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Title : DESCRIPTION OF FINITE ELEMENT MESH
==========================================
Problem_Type: Static Analysis
=======================
Profile of Problem Size
=======================
Dimension of Problem = 2
Number Nodes = 24
Degrees of Freedom per node = 3
Max No Nodes Per Element = 2
Number Elements = 35
Number Element Attributes = 2
Number Loaded Nodes = 20
Number Loaded Elements = 0
------------------------------------------------------------
Node# X_coord Y_coord Tx Ty Rz
------------------------------------------------------------
1 0.00000e+00 ft 0.00000E+00 ft -1 -2 -3
2 2.00000e+01 ft 0.00000E+00 ft -4 -5 -6
3 3.50000e+01 ft 0.00000E+00 ft -7 -8 -9
4 5.50000e+01 ft 0.00000E+00 ft -10 -11 -12
5 0.00000e+00 ft 1.00000E+01 ft 1 6 7
...... details of nodal coordinates and modeling dof removed ....
19 3.50000e+01 ft 4.00000E+01 ft 4 34 35
20 5.50000e+01 ft 4.00000E+01 ft 4 36 37
21 0.00000e+00 ft 5.00000E+01 ft 5 38 39
22 2.00000e+01 ft 5.00000E+01 ft 5 40 41
23 3.50000e+01 ft 5.00000E+01 ft 5 42 43
24 5.50000e+01 ft 5.00000E+01 ft 5 44 45
--------------------------------------------------------------------
Element# Type node[1] node[2] Element_Attr_Name
--------------------------------------------------------------------
1 FRAME_2D 1 5 mycolumn
2 FRAME_2D 5 9 mycolumn
3 FRAME_2D 9 13 mycolumn
4 FRAME_2D 13 17 mycolumn
...... details of element connectivity removed ....
33 FRAME_2D 21 22 mybeam
34 FRAME_2D 22 23 mybeam
35 FRAME_2D 23 24 mybeam
---------------------
Element Attribute Data :
---------------------
ELEMENT_ATTR No. 1 : name = "mycolumn"
: section = "mysection1"
: material = "mymaterial"
: type = FRAME_2D
: gdof [0] = 1 : gdof[1] = 2 : gdof[2] = 3
: Young's Modulus = E = 2.900e+04 ksi
: Yielding Stress = fy = 3.600e+01 ksi
: Poisson's ratio = nu = 2.500e-01
: Density = 1.024e-06 lb/in^3
: Inertia Izz = 1.542e+03 in^4
: Area = 4.740e+01 in^2
ELEMENT_ATTR No. 2 : name = "mybeam"
: section = "mysection2"
: material = "mymaterial"
: type = FRAME_2D
: gdof [0] = 1 : gdof[1] = 2 : gdof[2] = 3
: Young's Modulus = E = 2.900e+04 ksi
: Yielding Stress = fy = 3.600e+01 ksi
: Poisson's ratio = nu = 2.500e-01
: Density = 1.024e-06 lb/in^3
: Inertia Izz = 1.600e+03 in^4
: Area = 2.146e+01 in^2
EXTERNAL NODAL LOADINGS
------------------------------------------------
Node# Fx (lbf) Fy (lbf) Mz (lbf.in)
------------------------------------------------
5 4253.33 -24000.00 -960000.00
6 0.00 -42000.00 420000.00
7 0.00 -42000.00 -420000.00
8 0.00 -24000.00 960000.00
9 8506.67 -24000.00 -960000.00
10 0.00 -42000.00 420000.00
11 0.00 -42000.00 -420000.00
12 0.00 -24000.00 960000.00
13 12760.00 -24000.00 -960000.00
14 0.00 -42000.00 420000.00
15 0.00 -42000.00 -420000.00
16 0.00 -24000.00 960000.00
17 17013.33 -24000.00 -960000.00
18 0.00 -42000.00 420000.00
19 0.00 -42000.00 -420000.00
20 0.00 -24000.00 960000.00
21 21266.67 -20000.00 -800000.00
22 0.00 -35000.00 350000.00
23 0.00 -35000.00 -350000.00
24 0.00 -20000.00 800000.00
============= End of Finite Element Mesh Description ==============
------------------------------------------------------------
Node Displacement
No displ-x displ-y rot-z
------------------------------------------------------------
units in in rad
1 0.00000e+00 0.00000e+00 0.00000e+00
2 0.00000e+00 0.00000e+00 0.00000e+00
3 0.00000e+00 0.00000e+00 0.00000e+00
4 0.00000e+00 0.00000e+00 0.00000e+00
5 1.02973e-01 -7.40873e-03 -1.23470e-03
6 1.02973e-01 -1.64731e-02 -6.24404e-04
7 1.02973e-01 -1.90281e-02 -8.22556e-04
8 1.02973e-01 -1.27863e-02 -7.58887e-04
9 2.55749e-01 -1.34750e-02 -1.19639e-03
....... details of displacements removed .....
