【1】Problem Description ( Midas Gen Verification Example Eigen-9: Eigenvalue and static analysis of a 5- level pyramid building under lateral loads)
Perform the eigenvalue analysis of a pyramid building. Calculate the natural frequencies
and the displacements of each floor due to static lateral loads.
【2】MODEL Properties
Dimension
Length 70 × 12 in Width 70 × 12 in Height 5 × 12.125 × 12 in
Floor mass M = 100 psf = 1.7972 × 10 -6 kips ∙ sec 2 /in
Nodes 42 ~ 45 are the master nodes for the 4 th ~ 1 st levels in a decending order
respectively.
Gravitational acceleration g = 386.4 in/ sec 2
Mass and rotational mass moment of inertia at each floor.
Floor Master node Mass, M X =M Y Rotational mass moment of inertia, I m
4 42 0.0507246 238.6087
3 43 0.2028986 3817.7391
2 44 0.4565217 19327.3044
1 45 0.8115942 61083.8261
Element
Beam element
Material
Modulus of elasticity E = 29500 ksi
Poisson’s ratio
ν = 0.3
Section Property
Horizontal beams Area A = 13.5 in 2
Effective Shear Area A sy = 6.5016 in 2
A sz = 6.1105 in 2
Torsional stiffness I xx = 1.22 in 4
Moment of inertia I yy = 712.0 in 4 (Strong axis)
I zz = 22.5 in 4 (Weak axis)
Diagonals Area A = 11.7 in 2
Effective Shear Area A sy = 2.97 in 2
A sz = 7.532 in 2
Torsional stiffness I xx = 1.12 in 4
Moment of inertia I yy = 146.0 in 4 (Strong axis)
I zz = 49.1 in 4 (Weak axis)
Boundary Condition
Nodes 6 ~ 41 (at an increment of 5 ) ; Constrain all DOFs.
Nodes 42 ~ 45 ; Constrain Dx, Dy and Rz of all nodes at each
level to these nodes. (Master nodes)
【3】Midas Gen Model
【4】Midas 2 Abaqus Model
【5】Abaqus Model
【6】Results
Static Load Case
Eigen Analysis Load Case
mode 1
mode 2
mode 3
mode 5
mode 6
mode 8
mode 9
【7】Comparison of Results
| FEQUENCY(CYCLES/TIME) | ||
| Node | Midas GEN | ABAQUS |
| 1 | 8.27E+00 | 8.3266 |
| 2 | 8.27E+00 | 8.3266 |
| 3 | 1.59E+01 | 16.078 |
| 4 | 1.59E+01 | 16.078 |
| 5 | 1.64E+01 | 16.39 |
| 6 | 2.51E+01 | 25.447 |
| 7 | 2.51E+01 | 25.447 |
| 8 | 3.37E+01 | 33.732 |
| 9 | 4.19E+01 | 42.509 |
| Displacement X | ||
| Node | Midas GEN | ABAQUS |
| 1 | 1.81E+00 | 1.637 |
| 42 | 1.39E+00 | 1.30235 |
| 43 | 1.03E+00 | 0.998134 |
| 44 | 7.10E-01 | 0.697188 |
| 45 | 3.82E-01 | 0.374851 |
PS. 两者有差异的其中一个原因是，ABAQUS用的是欧拉两单元，没有考虑剪切效应。
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