Download - rcc-lec-01
-
7/27/2019 rcc-lec-01
1/59
1
-
7/27/2019 rcc-lec-01
2/59
By
Dr. Attaullah Shah
Swedish College of Engineering and TechnologyWah Cantt.
CE-401
Reinforced Concrete Design-II
-
7/27/2019 rcc-lec-01
3/59
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.
-
7/27/2019 rcc-lec-01
4/59
Columns subjected to eccentric loadings
-
7/27/2019 rcc-lec-01
5/59
-
7/27/2019 rcc-lec-01
6/59
Eccentric Compression
-
7/27/2019 rcc-lec-01
7/59
-
7/27/2019 rcc-lec-01
8/59
-
7/27/2019 rcc-lec-01
9/59
Interaction diagrams of combined bending and compression
-
7/27/2019 rcc-lec-01
10/59
-
7/27/2019 rcc-lec-01
11/59
-
7/27/2019 rcc-lec-01
12/59
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:
-
7/27/2019 rcc-lec-01
13/59
Behavior under Combined Bending and
Axial Loads
Axial Load and Moment Interaction DiagramGeneral
-
7/27/2019 rcc-lec-01
14/59
Behavior under Combined
Bend ing and Axial LoadsResultant Forces action at Centroid
( h/2 in this case )
s2
positiveisncompressiocs1n
TCCP
Moment about geometric center
2*
22*
2* 2s2c1s1n
hdT
ahCd
hCM
-
7/27/2019 rcc-lec-01
15/59
Columns in Pure Tens ion
Section is completely cracked (no concrete
axial capacity)
Uniform Strainy
N
1ii
sytensionn AfP
-
7/27/2019 rcc-lec-01
16/59
Columns
Strength Reduction Factor, f (ACI Code 9.3.2)
Axial tension, and axial tension with flexure.
f = 0.9
Axial compression and axial compression with
flexure.
Members with spiral reinforcement confirmingto 10.9.3 f 0.70
Other reinforced members f 0.65
(a)
(b)
-
7/27/2019 rcc-lec-01
17/59
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.
psi000,60y f
70.0
s
h
ddh
-
7/27/2019 rcc-lec-01
18/59
Column
-
7/27/2019 rcc-lec-01
19/59
Columns
Commentary:
Other sections:
f may be increased linearly to 0.9 as thestrain s increase in the tension steel. fPb
D i f C bi d B d i d
-
7/27/2019 rcc-lec-01
20/59
Design fo r Combined Bend ing and
Axial Load (Sho rt Column)
Design - select cross-section and reinforcement
to resist axial load and moment.
D i f C bi d B d i d
-
7/27/2019 rcc-lec-01
21/59
Design fo r Combined Bend ing and
Axial Load (Sho rt 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)
-
7/27/2019 rcc-lec-01
22/59
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 theproblem.
G l P d f
-
7/27/2019 rcc-lec-01
23/59
General Procedure fo r
Cons truct ion 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 andconcrete,Cc, Cs1 and Ts.
Determine Pn value.
Compute the Mn about the center.
Compute moment arm,e = Mn / Pn.
G l P d f
-
7/27/2019 rcc-lec-01
24/59
General Procedure fo r
Construct ion 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 0.9for the strain values
The tension component will be f = 0.9
-
7/27/2019 rcc-lec-01
25/59
Example: Ax ial Load vs . Moment
In terac t ion DiagramConsider 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.
-
7/27/2019 rcc-lec-01
26/59
Example: Ax ial Load vs . Moment
In teract ion DiagramGiven 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi
2 2st
2 2
g
2
st
2
g
8 1.27 in 10.16 in
20 in. 400 in
10.16 in 0.0254400 in
A
A
AA
r
-
7/27/2019 rcc-lec-01
27/59
Example: Ax ial Load vs . Moment
In teract ion DiagramGiven 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi
0 c g st y st
2 2
2
0.85
0.85 4 ksi 400 in 10.16 in
60 ksi 10.16 in
1935 k
P f A A f A
n 0
0.8 1935 k 1548 k
P rP
[ Point 1 ]
-
7/27/2019 rcc-lec-01
28/59
Example: Ax ial Load vs . Moment
In teract ion DiagramDetermine where the balance point, cb.
-
7/27/2019 rcc-lec-01
29/59
Example: Ax ial Load vs . Moment
In teract ion DiagramDetermine where the balance point, cb. Using similartriangles, where d = 20 in.2.5 in. = 17.5 in., one can
find cbb
b
b
17.5 in.0.003 0.003 0.00207
0.00317.5 in.
0.003 0.0020710.36 in.
c
c
c
-
7/27/2019 rcc-lec-01
30/59
Example: Ax ial Load vs . Moment
In teract ion DiagramDetermine the strain of the steel
bs1 cu
b
bs2 cu
b
2.5 in. 10.36 in. 2.5 in.
0.00310.36 in.
0.00228
10 in. 10.36 in. 10 in. 0.00310.36 in.
0.000104
c
c
cc
-
7/27/2019 rcc-lec-01
31/59
Example: Ax ial Load vs . Moment
In teract ion DiagramDetermine the stress in the steel
s1 s s1
s2 s s1
29000 ksi 0.00228
66 ksi 60 ksi compression
29000 ksi 0.000104
3.02 ksi compression
f E
f E
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
32/59
Example: Axial Load vs . Moment
In terac t ion DiagramCompute the forces in the column
c c 1
s1 s1 s1 c
2
2
s2
0.85
0.85 4 ksi 20 in. 0.85 10.36 in.
