Why are We Here? AASHTO LRFD Bridge Design Specifications Metal Pipe Section 12.7 Concrete Pipe Section Plastic Pipe Section 12.12

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1 Direct Design and Indirect Design of Concrete Pipe Part 1 Josh Beakley March 2011

2 Why are We Here? AASHTO LRFD Bridge Design Specifications Metal Pipe Section 12.7 Concrete Pipe Section Plastic Pipe Section 12.12

3 AASHTO Section General The structural design of the types of pipes indicated above may proceed by either of two methods: The direct design method at the strength limit state as specified in Article , 10 2 or The indirect design method at the service limit state as specified in Article

4 Indirect Design Method

5 For Special Cases, use the Direct Design Method

6 Fill Heights Type 2 Installation Pipe Size (in) Class III Class IV Class V I D I D I D I = Indirect Design in Accordance with AASHTO Section 12 D = Direct Design in Accordance with AASHTO Section 12

7 Benefits of the Indirect Design Method Its validity has been proven over time It is a simple method to use It is a proof-of of-performance f method

8 Benefits of the Current Direct Design Method It is simple (relatively speaking) It is safe It is proven

9 Intention for Direct Design Used for higher strength pipe that can not be found in ASTM C 76 Tables Used for larger diameter pipes Used for specific loads and load cases Used when stirrup reinforcement is required

10 Some Factors for Difference Reinforcement Proportions Size Factor Steel Reinforcement Properties Double Reinforcement

11 Conservative Designs The simplification of the direct design process for concrete pipe results in conservative designs. The designs are most conservative for smaller diameter pipe.

12 0.60Asi 10Asi A si > 66

13 Reinforcement Proportions

14 Reinforcement Proportions A so = 0.6 A si Previously - 075A 0.75 si A si

15 Correction for Larger Springline Reinforcing A Theory for Structural Behavior of Reinforced Concrete Pipe, Frank Heger, 1962

16 0.60Asi 10Asi A si > 66

17 Size Factor

18 Mc = Mc = Mc = Mc = 0.254

19 Three-Edge Bearing Test M = P r

20 Experimental vs FEM Results Pipe# 18SP (72.73 psi) (75 psi) (75 psi)

21 Location of First and Second Crack 1 st Crack 2 nd Crack 1st Crack 2nd Crack Small Diameter Large Diameter

22 Mc = Mc = Mc = Mc = 0.254

23 First Crack vs. Second Crack 5000 D-load Required for Second Crack Versus Pipe Diameter econd Crack D-load at S Dcrack i Dload i D i Pipe Inside Diameter (inches)

24

25 Nonreinforced Size Factor ASCE 27-00, Standard Practice for Direct Design of Precast Concrete Pipe for Jacking in Trenchless Construction

26 However, the author has also made experimental calculations based on the theory of plasticity and found reasonably good correspondence with the test results although it seems unlikely that an unreinforced concrete pipe might be calculated in accordance with a theory of this kind. After the occurrence of the first crack the pipe will not collapse, however, because a hinge is created at the crown. Calculation of Unreinforced Concrete Pipes Based on a New Theory for the Rupture, John B. Ingwersen, Danish Concrete Industry, Association

27 We calculate the moment at a specific location without any consideration of moment distribution as a result of the pipe size or reinforcement proportions

28 0.5 * P * r m = M sum 0.5*(DL u * D i /12) * D m/2 = M sum DL u = [48/(D i * D m )] * M sum Experimental Evaluation of SIDD Design Procedures for Shear, Radial Tension and Crack Width Control with Emphasis on Small Diameter Concrete Pipe, SG&H, 1993

29 Steel Properties

30 Stress-Strain Strain Curves

31 Actual Stress-Strain Strain Curves Stress vs. Strain Stress (psi) 1 i 2 i 3 i i 22 i 33 i Strain

32 University of Nebraska Proposal 120 Power Formula (Smooth Wire) ress (ksi) St Strain % f 1 Q Es s Q 1 (( Es s / Kf s R 1/ R py ) f pu fpu fpy Q Es R K

33 Compression/Tension in Bending Stresses 085*f` 0.85 c *b*a ba 085*f` 0.85 c *b*a ba N.A. A s f s A s f s Strains c = NA N.A. s = ε y f s = f y

34 Neutral Axis Iteration c = c = C = 0.5 C = 0.6 C = 0.7 s = s = s = Mild Steel T = A s f y T = A s f y T = A s f y Wire T = A s f T = A T = A s f s s s f s

35 Rebar versus Wire Stress-Strain Curves Stress 1 i MS i i 1 i Strain

36 We Force Ourselves to be Beyond the Yield Point

37 Rebar versus Wire Stress-Strain Curves When tested, the yield strength shall be determined at an extension under load of mm/mm ( in./in.) Stress 1 i MS i The material shall not exhibit a definite yield point as evidenced by a distinct drop of the beam or halt in the gage of the testing machine prior to reaching ultimate tensile load. 0 1 i 1 i Strain ASTM A82. Standard Specification For Steel Wire, Plain, for Concrete Reinforcement

38 Crack Control Work with Stresses Below Yield Stress-Strain Curves Stress 1 i MS i i 1 i Strain

39 When Does Crack Control Kick In?

40 University of Nebraska Proposal 120 Power Formula (Smooth Wire) ress (ksi) St Strain % f 1 Q Es s Q 1 (( Es s / Kf s R 1/ R py ) f pu fpu fpy Q Es R K

41 Double Reinforcement

42 LRFD5732FlexuralResistance Flexural Resistance

43 Concrete Design per AASHTO Section 12

44 085*f` 0.85 c *b*a ba a = 1 *C Nu Mu A s f y

45 A Weakness of Equation a- 1 One Layer of Steel UNO Behavior and Design of Buried Concrete Pipe 48 inch pipe

46 Strain Distribution

47 Two Cages cu = cu cu = yo C yo C o i o i d d i i i i Small Diameter Pipe Large Diameter Pipe

48 36 inch Class III Pipe Second Cage Flexure Neutral Axis C = 0.56 in Stress-Strain Curves Stress 1 i MS i i 1 i Strain

49 72 inch Class III Pipe Second Cage Crack Control Neutral Axis C = 1.15 in Stress-Strain Curves Stress 1 i MS i i 1 i Strain

50 To Be Continued..