# Elementary Structural Analysis (Civ-A1, Str-A1) Solutions

Your exam is fast approaching.  You might be working a job and have a family that needs your time.  The last thing you want to do is spend \$1,000 on a course to re-learn this material.

If that sounds like you, our Civ-A1 (Str-A1) help is for you.

About: The Elementary Structural Analysis exam is written nationally for civil/structural engineers.  The code for this exam is:

• Civil - 16-Civ-A1 (or you may see it like YY-Civ-A1, Civ-A1)
• Structural - 07-Str-A1 (or YY-Str-A1, Str-A1).

The exam tests candidate’s understanding and knowledge of the basic aspects of structural analysis, through stability, determinacy, methods of analyzing statically and kinetically indeterminate structures, concept of bending and shear and thereby bending and shear diagrams and influence line diagrams.

Format: 3-hour long, closed book exam. Out of the eight questions that are asked in the exam, only six needs to be attempted (choice is given among limited/specified problems).

Dates written: The exam is offered twice every year in the months of May and December.

Approved aids: Since the course is highly computational, an approved scientific calculator is permitted.

Nearly 6 exam questions ask you to identify determinate & indeterminate structures (beams, frames and trusses), from a given lot and then analyze the indeterminate structural member (which is mostly a 2d beam/frame/truss).  You'll also have to draw the bending moment and shear force diagrams (in case of beams and frames) and locate the points of positive/negative maxima and minima in those diagrams.

Since it is not specifically mentioned which method to use for the analysis,  the candidate can use any method of his/her liking.  However, since the exam is quite computational,  the general strategy for such problems should be as:

1. For statically indeterminate beams, the three moment equation (Clausius-Clapeyron equation) is simple and a fast way of obtaining the bending moments at the supports and joints. Then, the shear forces can be computed from the known bending moments or by using the equilibrium equation. Apart from this method, the force method can also be used.
2. For frames, though a lot of force and displacement methods are available, the slope deflection method proves quite efficient in solving the problem in less time. Another advantage of this method is that a single equation needs to be memorized to solve all sorts of frame problems and simple alterations are to be made, depending upon the given boundary condition. Again, once solved for the moments at the joints and supports, the shear forces are computed as in the case of beams. Once moments and shear forces are known, the bending moment diagram and shear force diagram can be drawn.

Pin Jointed Members (Trusses) -  This is probably the easiest problem out of the eight questions. A candidate needs to know how to solve truss problems using the method of joints or the method of sections. Both of these methods use the equilibrium equation of horizontal and vertical forces to compute the unknown forces in the given member of the truss. Certain rules need to be followed to know where from the analysis should start and how to proceed. The only concern in such a problem is that it is somewhat lengthy (problem has 2 parts), however, with practice this issue can be tackled.

There is one problem on the principle of virtual work, where at any given point in the structure (beam/frame/truss), lateral or vertical displacement needs to be calculated using the virtual work principle. To solve such problems and have a good hold on them, the virtual work principle needs to be understood and few related problems need to practiced.

There is also a problem on influence line diagrams, but it is not necessary since this problem is lengthy (2 parts) and has choice with the Virtual Work Principle Problem and a problem on Bending Moment/Shear Force.

So, if one has a good grasp of analyzing structures, (beams/ frames/trusses) then this paper should pose almost no challenge to the candidate.  Problems 1 to 4 (mandatory problems) and problems 5 to 6 (with choices) are all based on analyzing force response. However, the virtual method problem should be practiced to be on the safe side or to save time (since such problem takes less time to solve in comparison to force response problems provided in the choice section.)

Arshia Mousavi, Msc, works as a civil and structural engineering researcher and assistant at Queen’s University and is currently active in diagnosis and analysis for punching shear and bonding behaviour and retrofitting design of different types of structures such as a fibre-reinforced polymer (FRP) and reinforced concrete (RC) structures in ordinary, fire or severe conditions, in developing new testing setups. He has dedicated experience in civil and structural engineering. He has worked both in design and construction firms as well as laboratories.

#### Secondary References:

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