21 5.62354e-01 -2.29345e-02 -6.66741e-04
22 5.62354e-01 -4.88997e-02 -8.48912e-05
23 5.62354e-01 -5.50729e-02 -3.30685e-04
24 5.62354e-01 -3.63403e-02 6.32278e-05
MEMBER FORCES
------------------------------------------------------------------------------
Elmt No 1 :
Coords (X,Y) = ( 0.000 in, 60.000 in)
exx = -6.17394e-05 , curva = -0.00040508 , gamma = -3.10985e-04
Fx1 = 8.48669e+04 lbf Fy1 = 8.97143e+03 lbf Mz1 = 9.98366e+05 lbf.in
Fx2 = -8.48669e+04 lbf Fy2 = -8.97143e+03 lbf Mz2 = 7.82053e+04 lbf.in
Axial Force : x-direction = -8.48669e+04 lbf
Shear Force : y-direction = 8.97143e+03 lbf
Elmt No 6 :
Coords (X,Y) = ( 240.000 in, 60.000 in)
exx = -1.37276e-04 , curva = -0.00020486 , gamma = -7.05134e-04
Fx1 = 1.88700e+05 lbf Fy1 = 2.03420e+04 lbf Mz1 = 1.45319e+06 lbf.in
Fx2 = -1.88700e+05 lbf Fy2 = -2.03420e+04 lbf Mz2 = 9.87850e+05 lbf.in
Axial Force : x-direction = -1.88700e+05 lbf
Shear Force : y-direction = 2.03420e+04 lbf
Elmt No 11 :
Coords (X,Y) = ( 420.000 in, 60.000 in)
exx = -1.58567e-04 , curva = -0.00026987 , gamma = -5.77161e-04
Fx1 = 2.17967e+05 lbf Fy1 = 1.66502e+04 lbf Mz1 = 1.30552e+06 lbf.in
Fx2 = -2.17967e+05 lbf Fy2 = -1.66502e+04 lbf Mz2 = 6.92505e+05 lbf.in
Axial Force : x-direction = -2.17967e+05 lbf
Shear Force : y-direction = 1.66502e+04 lbf
Elmt No 16 :
Coords (X,Y) = ( 660.000 in, 60.000 in)
exx = -1.06552e-04 , curva = -0.00024898 , gamma = -6.18281e-04
Fx1 = 1.46467e+05 lbf Fy1 = 1.78364e+04 lbf Mz1 = 1.35297e+06 lbf.in
Fx2 = -1.46467e+05 lbf Fy2 = -1.78364e+04 lbf Mz2 = 7.87403e+05 lbf.in
Axial Force : x-direction = -1.46467e+05 lbf
Shear Force : y-direction = 1.78364e+04 lbf
==================================================================== External Forces Shear Forces in Columns ==================================================================== Roof 21,266.27 lbf Floor 4 17,013.33 lbf Element 1 8,971.43 lbf Floor 3 12,760.00 lbf Element 6 20,342.00 lbf Floor 2 8,506.67 lbf Element 11 16,650.20 lbf Floor 1 4,253.33 lbf Element 16 17,836.40 lbf ==================================================================== Total 63,800.00 lbf Total 63,800.03 lbf ==================================================================== And in the vertical direction we have: ==================================================================== Gravity Loads Axial Forces in Columns ==================================================================== Roof -110,000 lbf Floor 4 -132,000 lbf Element 1 -84,866.9 lbf Floor 3 -132,000 lbf Element 6 -188,700.0 lbf Floor 2 -132,000 lbf Element 11 -217,967.0 lbf Floor 1 -132,000 lbf Element 16 -146,467.0 lbf ==================================================================== Total -638,000 lbf Total -638,000.9 lbf ====================================================================
