========================================== 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).
Return to Home Page