1. EFFECTIVE TEACHING OF REINFORCED CONCRETE RICHARD MILLER, FPCI Professor of Civil Engineering University of Cincinnati Chair, PCI R&D Council 1

2. 2 Every once in a while, something changes how you think.

3. TAKING OVER SENIOR DESIGN 3 I started working with the Neihoff Studio at UC. Engineering students worked with architects, planners and political scientists. I had to THINK about: What IS an engineer.

4. 4 This article really made me think, too.

5. Michael Speaks – Design Thinking 5 I saw a lecture by Michael Speaks, Dean College of Design, U Kentucky on Design Thinking. It made me think, too. http://www.theberlage.nl/event s/details/2009_04_06_design_t hinking

6. Design Thinking Jeff Hawkins – Palm Pilot Inventor On Intelligence - http://www.onintelligence.org/ Intelligence is really –Storing Patterns –When the world does not fit the pattern, form a new pattern. –Intelligence is the ability to predict patterns. –Knowledge is produced, not found. 6

7. Design Thinking “Storing patterns” is what the Scientific American article was about. –Chess masters store patterns. –Athletes store patterns. –Engineers store patterns. 7 www.houseofstaunton.com

8. Design Thinking 8 Engineering is pattern recognition, pattern construction and pattern prediction!!!!!!!!

9. Design Thinking 9 Example: You recognize the pattern: I do this without thinking. I did not really think about it until I had to teach to my son (business major). Pattern:

10. Design Thinking 10 Constant “rule” e to the f(x) rule Trig function

11. Design Thinking Engineers do not just try to solve the problem, they REFRAME IT. Engineers ask “what if”. Engineers try to learn all they can about something. Engineers then extend and extrapolate that knowledge. 11

12. Design Thinking Speaks gives an example. –An architect wanted to use a new material for a building. –The engineers studied the material, characterized it and tested it. –In the end, the ENGINEERS gained knowledge and became more valuable. 12

13. Design Thinking Learn patterns Form new patterns Extend the patterns You can only ask “what if” if you know “what is.” 13

14. WE HAVE A REAL OPPORTUNITY! 14 Technology presents us with an opportunity to change how we teach. It goes to the heart of “What is an engineer.”

15. EXAMPLE 15 What really affects the performance of a concrete beam?

16. 16 First, we have teach them the basics and then show the patterns.

17. 17 M = (C or T) d M = Cd = Td Start with something they know! Simple linear theory. They know this pattern.

18. 18 Now introduce something new – this is the stress strain curve for concrete in compression. They don’t know non-linear materials. The beginning is linear!!!

19. 19 Walk them through the sequence. Here is a pattern they know. Uncracked

20. 20 Cracked – Linear – Now we start to extend the pattern. This “doesn’t fit the mold”. Remember, the beginning of the stress strain curve is linear!!! We ignore cracked concrete! Strain is linear with “y”. Plane sections remain plane.

21. 21 Now, we could introduce a new pattern and go this way: Linear elastic approach to a cracked member.

22. 22 But let’s go this way: Cracked – Non-linear Now we have a really different problem!pattern. Strain is still linear with “y”. Plane sections remain plane. Now, the stress strain curve is non linear!!!

23. 23 Now introduce  c = 0.003. Tell them it is a definition. It is supported by research, but other values can be justified. The code writers had to choose a reasonable value and they chose 0.003. If justified by future research, this could change. But this is KNOWLEDGE for the “what if”.

24. 24 Show a similarity – remind them that an integral is an area. dVol =  dA VOLUME OF COMPRESSION WEDGE Here, we EXTEND a known pattern!

25. 25 Show that the stress block is a “convenience” for integration.

26. 26 Notice that we still start with some theory. Using the baseball analogy: you have to start with the theory of “Hit the ball and run to first base!” But theory is introduced a little at a time, not all at once. If we taught baseball like engineering, 2 nd grade everyone would learn infield, 3 rd grade everyone would learn outfield, 4 th grade everyone would learn hitting in 5 th grade everyone would learn pitching, in 6 th grade everyone would learn baserunning. Maybe in 7 th grade you would actually play a game. Who would stick around for THAT??

27. 27 Consider the concrete beam shown which is designed for positive moment. The distance from the extreme compression fiber (top in this case) to the centroid of the reinforcing steel is called “d”, the effective depth. f c ’ = 5000 psi f y = 60 ksi THIS EXAMPLE USES NUMBERS!!!!

28. 28 Why use an example with NUMBERS??

29. 29 When you learn a new subject, it is easier to start with a “concrete” example rather than a theoretical one! (no pun intended … Or maybe just a little pun!)

30. 30 Let us assume the concrete stress strain curve can be modeled as a parabola. The ACI code allows the concrete stress-strain curve to be modeled as a parabola, trapezoid, triangle or any shape which the engineer can justify. There is a lot of research which shows that the pre-peak part of the curve can be modeled as a parabola if the concrete is normal strength.

