Verification of cantilever beam analysis in STAAD

Question

Never having used STAAD for modal analysis before, I referred to Example 15 of the STAAD verification manual which demonstrates how the natural frequency of a simply supported beam . 
 For my requirement , I first I attempted to model a simple cantilever beam in STAAD so I could compare the results with manually calculated values. 
 For information my input file is shown along the message. 
 I modelled the beam with the section properties and material properties as below 
 Ax & Az = 0.56m2 
 Ixx=Izz = 1.30415 m4 
 E=205KN/mm2 
 l = 22m 
 POISSON 0.3 DENSITY 325.3 kN/m3 
 I divided the beam up with a series of node points to ensure the mass of the beam was uniformly distributed . 
 I fully restrained the beam at one end and all other intermediate nodes were free. 
 I get the following results: -

Mode

Natural frequency, Hz 
 (Manual analysis)

Natural frequency, Hz 
 (STAAD analysis, basic)

1

4.43

4.393

2

27.79 
 
 27.479

3

77.79

28.313

4

152.44

76.806

5

84.819

I am looking for an explanation on following issues 
 1. In analysis by STAAD i am getting only 5 modes of frequency .How to increase the number modes? 
 ( i tried increasing cutoff modes also tried increasing number of nodes but no change in result) 
 2. Mode shape 3 (28.313 Hz) & 5 (84.819) given by STAAD analysis is the axial mode. How to avoid the axial modes in analysis. 
 
 Input file : 
 STAAD PLANE START JOB INFORMATION ENGINEER DATE 09-Sep-14 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 0 22 0; 3 0 11 0; 4 0 5.5 0; 5 0 16.5 0; 6 0 2.75 0; 7 0 8.25 0; 8 0 13.75 0; 9 0 19.25 0; 10 0 3.66667 0; 11 0 4.58333 0; 12 0 0.916667 0; 13 0 1.83333 0; 14 0 6.41667 0; 15 0 7.33333 0; 16 0 9.16667 0; 17 0 10.0833 0; 18 0 11.9167 0; 19 0 12.8333 0; 20 0 14.6667 0; 21 0 15.5833 0; 22 0 17.4167 0; 23 0 18.3333 0; 24 0 20.1667 0; 25 0 21.0833 0; MEMBER INCIDENCES 1 1 12; 2 3 18; 3 4 14; 4 5 22; 5 6 10; 6 7 16; 7 8 20; 8 9 24; 9 10 11; 10 11 4; 11 12 13; 12 13 6; 13 14 15; 14 15 7; 15 16 17; 16 17 3; 17 18 19; 18 19 8; 19 20 21; 20 21 5; 21 22 23; 22 23 9; 23 24 25; 24 25 2; DEFINE MATERIAL START ISOTROPIC STEEL1 E 2.06e+008 POISSON 0.3 DENSITY 325.3 ALPHA 1.2e-005 DAMP 0.03 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 1 TO 24 PRIS AX 0.56 AZ 0.56 IX 1.30415 IZ 1.30415 CONSTANTS MATERIAL STEEL1 ALL CUT OFF MODE SHAPE 20 SUPPORTS 1 FIXED LOAD 1 SELFWEIGHT X -1 SELFWEIGHT Y -1 MODAL CALCULATION REQUESTED PERFORM ANALYSIS PERFORM ANALYSIS PRINT MODE SHAPES FINISH 
 I would appreciate any assistance anyone could give me with this.

Kris Sathia · Accepted Answer

In Section Wizard, I used the module named Free Sketch. One can draw the shape of the section on a graph-paper type of an interface. There is also an editing facility through which the coordinates of the vertices of the cross section can be entered in an edit box. 
 Attached is the section that I created using that module.

Modestas · Answer

1. Use a command CUT OFF FREQUENCY. The default value is 108 cps, so may assign a higher value, i.e. 500 to get more mode shapes. 
 2. Remove the mass in Y direction (SELFWEIGHT Y -1).

Modestas · Answer

Use command CUT OFF FREQUENCY 1000 or even higher.

Modestas · Answer

You need to use command CUT OFF MODE SHAPE together with command CUT OFF FEQUENCY. I.e. 
 CUT OFF MODE SHAPE 20 
 CUT OFF FREQUENCY 10000 
 Please read chapter 1.18.3.2 Mass Modeling in the Technical Reference manual for more information about mass modeling in STAAD.Pro.

Kris Sathia · Answer

In our opinion, the beam model and plate model are not representing the same physical structure for the following reason. 
 In the beam model, at any representative location along the length of the beam, all points on the cross section move in tandem. It is as though they are all rigidly connected to each other in the local Y-Z plane of the cross section. That is the nature of a beam model. 
 In the plate model, if you consider any representative ring, each point on the ring can undergo bending independent of other points on that ring. Due to this, the ring will not maintain the shape of a circle. For example, one point on the ring can bend in one direction while a point diametrically opposite to it can bend in a completely unrelated manner. 
 There is also the Poisson's behavior in the plate model that does not exist in the beam model. 
 These differences are significant enough to produce variations in the frequencies. 
 Instead of a hollow cylinder with a lid at one end, had this been a solid cylinder throughout its length, there is a possibility that the results might have been more similar in nature to the beam model.

Modestas · Answer

The diameter of the solid cylinder should be much less so that its sectional properties would match with your model of beam members.

Kris Sathia · Answer

In the beam model, the area and moment of inertia have to be equivalent to those that one would compute for the cross section of the solid cylinder. I used the Section Wizard program to calculate them and obtained 
 Area = 138019 sq.cm 
 Largest moment of Inertia = 1517414822 cm^4 
 I assigned these values to the beam model using the command 
 UNIT CMS 
 MEMBER PROPERTY AMERICAN 
 1 TO 24 PRIS AX 138019 IZ 1517414822 
 With this modification, the frequency of the lowest mode of the beam model is 3.01 cycles/sec. The lowest frequency of the solid model is 2.96 cycles/sec - a 2% difference. 
 The shape of the innermost elements that look like wedges is not correct. Along the two triangular faces, you have a node along the mid-point of one of the sides of the triangles. A screenshot of one of those elements is shown. 
 
 The mid-side node needs to be eliminated and the element incidence needs to be specified using the sequence 
 A-B-C-A-D-E-F-D 
 where A, B and C are the vertices of the triangle at one end of the wedge, and D, E and F are the vertices at the other end. 
 The modified beam model is attached.

Kris Sathia · Answer

Using the solid element model to represent the vessel wall and the liquid inside is not a good idea since you are using that model to calculate the frequency of the structure when it is filled with the liquid. You should use some other software for that. 
 The model is OK only if you want to find the stresses in the tank due to the static weight or hydrostatic pressures due to the liquid. Even in that case, while the tank wall can be modeled using solids, it may not be correct to model the stored liquid using solid elements, since those elements are meant to contribute only to the load and not the stiffness. In STAAD, the modulus of elasticity and Poisson's ratio are required for all solids, and all of them are treated as contributing to the stiffness of the model. 
 The earlier model consisting of plates is OK for finding the frequency of the structure when the tank is empty. However, it is a challenge to find an equivalent beam model that would produce the same frequency as that plate model.

Kris Sathia · Answer

It is perhaps possible, but it is going to take some effort and time. The question is, of what use would such a model be? Isn't the model with plates or solids a better representation of the vessel than an equivalent beam model?