I have basic querry regarding Frequency calculation  in STAAD . 

I have modelled 50mt High Trestle in STAAD with all Conv loads acting at the top four nodes of Trestle.Now to calculate Frq of the strucutre in STAAD , I have followed below steps: 1)  Define one Load case as DL +0.5LL . 2)  Define Hinge at nodal points. 3)  Found out the reaction at each point in all three directions. e.g  for particular       node    FZ 3 FY 10 FZ 4 4)  Then i applied FY direction  force in all direction for above node i.e FX 10 FY 10 FZ 10 and deleted hinge support at every node except at ground support. 5) Lastly, I have given command MODAl CALCULATION REQUESTED and found out the first mode frq from the output of  Eigenvalue solution of STAAD. 

First of all,i would like to ask whether my method is correct or faulty.Secondly, what i can't get is why to applied same lump mass in all direction in STAAD (What i read from STAAD help) . 

Ans

This procedure is called mass modelling.The explanation is given in STAAD technical manual.You can the the link for details. 

The procedure what u have adopted is correct.Frequency adopted shall to corresponding to maximum mass participation in each direction X,Y and Z.Alternately I am putting one more way to calculate the same .Also a file for  Rayleigh frequency is added.Necessary load reduction can be done at your end. 

********************************************** Modal analysis input file 

STAAD SPACE START JOB INFORMATION ENGINEER DATE 24-Jan-11 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 0 4 0; 3 4 0 0; 4 4 4 0; 5 0 0 -4; 6 0 4 -4; 7 4 0 -4; 8 4 4 -4; MEMBER INCIDENCES 1 1 2; 2 3 4; 3 2 4; 4 5 6; 5 7 8; 6 6 8; 7 2 6; 8 4 8; DEFINE MATERIAL START ISOTROPIC CONCRETE E 2.17185e+007 POISSON 0.17 

DENSITY 23.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 1 2 4 5 PRIS YD 0.45 ZD 0.45 3 6 TO 8 PRIS YD 0.4 ZD 0.3 CONSTANTS MATERIAL CONCRETE ALL SUPPORTS 1 3 5 7 FIXED CUTOFF MODE SHAPE 100 LOAD 1 LOADTYPE None  TITLE Modal analysis SELFWEIGHT X 1 SELFWEIGHT Z 1 SELFWEIGHT Y 1 MEMBER LOAD 3 6 TO 8 UNI GX 15 3 6 TO 8 UNI GZ 15 3 6 TO 8 UNI GY 15 FLOOR LOAD YRANGE 4 4 FLOAD 3.75 XRANGE 0 4  ZRANGE -4 0  GX YRANGE 4 4 FLOAD 3.75 XRANGE 0 4  ZRANGE -4 0  GZ YRANGE 4 4 FLOAD 3.75 XRANGE 0 4  ZRANGE -4 0  GY FLOOR LOAD YRANGE 4 4 FLOAD 5 XRANGE 0 4  ZRANGE -4 0  GX YRANGE 4 4 FLOAD 5 XRANGE 0 4  ZRANGE -4 0  GZ YRANGE 4 4 FLOAD 5 XRANGE 0 4  ZRANGE -4 0  GY MODAL CALCULATION REQUESTED PERFORM ANALYSIS FINISH ****************************************** 

Rayleigh method input file 

STAAD SPACE START JOB INFORMATION ENGINEER DATE 24-Jan-11 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 0 4 0; 3 4 0 0; 4 4 4 0; 5 0 0 -4; 6 0 4 -4; 7 4 0 -4; 8 4 4 -4; MEMBER INCIDENCES 1 1 2; 2 3 4; 3 2 4; 4 5 6; 5 7 8; 6 6 8; 7 2 6; 8 4 8; DEFINE MATERIAL START 

