[Midas Gen][ABAQUS][Midas2Abaqus] Midas Gen Verification Example Eigen-9: Eigenvalue and static analysis of a 5- level pyramid building under lateral loads [ Midas Gen 验证实例 Eigen-9: 5层金字塔结构的特征值分析及侧向水平力静力分析]

【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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