centre.
Nodal direct and shear stresses for loads applied to section.
Problem definition plot showing nodes & elements

SEE ALSO

BAS007, BAS008, PROC014, PROC022 & PROC044

THEORY

This is a hybrid program composed of two principal sections. The first module calculates properties for a section composed of flat plates. The second module applies etb loading, based on the properties of the first module, to a shear flow distribution model constructed from elements of FE formulation having three nodes and quadratic order displacement functions.

GUIDANCE

Some degree of confidence in correct shear centre calculations is obtained by Psz or Psy being close to zero for each of ez and ey. This indicates correct shear force distribution and the shear centre output is otherwise invalid.

INPUT FORMAT

DAT017title
dataconstrained node
NODEzy
tabdelimiteddata
ELEMENT1stN3rdNt
entertabdelimiteddata
CASEPxPyPzMxMyMz
entertabdelimiteddata
ENDDAT

EXAMPLE

Input

DAT017long stalk tee 5x10
1constrained node
NODEzy
151.4191.5
2106.4159.7
3161.4128
4-16.04-52.29
ELEMENT1stN3rdNt
11218.3
22318.3
3249.15
CASEPxPyPzMxMyMz
11E40010000
201E4001E50
3001E4001E5
41E41E41E41001E51E5
ENDDAT

Output

OUTPUT long stalk tee 5x10
etb properties
4564Aarea
107.7ybarneutral axis position
2.205E7Iz2nd MoA
76.35zbarneutral axis position
9.444E6Iy2nd MoA
-29.98theta12angle of prin.planes
2.833E7I12nd MoA
3.159E6I22nd MoA
78.78K1min rad gir
26.31K2min rad gir
106ezshear centre coord
159.1eyshear centre coord
shear centre verification data
0.9984sumP2.2
3.763E-4sumP1.2
3.375E-3sumP2.1
0.9892sumP1.1
nodal direct stresses
NodeCase1Case2Case3Case4
12.191-3.349-2.274-3.431
22.191-1.607-1.268-0.6843
32.1910.134-0.26432.061
42.191-2.042-0.5219-0.3732
element shear stresses @ 2nd node
ElementCase1Case2Case3Case4
1-0.24742.71-3.349-0.8864
2-0.24681.544-4.024-2.726
3-0.45083.8522.2415.642
END017