ISOTROPIC CONCRETE E 2.17185e+007 POISSON 0.17 DENSITY 23.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 1 2 4 5 PRIS YD 0.45 ZD 0.45 3 6 TO 8 PRIS YD 0.4 ZD 0.3 CONSTANTS MATERIAL CONCRETE ALL SUPPORTS 1 3 5 7 FIXED CUTOFF MODE SHAPE 50 LOAD 1 LOADTYPE None  TITLE Rayleigh frequency X CALCULATE RAYLEIGH FREQUENCY SELFWEIGHT X -1 LIST 1 TO 8 MEMBER LOAD 3 6 TO 8 UNI GX -15 FLOOR LOAD YRANGE 4 4 FLOAD -3.75 XRANGE 0 4  ZRANGE -4 0  GX FLOOR LOAD YRANGE 4 4 FLOAD -5 XRANGE 0 4  ZRANGE -4 0  GX LOAD 2 LOADTYPE None  TITLE Rayleigh frequency Z CALCULATE RAYLEIGH FREQUENCY SELFWEIGHT Z -1 LIST 1 TO 8 MEMBER LOAD 3 6 TO 8 UNI GZ -15 FLOOR LOAD YRANGE 4 4 FLOAD -3.75 XRANGE 0 4  ZRANGE -4 0  GZ FLOOR LOAD YRANGE 4 4 FLOAD -5 XRANGE 0 4  ZRANGE -4 0  GZ PERFORM ANALYSIS FINISH 

For Calculating frequency by Rayleigh method..it is not required to input CUTOFF MODE SHAPE. 

In example 1 in STAAD menu,they have furnished the method of calculating Rayleigh frequency. 

Q I have taken a part para from your earlier reply as follows :- 

"Even if the loading is known to be only in one direction there is usually mass motion in other directions at some or all joints and these mass directions (“loads” in weight units) must be entered to be correct" 

As you mentioned that though loading is in one direction there will be motion in all directions and so we have to apply load in all directions.Now,I'm finding only Frequnecy of a structure and nothing more.I have applied load in X-direction same as in Y-direction.Hence,it will calculate the displacment out of that load in X-direction and from that Time period and frq.But in actualy case it may happen that this load is more or less in X-direction in respect to what we have applied .In that condition is it not possible that time period will be different????? 

Also one more confusion in my mind is that,if the structure has got some forces already in lateral directions (Say if apply forces of incline conv. gallery modeled in STAAd at the top of trestles) in DL and LL then how to consider them while calculating joint weight at the nodes and frq. 

Ans : Firstly natural frequency is a free vibration problem. 

It is a function of mass and stiffness. 

Hence when you require to know the frequency of a system in all three direction.. 

Say for X direction-Natural frequency is a function of mass and stiffness in X direction. Say for Z direction-Natural frequency is a function of mass and stiffness in Z direction. Say for Y direction-Natural frequency is a function of mass and stiffness in Y direction. 

In all this direction please note natural frequency is dependent on mass and not on horizontal force..which cant be. 

Hope this clarify your doubt. 

Q: While using STAAD to chek any structure for resonance due to applied loads, is it mandatory to compare frequencies in all mode shapes to the

natural frequency? 

In general, I am being told to take the frequency corresponding to the mode shape where the mass participation is more than 95% in Y direction. Is it correct. 

Ans : fundamental frequancy is dependent of mass and stiffeness of the system (independent of the direction) 

where as Rayleighy frequency is different in different directions. in cases where mass participation in fundamental mode in given direction is close to 100% then rayleigh frequency in that direction is almost equal to fundamental frequency. 

rayleigh frequcy can be calculated by fr=1/2pi*(sqrt(m/k)) 

mass is same in all casses where as stiffeness is different in different directions, so raleigh frequency in particular direction is dependent of  mass and stiffness in that particular direction

As understanding is Rayleigh method of obtaining frequency is an approximate method,whereas modal analysis using Eigen value problem in much better and accurate. 

In  Rayleigh method, frequency of the structure corresponds to the general direction of the deflection generated by the load. 

In my opinion the frequency obtained from both this method will be different even in first mode. 

I have uploaded the STAAD file on Modal analysis and Rayleigh frequency to give idea of how to  calculate these frequency in a software. 

However many experts are there in the forum who can much better expalin the theoritical background of both these methods. 