31. 31 Again, the example uses numbers! Note: we could do “what if’s with different values of extreme fiber strain and use numerical integration! You may have to show them how to write the equation of a parabola to fit this curve.

32. 32 The values of c and f s are not known. Assume that the steel yields and f s = f y. The integral is just a volume. The area of the parabola is (2/3)cf c ’. Multiply by width, b, to get volume! Apply equilibrium C=T.

33. 33 The centroid of a parabolic area is (3/8)c from the vertex. Don’t Assume They Remember Geometry Always use your units!

34. 34 Does the steel yield? C = 5.4” YES

35. 35 Whitney Stress Block Now show the stress block:

36. 36

37. 37 Assume steel yields f s = f y.

38. 38 Assume steel yields f s = f y.

39. 39 Does the steel yield? C = 5.3” YES

40. Difference ParabolaStress Block C inch5.45.3 M n k-in30553040 40 Good place to point out that ANYTHING + 10% is good in concrete!

41. 41 Wait a minute!! What happened to the k factors for the stress block??? At this point, you can introduce these factors and show how the stress block was “calibrated”.

42. 42 However, ask yourself this about the k factors for the stress block: Are they necessary for student understanding or just confusing? Is it useful to the students at this point? Will they even remember? It is probably a good idea to make the aware of how the stress block was calibrated – but don’t dwell on it.

43. Effect of parameters on M n Again, the tendency here is to do this “theoretically”. This is a good chance to get the students “doing something”. Have them bring lap tops and work in groups. They form patterns and ask “WHAT IF”. 43

44. 44 f c ’ = 5000 psi f y = 60 ksi M n = 3040 k-in = M initial Now we can explore changing the parameters. We could do this theoretically or with a numerical example Problem – what if we start to change things on this beam??

45. 45 The students can make a simple spreadsheet program like this: (or you can make it for them).

46. This shows the variation of M n with A s. This graph is NOT multiplied by  46

47. This shows the effect of reducing the moment by . Note that once the tension control limit is passed, there is little gain for more steel. 47

48. This shows the effect of varying d. 48

49. Here is the effect of the variation of d, but the moment is multiplied by . 49

50. This shows the effect of varying f c ’. Note that the section is tension controlled in all cases. 50

51. This shows the effect of varying b. Again, all sections are tension controlled. 51

52. Here is a normalized graph. The  factor is NOT applied. Note that A s and d have the largest effect on moment. The concrete strength and b have almost no effect. This graph is normalized. The point 1,1 is the beam with A s = 3 in 2, b = 10 in, d = 19 in and f c ’ = 5ksi. The x axis is the fraction of the original parameter, e.g. 0.5 would be d = 9.5 inches. The y axis is the ratio of the moment capacity to the moment capacity of the original cross section. 52

53. 53 Now bring in the theory:

54. 54 Clearly parabolic in A s

55. 55 Linear in d, as long as the steel yields (a/2 is constant). When the steel does NOT yield, f s depends on d, but there is only a slight deviation from linear.

56. 56 The variation of b and f c ’ are the same. Note that these graphs all have the steel yielding.

57. 1.57 An interesting note on tension control: Before this, we all remember ρ max =0.75 ρ bal. To define tension control, Bob Mast calculated the ductility (basically δ max / δ y ) and then found the extreme fiber strains that corresponded to the same ductility. In the AASHTO LRFD Bridge Specification, there are values of ε for tension control of steel with yield strengths above 60ksi where the stress/strain curve is not elastic/perfectly plastic. We used the computer to calculate the ductility for a number of different beam shapes with GR 60 steel. We then recalculated them with GR 100 steel and found values of ε that provided the same ductility. This is a really good example of “what if” engineering!

58. 58 Another Example: A Square Column:

59. 59 A simple EXCEL Sheet will plot the interaction diagram. “Goal Seek” finds important points like zeros and yield.

60. 60 We are all familiar with this graph from textbooks; the effect of increasing the amount of steel.

61. 61 But you almost NEVER see the effect of f c ’!

62. Why this works better Students still learn theory, just in a different order. Students learn in a way more understandable to them. Students get to DO something, not just listen to you. Students FORM PATTERNS Students EXTEND PATTERNS Students ask “WHAT IF”. 62

63. When to Change Up 63 Sometimes covering theory first works better. Shear in prestressed beams:

64. 64 The elements of this equation are very confusing. If you derive the equation, the meaning an application of the terms becomes clear.

65. EFFECTIVE TEACHING Remember the students are in unfamiliar territory. Teach to their style of learning, not yours. –Students tend to like “concrete” examples first, theory later. Get them ACTIVE! They learn more by doing. Teach INTELLIGENCE not just KNOWLEDGE. 65