
CALCS	BAS017 SECTION SHEAR FLOW by flat plate stiffness method

NOTATION
constrained node	single freedom of fe model (not implemented)
NODE	identity, number between 1 to 50
z y	coordinate position vectors, in plane of section
ELEMENT	shear flow model element
1stN	node, 1st end point at element mid thickness
2ndN	2nd element node, calculated- mid point between 1stN & 3rdN
3rdN	node, 3rd end point at element mid thickness
t	thickness, element, constant
Case	combined load case, transverse loading
Pz	force, parallel to z axis, thru shear centre
Py	force, parallel to y axis, thru shear centre
Mx	moment, parallel to longitudinal axis
ez ey	shear centre position coordinate vectors
sumPz sumPy	force, total shear acting in section parallel to z & y axes
etb props	see bas008
fs(2N)	stress, shear, average at element 2nd node
Ps	force, shear, average thru element
Ps1 Ps2	force, 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

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
DAT017	title
data	constrained node
NODE	z	y
tab	delimited	data
ELEMENT	1stN	3rdN	t
enter	tab	delimited	data
CASE	Px	Py	Pz	Mx	My	Mz
en	ter	tab	de	limit	ed	data
ENDDAT
EXAMPLE
Input
DAT017	long stalk tee 5x10
1	constrained node
NODE	z	y
1	51.4	191.5
2	106.4	159.7
3	161.4	128
4	-16.04	-52.29
ELEMENT	1stN	3rdN	t
1	1	2	18.3
2	2	3	18.3
3	2	4	9.15
CASE	Px	Py	Pz	Mx	My	Mz
1	1E4	0	0	100	0	0
2	0	1E4	0	0	1E5	0
3	0	0	1E4	0	0	1E5
4	1E4	1E4	1E4	100	1E5	1E5
ENDDAT
Output
OUTPUT long stalk tee 5x10
etb properties
4564	A	area
107.7	ybar	neutral axis position
2.205E7	Iz	2nd MoA
76.35	zbar	neutral axis position
9.444E6	Iy	2nd MoA
-29.98	theta12	angle of prin.planes
2.833E7	I1	2nd MoA
3.159E6	I2	2nd MoA
78.78	K1	min rad gir
26.31	K2	min rad gir
106	ez	shear centre coord
159.1	ey	shear centre coord
shear centre verification data
0.9984	sumP2.2
3.763E-4	sumP1.2
3.375E-3	sumP2.1
0.9892	sumP1.1
nodal direct stresses
Node	Case1	Case2	Case3	Case4
1	2.191	-3.349	-2.274	-3.431
2	2.191	-1.607	-1.268	-0.6843
3	2.191	0.134	-0.2643	2.061
4	2.191	-2.042	-0.5219	-0.3732
element shear stresses @ 2nd node
Element	Case1	Case2	Case3	Case4
1	-0.2474	2.71	-3.349	-0.8864
2	-0.2468	1.544	-4.024	-2.726
3	-0.4508	3.852	2.241	5.642
END017

NOTATION

APPLICATION

OUTPUT

SEE ALSO

THEORY

GUIDANCE

INPUT FORMAT

EXAMPLE

Input

Output