That 90% or 95% mass participation is mainly to check the base shear value obtained in STAAD. Otherwise the base shear what you are getting in STAAD will not be correct, hence we have to increase the number of modes to get more mass participation. 

In STAAD another option is given to rectify this, Missing mass participation - but I have used it and found not working well. 

Q:  am still not free of the anxiety as to which of the two is the natural frquency Whether the time of the frquency of the first mode may be considered as natural time period. Please clarify and help in removing the confusion prevailing  among many of our friends and colleagues.

Ans Please find below some quote taken from a good reference regarding the importance of natural frquencies and mode shapes. 

Dynamic Aspects: The natural frequencies and mode shapes are the primary parameters that affect the response of a structure under dynamic loading

[1]. The free vibration problem is solved to extract these values. Since no external forcing function is involved, the natural frequencies and mode shapes are direct functions of the stiffness and mass distribution in the structure. The frequency and mode shape obtained may vary significantly depending upon the mass modelling. This, in turn, affects the response spectrum and

forced vibration analysis result. When the modal frequencies of a structure are known the designer can ensure that the frequency of any applied periodic loading will not coincide with a modal frequency and hence cause resonance. Thus extreme caution should be exercised in mass modelling a dynamic analysis problem. 

Mode shapes is the shape assumed by the body vibrating with certain frequency in order for inertia forces to cancel out elastic stiffness forces. Most often, only the first few modes are of interest. 

Rayleigh frequency method is a very basic method of determining the natural frequency of the structure. For typical structure where the mass and stiffness distribution is very, very uniform, the frequency determined by this method is close to that determined by other methods. The basis of the method is the conservation of energy, which requires that total energy is conserved or which means that maximum kinetic energy is converted to maximum potential energy without any loss due to damping, etc. 

Rayleigh frequency is determined by equating maximum kinetic energy to the maximum potential energy of the system. This method is very accurate for SDOF system but its utility is very limited for MDOF systems. 

Since this method only estimates one and only one frequency, there is no reason to input any cut off mode. 

The mode shapes you get are normalized values i.e. these are not absolute values but relative values i.e. normalized with respect to the highest number. It just signifies the shape i.e. all other values have been divided by the maximum number. 

The reason for that is we are more interested in the shape rather than the absolute values. 

The mode with lowest frequency is generally treated as mode 1 and thereafter in increasing order of the frequency. Lowest frequency implies relatively lowest stiffness and/or highest mass which is logical since you would expect such a mode to be of more consequence than the one which has higher stiffness and/or lower mass. 

  The solution methods generally provide the output in such a format such that the result is ordered in such a way. Modes are ordered in increasing order of frequency. That is also the one of the reason why people generally say first few modes are more important than the rest. 

Q : I am using STAAD Pro software for analysis and design of buildings generally G+4 to G+6. The design of beams is generally governed by the max moment at a section d from the face of the column but the STAAD Analysis gives the values of the moments at the centre or nodal point thereby the beam will be designed for the higher moments and turns to be uneconomically. 

My issues are: 1) How to capture the moments at the section d from the face of the column if in a structure where there are no of properties defined. If any one has modelled the structure considering this aspect, kindly guide me as what the STAAD parameters has to be given in the input and how to interpret the results. 2) Are there any other ways to resolve this problem. 3) While designing the foundations, what are the load combinations to be considered? Is it sufficient to consider the partial safety factors for loads as per

IS 456 Page 68 under the limit state of serviceability 

Ans :

First of all your idea of moment at a distance d from the face of the column is not correct and it should be at at the face of the support. 2.For shear only the Vu is at a distance of d from the face of the support. 3.For finding the values of moment at the face of the support and for shear at the distance of d , go to the Properties menu by right clicking after analysis in that you can find the BM, S.F, Torsion at various span points. 4.For the footing you have to consider the worst Ultimate combination and the value of B.C is also to be Ultimate value. Hope you can try and send your queries for more doubts. 

