For non engineers, structural analysis may seem like an overly complex subject. A person who is not a civil engineer will never be required or even allowed to solve a real structure, but it is still good to give some general idea for learning. This came to my mind when I heard a question once, from a nonengineer, who drew sketch of a really simple structure and asked if we solve this member by member such as column by column, slab by slab and beam by beam. This is of course not correct and civil engineers know that it doesn’t work that way…

So for people who are not civil engineers, let’s provide a roadmap here. To analyze a structure, first, we make a model of the structure. This will indeed look like a sketch of the skeleton of the structure but there is much more to it. This model has to include certain things, in order to adequately represent the structure we want to solve. In other words, we are making a mathematical representation of the structure on sketch here (could be 2D for simple symmetrical cases but in reality it is almost always 3D and done with computer). So what should it include? Things such as:

Support conditions
Dimensions of members
Connection conditions or members to each other
Stiffness of members (from which global stiffness is calculated)

This model can be as a skeletal structure, but for complex parts of the structure the members can be divided into much smaller parts as well – which is called the finite element method (we can make the whole structure like this too). We may also want to analyze the whole structure by finite elements, which would be more calculation intensive.

The critical part here is, the calculation of overall stiffness and then displacements based on applying certain external loads to a structure of certain shape and stiffness. From this we obtain the overall deformation and reaction loads on the structure, from which individual member loads (and the stresses they create in members) and deformations can be calculated. With rare exceptions, today this is done exclusively by computers using structural analysis software because calculation of overall stiffness and then the deformations under external loads are too calculation intensive which require very large matrices, even if we were able to adequately represent the structure as a skeletal one by capturing all necessary details.. And in cases where finite elements are involved, the calculations are much more, which also require advanced mathematical methods. (Here you may ask, how the Empire States was built before computers existed… the answer is: making simplifying assumptions – and a lot of them which inevitably means inefficiencies no matter how well engineering judgment are exercised. After Newtons laws and calculus, the principles of structural analysis has gradually been established since 1700s and the engineers found very clever ways indeed, to apply them to build large buildings or bridges… even before computers.)

In real structures we also take into account dynamic effects such as earthquake and wind, plus deformations which can stay in elastic region (temporary) or become plastic (permanent). Of course this is all assuming the foundation is fixed to the ground which cannot be assumed in certain more complex cases (i.e. when the structure is too stiff and heavy and the soil is not very stiff), where we much also take soil structure interaction into account.

Even if designing structures needs an engineering degree, a non engineer may still want to study the subjects for learning. In such case, the courses to study would be statics, and then strength of materials and then structural analysis, for a standard undergraduate level knowledge. By studying these, one can learn the fundamental principles to analyze structures. Of course the real structures are far more complex than seen in these courses while studying subject matters. And most importantly a licensed engineer’s review and stamp is needed for an officially valid design.

As an example, even to analyze the simple frame as seen above, one must make considerable hand calculations, mostly involving dull matrix calculation (of course after correctly implementing structural analysis principles) if wanted to solve manually. As a result, the whole force deformation relationship of the structure will be obtained.