2. CE-401 Reinforced Concrete Design-II
By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

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 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 = ) 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, 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, 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. Example: Axial Load vs. Moment Interaction Diagram
Point c (in) Pn Mn e k
k 253 k-ft 2 in
k 351 k-ft in
k 500 k-ft in
k 556 k-ft in
k 531 k-ft in
k 471 k-ft in
8 ~ k 395 k-ft infinity
k k-ft

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

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

55. ACI Design Aids for Columns

56. Design Example 8.3

58. Bar splicing in Columns

59. Assignment No.1: (Total Marks100 each question carries 50 marks
Design and Rectangular Column to carry dead load of 250K live load of 350K dead load moment 150ft-K and live load moment of 350ft-K Assume material properties.
Determine the main steel required
Determine the ties spacing
Draw final neat to the scale sketch on graph paper
Due Date: Sep,