It is incorrect to derive results from a mismatch with modelling. Please remember that a structure modelled by line elements - 2D/3D beam would give different results as compared to modelling the columns and beams by solid finite elements. I do not know whether you model the slab or not. Further, we use gross section of concrete as effective and neglect reinforcement in evaluating stiffness. We use an ad-hoc value of modulus of elasticity of concrete. There is no justification of selectively applying a correction. 

As an exercise, try to model a 2D portal frame - single bay. single storey using solid finite elements for the two columns and beam and compare the first mode frequency with that of modelling by 2D beam elements of the beam and two columns and note the difference in results. 

We have accepted that modelling as a 3D frame is sufficient as a design practice. Use the results as such without trying to reduce it selectively based on column/beam thickness 

Q:  To design a beam with the results from staad results, we design the support reinforcement considering the nodal moment given by staad at that support. But one of my client wants me to consider the moment at support face. That means if the column dimension is Cx then consider the moment at Cx distance from support node.     Certainly the moment is much lower there and reinf. requiremnt is much less. But as we extend the beam reinf. in column with proper bond length i think they act monolithically and the moment at the node connecting column and beam should be considered. 

Ans : Technically speaking your client is correct. I append below an extract from a technical literature. 

As we know, the beams and columns of our actual structure are represented by lines in the computer model. In the actual structure, a beam spans a distance which is the clear span between the faces of columns. But in the computer model, the line for the beam spans between the centerlines of the column. The half-depth portion of either column is considerably stiffer than the beam itself from the standpoint of bending. To take advantage of this additional stiffness, we may declare that the start and end faces of the beam are offset from the node by a distance equal to the half-column-depths. 

As I understand etabs considers design moment at Cx/4 from the centre of column towards the face of support.

Your client is quite right, but actually carrying out such a design would be quite tedious as each beam element would have to assigned offsets equal to half the width of the column.

Kindly refer to IS code 456:2000 clauses. ALso refer the book by Devas Menon. 

IS code clearly says that crtical section for the moment is at  face of the support and for shear is at "d" from the face of the support.Normally in staad wat we do is if the columns are of smaller section modulus we go for the nodal moment, as you take for the convinience and it hardly overestimates the design moments but if the supports are of higher section modulus say column of size 800x800 we've to take the moment at face of the support otherwise

design will be very uneconomical. even torsion also can be taken at face of the support because at beam column junction the'll be infinite stiffness to take care of moments,shear and torsion whatever  the  value software shows. Ref 22.6 of IS456-2000 for detailed explanation. 

Comments  from experts on the above  are welcomed. As per IS 456 clause 22.6.1 for monolithic construction, moments computed at face of supports shall be used in design of members at those sections 

Beams support moments/column moments The support moments so obtained from analysis are at centreline of coulmn and these needs to be reduced to arrive at moments at column face for purpose of Beam support moments The reduction in support moments is appreciable if column dimension is more. Similarily column moments also needs to be reduced at top and bottom faces of beam in respective storey. Column EQ design moments Further the column EQ moments are also based on clear height of columns as per manual design practice. The seismic moments worked based on centerline analysis needs to be corrected for face (by reducing) 

Mid span moments in beams The moment at midspan is calculated by deducting SS moment of beam from average of support moments(at two ends of beam) Thus simply supported moment worked based on centerline needs to be reduced by deducting a small correction moment Mc' = w*C^2/8 (C is the width of support i.e column dimension in case of frame construction and w is the beam loading). But since this value is very very small , it is ignored for better.Moreover for keeping certain redundancy in designs , some minimum span moments must be adhered irrespective of calculated value being smaller . 

Moments at center line But in case- an RCC joint is designed specifically,I think the moments at centerline needs to be followed In practice column moments are generally NOT reduced, though beam support moments at faces can be/(are) reduced. This will also help to adhere to strong column-weak beam theory and design is   better from EQ considerations. 

From academic point of view - - may be corrected for better understanding of concept : AT RCC JOINT:concrete volume at a joint is neither a column nor a beam but a joint which   has got tremendous stiffness in vertical as also in horizontal direction due to continued conc   members(Beams in horz and columns in vertical directions) .The joint needs ductility for   resisting EQ and reinforcement in form of ties are provided.It is the JOINT ductility and this joint   ductility is projected into the connected beams /columns as per specified detailing practice. 