/* [f] : Apply full-fixity to columns at foundation level */
for(nodeno = 1; nodeno <= 4; nodeno = nodeno + 1) {
FixNode( nodeno, [ 1, 1, 1 ]);
}
for(nodeno = 5; nodeno <= 24; nodeno = nodeno + 1) {
FixNode( nodeno, [ 0, 1, 1 ]);
}
LinkNode([ 5, 6, 7, 8 ], [ 1, 0, 0] );
LinkNode([ 9, 10, 11, 12 ], [ 1, 0, 0] );
LinkNode([ 13, 14, 15, 16 ], [ 1, 0, 0] );
LinkNode([ 17, 18, 19, 20 ], [ 1, 0, 0] );
LinkNode([ 21, 22, 23, 24 ], [ 1, 0, 0] );
Overall displacements in the frame will now be represented with five global degrees of freedom. Details of the stiffness and load vector are:
MATRIX : "eload"
row/col 1
units
1 lbf 4.25333e+03
2 lbf 8.50667e+03
3 lbf 1.27600e+04
4 lbf 1.70133e+04
5 lbf 2.12667e+04
SKYLINE MATRIX : "stiff"
row/col 1 2 3 4 5
units N/m N/m N/m N/m N/m
1 4.35045e+08 -2.17523e+08 0.00000e+00 0.00000e+00 0.00000e+00
2 -2.17523e+08 4.35045e+08 -2.17523e+08 0.00000e+00 0.00000e+00
3 0.00000e+00 -2.17523e+08 4.35045e+08 -2.17523e+08 0.00000e+00
4 0.00000e+00 0.00000e+00 -2.17523e+08 4.35045e+08 -2.17523e+08
5 0.00000e+00 0.00000e+00 0.00000e+00 -2.17523e+08 2.17523e+08
A summary of output is:
------------------------------------------------------------
Node Displacement
No displ-x displ-y rot-z
------------------------------------------------------------
units in in rad
1 0.00000e+00 0.00000e+00 0.00000e+00
2 0.00000e+00 0.00000e+00 0.00000e+00
3 0.00000e+00 0.00000e+00 0.00000e+00
4 0.00000e+00 0.00000e+00 0.00000e+00
5 5.13652e-02 0.00000e+00 0.00000e+00
6 5.13652e-02 0.00000e+00 0.00000e+00
7 5.13652e-02 0.00000e+00 0.00000e+00
8 5.13652e-02 0.00000e+00 0.00000e+00
9 9.93061e-02 0.00000e+00 0.00000e+00
10 9.93061e-02 0.00000e+00 0.00000e+00
...... details of displacements removed ......
21 1.88339e-01 0.00000e+00 0.00000e+00
22 1.88339e-01 0.00000e+00 0.00000e+00
23 1.88339e-01 0.00000e+00 0.00000e+00
24 1.88339e-01 0.00000e+00 0.00000e+00
MEMBER FORCES
------------------------------------------------------------------------------
Elmt No 1 :
Axial Force : x-direction = 0.00000e+00 lbf
Shear Force : y-direction = 1.59500e+04 lbf
Elmt No 6 :
Axial Force : x-direction = 0.00000e+00 lbf
Shear Force : y-direction = 1.59500e+04 lbf
Elmt No 11 :
Axial Force : x-direction = 0.00000e+00 lbf
Shear Force : y-direction = 1.59500e+04 lbf
Elmt No 16 :
Axial Force : x-direction = 0.00000e+00 lbf
Shear Force : y-direction = 1.59500e+04 lbf
Fixing nodal rotations increases the overall stiffness of the structure -- the result is lateral displacements in the shear structure which are smaller than for the moment resistant frame (i.e. 1.8834e-01 inches versus 5.6235e-01 inches). Again, notice that shear forces across the base of the structure are balanced by the external loads (i.e 4 times 1.59500e+04 lbf = 6.3800e+04 lbf).
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