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

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.

Columns subjected to eccentric loadings

Eccentric Compression

Interaction diagrams of combined bending and compression

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 Any combination of P and M outside the envelope will cause failure. Note:

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

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

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

Columns Strength Reduction Factor,  (ACI Code 9.3.2) Axial tension, and axial tension with flexure.  = 0.9 Axial compression and axial compression with flexure. Members with spiral reinforcement confirming to  Other reinforced members  (a) (b)

Columns Except for low values of axial compression,  may be increased as follows: when and reinforcement is symmetric and d s = distance from extreme tension fiber to centroid of tension reinforcement. Then  may be increased linearly to 0.9 as  P n decreases from 0.10f c A g to zero.

Column

Columns Commentary: Other sections:  may be increased linearly to 0.9 as the strain  s increase in the tension steel.  P b

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

Design for Combined Bending and Axial Load (Short Column) Column Types 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 1) 2)

General Procedure The interaction diagram for a column is constructed using a series of values for P n and M n. The plot shows the outside envelope of the problem.

General Procedure for Construction of ID − Compute P 0 and determine maximum P n in compression − Select a “c” value (multiple values) − Calculate the stress in the steel components. − Calculate the forces in the steel and concrete,C c, C s1 and T s. − Determine P n value. − Compute the M n about the center. − Compute moment arm,e = M n / P n.

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 P n verse M n. − Determine  P n and  M n. − Find the maximum compression level. − Find the  will vary linearly from 0.65 to 0.9 for the strain values − The tension component will be  = 0.9

Example: Axial Load vs. Moment Interaction Diagram Consider an square column (20 in x 20 in.) with 8 #10 (  = ) and f c = 4 ksi and f y = 60 ksi. Draw the interaction diagram.

Example: Axial Load vs. Moment Interaction Diagram Given 8 # 10 (1.27 in 2 ) and f c = 4 ksi and f y = 60 ksi

Example: Axial Load vs. Moment Interaction Diagram Given 8 # 10 (1.27 in 2 ) and f c = 4 ksi and f y = 60 ksi [ Point 1 ]

Example: Axial Load vs. Moment Interaction Diagram Determine where the balance point, c b.

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

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

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

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

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

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

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 ]

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)

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

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

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

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 ]

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

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

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

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

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 ]

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

Example: Axial Load vs. Moment Interaction Diagram Pointc (in) P n M n e k k253 k-ft 2 in k351 k-ft 3.2 in k500 k-ft 7.13 in k556 k-ft11.42 in k531 k-ft16.20 in k471 k-ft37.35 in 8~4.5 0 k395 k-ftinfinity k 0 k-ft

Example: Axial Load vs. Moment Interaction Diagram Use a series of c values to obtain the P n verses M n.

Example: Axial Load vs. Moment Interaction Diagram Max. compression Max. tension CbCb Location of the linearly varying 

ACI Design Aids for Columns

Design Example 8.3

Bar splicing in Columns

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,