• Problem 1
• Problem 2
• Problem 3
• Problem 4
• Problem 5

Problem 1

• Correct calculation of the reaction forces.
• Correct calculation of the internal forces for either half of the structure.

The answer below shows a common mistake where the sense of the vertical reaction forces was calculated incorrectly. I did not deduct many points for this error, although probably should have deducted more. The algebraic mistake of misplacing the signs is a small error, however careful inspection of the resulting free body diagram shows that it will tend to rotate clockwise; the failure to see that in the free body diagram is a major error.

Problem 2

The following example also uses a force transformation approach, but does the transformation in a different order.

Here is yet another solution that first uses an algebraic approach, and then checks the answer at the end by solving again using a force transformation approach. This is a very important technique in problem solving: whenever you can, attempt to verify your answer by solving with an alternative method.

A common error on this problem was to fail to prove that the resultant force acted at the lower left corner. In particular, many people used a "tip-to-tail" approach to find the magnitude and direction of the resultant, which is fine, but then implicitly assumed that the resultant acted at the corner, getting the correct answer by coincidence. As emphasized in lecture, the tip-to-tail method applies only when a force system is concurrent, which is not the case for this problem. Note that if the magnitudes of the forces were slightly different, say if the vertical force were 4K instead of 5K, the resultant would not act through the corner.

Problem 3

Problem 4

A number of people noted that the curves were not precise in terms of scale and the location of maximum points and zero points. Other answers were accepted when justification was provided.

Problem 5

a)

The following is a very good answer for this problem.

Many people seemed to be thrown off by the word "motivation". The question aimed as asking the advantages that load smearing brings to the process. The answer above describes the motivation very well: to simplify the calculation process by putting loads in the same terms.

The following answer also makes this point:

Many people said the motivation was approximation, but this amounted to a restatement of the question, which defined load smearing as approximation. It was also common to confuse load smearing with the tributary width method (some people said that load smearing did not work well for cantilevers, which is true for tributary width, but has nothing to do with load smearing).

b)

The key to this problem was to discuss behavior at the scale of the beam rather than the scale of the material. (Recall the lecture on Structural Behavior and Design Approaches, which emphasizes the interpretation of strength, stiffness, stability, and ductility at different levels of scale).

The following answer is very good:

Another sticking point on this problem seemed to be the phrase "Briefly describe in qualitative terms", which simply means to write a brief narrative. Here is another good example of a a brief description in qualitative terms.

There were several possible answers for this problem, here are themes that generally got full credit:

• The designer knows that the structure will see loads that are not addressed in the code.
• The design wants the flexibility to change use later during the life of the structure.
• The designer and owner want a building that is safer and more durable than code minimums.

People who mentioned the lawn balcony example with graduation-day loads generally got full credit. Cases such a corridors did not get credit, since these are covered by building codes.

Here is a good example answer:

Here is an example of a novel loading condition:

And still more novel...

The following is a very good answer for this problem:

Many people said that Hooke's law means that stress is proportional to strain, although as the answer above points out, strictly speaking it refers to forces and deformations; that answer still received full credit. There are a couple of explanations for why it is not always true, the most common is that even materials that obey Hooke's law eventually yield or fracture. Another explanation is that some materials, such as concrete and rubber, do not exhibit proportional behavior even in the elastic range.