By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

2. ByDr. Attaullah ShahSwedish College of Engineering and Technology Wah Cantt. CE-401 Reinforced Concrete Design-II

3. Course Outline: Analysis & design of axially loaded columns, Eccentrically loaded columns by USD Analysis & design of strip footing for wall, spread footings for columns and combined footings by USD. Design of retaining wall. Introduction to limit states. Detailing of reinforcement. Introduction to design of staircases and water tanks.

4. Columns subjected to eccentric loadings

6. Eccentric Compression

9. Interaction diagrams of combined bending and compression

12. Behavior under Combined Bending and Axial Loads Interaction Diagram Between Axial Load and Moment ( Failure Envelope ) Concrete crushes before steel yields Steel yields before concrete crushes Note: Any combination of P and M outside the envelope will cause failure.

13. Behavior under Combined Bending and Axial Loads Axial Load and Moment Interaction Diagram – General

14. Behavior under Combined Bending and Axial Loads Resultant Forces action at Centroid ( h/2 in this case ) Moment about geometric center

15. Columns in Pure Tension Section is completely cracked (no concrete axial capacity) Uniform Strain

16. Columns Strength Reduction Factor, f (ACI Code 9.3.2) (a) Axial tension, and axial tension with flexure. f = 0.9 Axial compression and axial compression with flexure. (b) Members with spiral reinforcement confirming to 10.9.3 f = 0.70 Other reinforced members f = 0.65

17. Columns Except for low values of axial compression, f may be increased as follows: when and reinforcement is symmetric and ds = distance from extreme tension fiber to centroid of tension reinforcement. Then f may be increased linearly to 0.9 as fPn decreases from 0.10fc Ag to zero.

18. Column

19. Columns Commentary: Other sections: f may be increased linearly to 0.9 as the strain es increase in the tension steel. fPb

20. Design for Combined Bending and Axial Load (Short Column) Design - select cross-section and reinforcement to resist axial load and moment.

21. Design for Combined Bending and Axial Load (Short Column) Column Types 1) Spiral Column - more efficient for e/h < 0.1, but forming and spiral expensive Tied Column - Bars in four faces used when e/h < 0.2 and for biaxial bending 2)

22. General Procedure The interaction diagram for a column is constructed using a series of values for Pn and Mn. The plot shows the outside envelope of the problem.

23. General Procedure for Construction of ID • Compute P0 and determine maximum Pn in compression • Select a “c” value (multiple values) • Calculate the stress in the steel components. • Calculate the forces in the steel and concrete,Cc, Cs1 and Ts. • Determine Pn value. • Compute the Mn about the center. • Compute moment arm,e = Mn / Pn.

24. General Procedure for Construction of ID • Repeat with series of c values (10) to obtain a series of values. • Obtain the maximum tension value. • Plot Pn verse Mn. • Determine fPn and fMn. • Find the maximum compression level. • Find the f will vary linearly from 0.65 to 0.9 for the strain values • The tension component will be f = 0.9

25. Example: Axial Load vs. Moment Interaction Diagram Consider an square column (20 in x 20 in.) with 8 #10 (r = 0.0254) and fc = 4 ksi and fy = 60 ksi. Draw the interaction diagram.

26. Example: Axial Load vs. Moment Interaction Diagram Given 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi

27. Example: Axial Load vs. Moment Interaction Diagram Given 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi [ Point 1 ]

28. Example: Axial Load vs. Moment Interaction Diagram Determine where the balance point, cb.

29. Example: Axial Load vs. Moment Interaction Diagram Determine where the balance point, cb. Using similar triangles, where d = 20 in. – 2.5 in. = 17.5 in., one can find cb

30. Example: Axial Load vs. Moment Interaction Diagram Determine the strain of the steel

31. Example: Axial Load vs. Moment Interaction Diagram Determine the stress in the steel

32. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

33. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

34. Example: Axial Load vs. Moment Interaction Diagram Compute the moment about the center

35. Example: Axial Load vs. Moment Interaction Diagram A single point from interaction diagram, (585.6 k, 556.9 k-ft). The eccentricity of the point is defined as [ Point 2 ]

36. Example: Axial Load vs. Moment Interaction Diagram Now select a series of additional points by selecting values of c. Select c = 17.5 in. Determine the strain of the steel. (c is at the location of the tension steel)

37. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

38. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

39. Example: Axial Load vs. Moment Interaction Diagram Compute the moment about the center

40. Example: Axial Load vs. Moment Interaction Diagram A single point from interaction diagram, (1314 k, 351.1 k-ft). The eccentricity of the point is defined as [ Point 3 ]

41. Example: Axial Load vs. Moment Interaction Diagram Select c = 6 in.Determine the strain of the steel, c =6 in.

42. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

43. Example: Axial Load vs. Moment Interaction Diagram Compute the forces in the column

44. Example: Axial Load vs. Moment Interaction Diagram Compute the moment about the center

45. Example: Axial Load Vs. Moment Interaction Diagram A single point from interaction diagram, (151 k, 471 k-ft). The eccentricity of the point is defined as [ Point 4 ]

46. Example: Axial Load vs. Moment Interaction Diagram Select point of straight tension.The maximum tension in the column is [ Point 5 ]

47. Point c (in) Pn Mn e 1 - 1548 k 0 0 2 20 1515 k 253 k-ft 2 in 3 17.5 1314 k 351 k-ft 3.2 in 4 12.5 841 k 500 k-ft 7.13 in 5 10.36 585 k 556 k-ft 11.42 in 6 8.0 393 k 531 k-ft 16.20 in 7 6.0 151 k 471 k-ft 37.35 in 8 ~4.5 0 k 395 k-ft infinity 9 0 -610 k 0 k-ft Example: Axial Load vs. Moment Interaction Diagram

48. Example: Axial Load vs. Moment Interaction Diagram Use a series of c values to obtain the Pn verses Mn.

49. Max. compression Location of the linearly varying f. Max. tension Example: Axial Load vs. Moment Interaction Diagram Cb