Distribution for Quiz 1

     89              
     89  79          
     88  79          
     88  79          
     87  78                      
     86  77                      
     86  76                      
     86  76                      
 99  86  76  69                  
 99  85  75  69                  
 99  84  75  69                  
 96  84  74  68                  
 96  83  74  67                  
 95  83  73  67                  
 95  82  73  67                  
 93  82  73  66  59              
 93  82  72  66  59              
 93  82  72  66  57              
 92  82  72  64  56              
 92  81  71  64  55  49          
 92  81  71  63  54  46  39      
 91  81  71  63  54  44  39  28  
 90  80  70  61  51  43  37  23  
 90  80  70  61  51  42  35  21  18

Mean: 72, Median 75

Distribution for Quiz 2

                    59          
                    58          
                    58          
                    58  49      
                    57  48      
                69  57  48      
                67  57  46  39  
            79  66  56  46  39  27
            77  66  56  46  38  27  
            76  65  56  46  38  26  
        89  75  65  55  46  37  26  
        88  74  65  55  45  35  26  
        87  73  64  54  44  34  25  
        85  72  63  53  44  33  24  
        85  72  63  53  44  33  21  
    94  85  72  62  53  43  33  21  
    93  84  71  61  53  42  32  21  
    91  84  70  60  53  40  31  20 
    90  83  70  60  51  40  30  20  13   4

Mean: 54, Median 55

Problem 1

The key elements of a correct solution:

• Find the maximum shear and the corresponding depth required.
• Find the maximum bending moment and the corresponding depth required.
• Choose the correct depth to satisfy both criteria (i.e. the larger)

Problem 2

This problem is different than problem 1 in that it asks to check a given member size rather than determine a size that is not given. Checking a given size is simpler because it may not be necessary to check all criteria. As soon as you find one criteria that is violated, then the solution is over; the member does not work.

In any compression member, there are three fundamental failure modes: strong-axis buckling, weak-axis buckling, and crushing. In this problem, only the weak axis buckling criterion is violated. People who checked that first didn't need to check anything else.

There was a very common error on this problem, as follows:

Note that the final answer is based on comparing buckling capacity and crushing capacity, however this has no bearing on the question of whether the member can safely resist the 6 kip compression force. Remember the basic concept of structural design:

Capacity >= Demand

Problem 3

Note that there are several possible explanations for part c). Many people based their answer on the assumption that the moment in the column would remain the same when the column length increased, however this assumption is not valid; changing the dimensions of a structure, particularly an indeterminate structure, usually changes the distribution of moments. Answers based on that assumption did not receive full credit.

Problem 4

Ideally, the answers for parts a) and b) should include some supporting reasoning, although gut-level correct answers were accepted in full.

In addition to the method of joints solution for part c), it is also possible to do a very simple method of sections solution, as shown below.

Problem 5

a)

Any of the following aspects of behavior were accepted:

• Material yielding
• Material non-linearity (like rubber).
• Large displacements where the deformed geometry is significantly different from the original geometry, as with low-emodulus.
• Buckling.
• Cable structures where the geometry depends on the load condition.

b)

c)

d)

ΚΚ