Moment Distribution Method 4

[pravi]

I have been using Moment Distribution Method to analyse continuous beams and portal frames, as righting programes in spreadsheets becomes very easy. Every body now-a-days use stiffness method, is it ok if I continue with MDM for the analysis?

 

[JAE]

Moment distribution analysis, in reality, IS a stiffness method. It is just a different way to solve the equations simulaneously. There is nothing wrong with using MDM for your analysis. The formal stiffness method is just easier for programming and that is why it is used so often in software products.

MDM, though, is a bit more cumbersome to use and program but if you already have a spreadsheet that performs well, and you can cross check it with another software product, go ahead and use it.

 

[pravi]

Thanks JAE, You have boosted my confidence.

 

[AlohaBob]

I made spreadsheets too for MD.

Just a caution though. Be sure to distribute moment due to displacement as well as FM from loads. These Moments are significant.

 

[trilinga]

A few more points to compare.

1. MDM is OK for small problems such as continuous beams and small frames. However, it will be very labourious for multibay, multistoreyed frames.

2. In MDM, one has to go through the required number of cycles before the results converge to a reasonable accuracy level. Matrix method gives the required accuracy in a single stage analysis.

3. Matrix method of analysis is more convenient for programming.

4. MDM does not give the displacements and member deflections. One needs to do further elaborate computations to get the dispacements. Matrix method gives the displacements (in stiffness formulation)as the first result. The calculation of member forces from displacements is much easier in Matrix method.

5. Matrix method is highly suitable if one has to work out different load combinations to arrive at the governing forces and moments. The displcements and the member forces due to different load cases are worked out simultaneously in Matrix analysis and the load combination is only a factored addition of the load cases..

5. Last but not the least, MDM is useful only for static analysis,while by Matrix method we can solve both static and dynamic problems.

Cheers and a very happy new year to all.

Trilinga

 

[dik]

I guess, for frames, there's the portal method <G>...

 

[koodi]

Moment distribution is my favorite method of structural analysis. Even though this thread appears a little stale. So here's my take on everyone's comments:

JAE,
A more adsact description of moment distribution analysis is that it is a &quot;numerical method.&quot; It is also a lot harder to write a finite element program than a MD program, particulary in excel. Obviously MD can't do everything FE does--apples & oranges.

AlohaBob,
For some transient loads it may be more correct not to account for displacements. As the moments may not be able to redistribute fast enough to produce the static case (i.e. sideway).

trilinga,
I'm not sure what types of dynamics problems your working on, but it is possible to do a seismic analysis using moment distribution. Per JAE's comment above neither method brings anything new to the table, they're just diffent ways to get to the answer.

 

[trilinga]

koodi

I have been in the field of structural analysis and design for the past 25 years. In the earlier days when computer was a dream in a design office, MDM was the most favoured method of frame analysis to all. I have carried out seismic analysis using MDM by the equivalent static method in which you calculate the (approximate) nodal equivalent static forces due to seismic loading (considering the frame as a Single Degree Of Freedom system) and perform a static analysis. But the present day codes do not accept this method but insist on the Response spectrum method. You require the different natural frequencies of the frame and find the response of the frame to a given excitation using the site specific Response spectrum. I have not heard of anyone performing this analysis using MDM. I will be very happy to know if you have a way to use Moment Distribution for this.

Solving the Dynamic differential equation of a Multiple Degree Freedom system is done very systematically using Matrix method.

I am not underestimating MDM but would like to highlight that it can not cater for the present day's stringent engineering requirements.

Cheers

 

[trilinga]

A small correction in my post. The earlier seismic analysis did not treat the frame as a SDOF but a cantilever stick with its masses lumped at the different storey levels.

 

[koodi]

trilinga,
No, obviously, moment distribution cannot solve for natural frequencies.

I was speaking of &quot;the matrix method&quot; as it applies to creating a stiffness matrix (composed of stick elements only), applying the boundary conditions, and solving for the member forces displacements. This is not the same as assuming an oscillation and then solving for the natural frequencies. Apparantly, your definition of &quot;the matrix method&quot; is that it encompasses all of math.