Mostly beam widths are less than column dimensions , the continuation of lateral column ties take care of Joint ductility in addition to holding the column bars. It may be noted that Slenderness of columns is always based on clear column heights. However assuming common conc volume at joint as a column is fine as per discussion at top. 

Manual practice of design for column moments EQ moments are worked based on clear column heights , though gravity load moments taken from centerline analysis are not disturbed. 

If the columns and beams are assumed as LINE ELEMENTS, then use the same values of forces [moments and shears] for design rather than trying to be smart in trying to reduce forces. The analysis is for an assumed IDEAL member - apart from the fact of using centre line distances for line elements, the analysis assumes entire concrete section [gross area of concrete ignoring reinforcement] and no assumption is made in analysis whereas in design the Neutral axis will vary continuously as the moment is not constant. The effect of slab is ignored in analysis [whereas T-section is assumed for design of middle section] 

Please try to analyse  a hypothetical case of a simple portal frame - line elements vs solid 3D finite elements line elements could be two noded 3 DOF elements; necessarily, there will be a lot of 3D solid finite elements to maintain aspect ratio the verical loads may be only self weight and horizontal load applied only at beam level, say 5%g you will be surprised / shocked with outcome of results 

WE SHOULD AGREE THAT ANALYSIS IS AN ILLUSION, particularly for reinforced concrete elements. If one wants to reduce the moment at face of the column thinking that he is smart, let him please himself I WILL NOT be that smart like such persons who selectively tries to interpret. 

In routine designs, the face moments are seldom worked out and designs are done based on centerline values. But since the topic of computing moments at face   has come on sefi, view point were given by many eminent members in light of   Codal provision (clause 22.6.1 IS 456-2000) For monolithic constructions , moments computed at face of supports shall be used in design of members at those sections. 

Generally in exceptional cases wherein some member has congestion of reinf a designer is compelled to go for face moments rather than CL..It is not a routine .But discussion is meant to understand the basis of face moments as allowed by the Code.However advice from Prof ARC sir is in direction for sound engineering of structures. 

Q Q Q : Please give explanation on Modelling with member offset and without- which one is correct and its effects in analysis and design Best Regards, 

Ans : n my openion & experience with software for acurate analysis you have to modeled the exact building in staad. Modeling Building with offset is time taking. 

Q When modelling a building in STAAD, we give member end offsets for beams to model the beam from face of column to face of column instead of center to center. 

  But if there is offset in plan (beam centerline does not coincide with column centerline because wall is inner or outer flush), how should we provide the offset command? 

  Is it better to model the structure with column centerline as nodes and specify plan offsets for the beams? 

  Or is it better to model the structure with beams going along node to node line and set offsets for the columns? 

  How to incorporate it in analysis to include moment on column due to eccentricity of beam load? 

  How to incorporate it in design - any parameters to set? 

Ans "Is it better to model the structure with column centerline as nodes and specify plan offsets for the beams? 

  Or is it better to model the structure with beams going along node to node line and set offsets for the columns?" 

Actually the 1st method is more accurate (for various reasons), but cumbersome. So we (universally invariably, I presume) follow the 2nd method. 

 As the cross sectional properties (Moment of Inertia/Section Modulus) of the columns are correct only if it is modelled  at column center line.    Normally the engineers go by the beam center lines and do not use offset commands, the results would be on the safer side. 

In the design stage, the additional moment on the column due to the offset beam centerline may be considered, if the off-set is considerable. 

It is OK for most of the practical cases. Please ponder over the following situations: 1. In case of more than 10 storeies it may be possible to make use of the columns of various cross sections say from 300x300 to 300x1500 and more. In that case how can we assume the C.L and also the columns outside flush in the exterior columns? 2. Also if the architect proposes the brick wall flush to out side that is to say on one side is it ok to consider the wall reactions on the C.L? Because we can not take much pain we can not simply for an easy means. If you propose of other sefians have some good idea let me learn since STAADPRO is a good software for day to-day works.