different methods exploit different characteristics. eg the unit load method says the deflection at the redundancy is zero. if you remove the redundancy you can calculate a deflection; a deflection that the redundancy prevents. apply a unit load (at the redundancy location) you can determine the redundant load.
Some methods are better for hand calculation. Others are more suitable for a computer. It would be almost impossible to solve a 50 x 50 matrix by hand but it's a breeze with a computer.
The slope deflection method was common in engineering offices prior to the Hardy Cross moment distribution method which became the preferred method by many engineers prior to the advent of computers. Today, many engineers use structural software to solve determinate as well as indeterminate structures.
An engineer who knows the principles involved in the various methods of solving indeterminate structures has a much better understanding of structural theory than the guy who plunks data into a computer and awaits the output.
The vast majority of computer applications utilize some permutation of the stiffness matrix method. Since most indeterminate work is done with the aid of a computer, that's an important method to know.
As others have mentioned, when doing hand calculations, the best method often depends on the information available and the parameter of interest. For developing intuition via hand calculations, I like the moment distribution method the best. While virtual work seems very elegant, the energy stuff still feels like voodoo to me at times.
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The simple answer is:
1. Statically indeterminate structures can't be analyzed with statics.
2. Statics is used for hand calculations of statically determinate structure because it is much easier for hand calculation.
There are really only two general methods for analysing indeterminate structures.
1. Flexiblity, force, compatibility method.
2. Stiffness, displacement, equilibrium method.
"i need the very salient points" ... MDM is not something you can write on the back of a "fag packet". if you research (google, wiki) MDM (or Hardy Cross).
i guess MDM distributes moment along a beam with many supports.
My goodness..., if you are going to call yourself a Structural Engineer, why not invest in a couple of good textbooks on the basics of Structural Analysis, both Statically Determinate and Statically Indeterminate? A couple of computer programs, does not an engineer make. Understanding these basic, longhand, fundamental methods of analyzing various structural problems will help you understand all of the structural problems you face, and how and why they act the way they do. You need to have a gut feel for this structural action if you are going to do a good job of designing the structure. And, if you are too lazy to do a little of your own digging on the subject, you probably shouldn’t be doing this type of work. On the fundamentals, you learn by doing, over and over again, until you understand, without a second thought. You won’t learn by a few guys giving you some offhand comments, although a number of the answers above are very instructive.
This will not get you up to speed on moment distribution but it will give you an idea of what’s involved.
1. Pretend all spans are fixed and calculate their end moments (wL^2/12 for uniform load, PL/8 for point load center span, other end moments per loading conditions).
2. Calculate the span stiffnesses (EI/L).
3. Combine the stiffnesses of adjoining members and proportion each member’s stiffness at each joint.
4. Balance the unbalanced moment.
5. Carry over half of the balancing moment to the adjacent joints.
6. Do not balance an actual fixed end moment; it simply “absorbs” the moment carried over to it.
7. Lather, rinse, repeat to the degree of accuracy you want.
A trick that will simplify the process considerably: if an end span has a pinned end the stiffness of that span is ¾ what it would otherwise be. By doing that you can balance that moment only once and not carry over any moment to it. That cuts the amount of steps.
This should all be clear as mud right now but if you study up on the method it will make more sense.
![[king]](/data/assets/smilies/king.gif "[king] [king]")