598.8 k
0.85
3 1.27 in 60 ksi 0.85 4 ksi
215.6 k
2 1.27 in 3.02 ksi 0.85 4 ksi
0.97 k neglect
C f b c
C A f f
C
-
7/27/2019 rcc-lec-01
33/59
Example: Ax ial Load vs . Moment
In teract ion DiagramCompute the forces in the column
2s s s
n c s1 s2 s
3 1.27 in 60 ksi
228.6 k
599.8 k 215.6 k 228.6 k 585.8 k
T A f
P C C C T
-
7/27/2019 rcc-lec-01
34/59
Example: Ax ial Load vs. Moment
In terac t ion Diagram
Compute the moment about the center
c s1 1 s 32 2 2 2
0.85 10.85 in.20 in.599.8 k2 2
20 in.215.6 k 2.5 in.
220 in.
228.6 k 17.5 in.2
6682.2 k-in 556.9 k-ft
h a h hM C C d T d
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
35/59
Example: Axial Load vs . Moment
In terac t ion Diagram
A single point from interaction diagram,(585.6 k, 556.9 k-ft). The eccentricity of the point is
defined as
6682.2 k-in11.41 in.
585.8 k
Me
P
[ Point 2 ]
-
7/27/2019 rcc-lec-01
36/59
Example: Ax ial Load vs . Moment
In teract ion DiagramNow select a series of additional points by selectingvalues of c. Select c = 17.5 in. Determine the strain
of the steel. (c is at the location of the tension steel)
s1 cu
s1
s2 cu
s2
2.5 in. 17.5 in. 2.5 in.0.003
17.5 in.
0.00257 74.5 ksi 60 ksi (compression)
10 in. 17.5 in. 10 in.0.003
17.5 in.
0.00129 37.3 ksi (compression)
c
c
f
c
c
f
-
7/27/2019 rcc-lec-01
37/59
Example: Ax ial Load vs . Moment
In teract ion DiagramCompute the forces in the column
c c 1
2
s1 s1 s1 c
2
s2
0.85 0.85 4 ksi 20 in. 0.85 17.5 in.
1012 k
0.85 3 1.27 in 60 ksi 0.85 4 ksi
216 k
2 1.27 in 37.3 ksi 0.85 4 ksi
86 k
C f b c
C A f f
C
-
7/27/2019 rcc-lec-01
38/59
Example: Ax ial Load vs . Moment
In teract ion DiagramCompute the forces in the column
2
s s s
n
3 1.27 in 0 ksi
0 k
1012 k 216 k 86 k
1314 k
T A f
P
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
39/59
Example: Axial Load vs . Moment
In terac t ion Diagram
Compute the moment about the center
c s1 12 2 2
0.85 17.5 in.20 in.1012 k
2 2
20 in.
216 k 2.5 in.2
4213 k-in 351.1 k-ft
h a hM C C d
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
40/59
Example: Axial Load vs . Moment
In terac t ion Diagram
A single point from interaction diagram,
(1314 k, 351.1 k-ft). The eccentricity of the point is
defined as
4213 k-in3.2 in.
1314 k
Me
P
[ Point 3 ]
Example: Ax ial Load vs Moment
-
7/27/2019 rcc-lec-01
41/59
Example: Ax ial Load vs. Moment
In terac t ion Diagram
Select c = 6 in. Determine the strain of the steel, c =6 in.
s1 cu
s1
s2 cu
s2
s3 cu
2.5 in. 6 in. 2.5 in.0.003
6 in.
0.00175 50.75 ksi (compression)
10 in. 6 in. 10 in.0.003
6 in.
0.002 58 ksi (tension)
17.5 in. 6 in.
c
c
f
c
c
f
c
c
s3
17.5 in.0.003
6 in.
0.00575 60 ksi (tension)f
Example: Ax ial Load vs Moment
-
7/27/2019 rcc-lec-01
42/59
Example: Ax ial Load vs . Moment
In teract ion DiagramCompute the forces in the column
c c 1
s1 s1 s1 c
2
2
s2
0.85
0.85 4 ksi 20 in. 0.85 6 in.
346.8 k
0.85
3 1.27 in 50.75 ksi 0.85 4 ksi
180.4 k C2 1.27 in 58 ksi
147.3 k T
C f b c
C A f f
C
-
7/27/2019 rcc-lec-01
43/59
-
7/27/2019 rcc-lec-01
44/59
Example: Axial Load vs. Moment
In teract ion Diagram
Compute the moment about the center
c s1 1 s 32 2 2 2
0.85 6 in.346.8 k 10 in.
2
180.4 k 10 in. 2.5 in.
228.6 k 17.5 in. 10 in.
5651 k-in 470.9 k-ft
h a h hM C C d T d
-
7/27/2019 rcc-lec-01
45/59
Example: Axial Load Vs. Moment
In teract ion Diagram
A single point from interaction diagram,
(151 k, 471 k-ft). The eccentricity of the point is
defined as
5651.2 k-in37.35 in.
151.3 k
Me
P
[ Point 4 ]
-
7/27/2019 rcc-lec-01
46/59
Example: Axial Load vs. Moment
In terac t ion Diagram
Select point of straight tension. The maximum tension
in the column is
2
n s y 8 1.27 in 60 ksi
610 k
P A f
[ Point 5 ]
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
47/59
Example: Axial Load vs . Moment
In teract ion Diagram
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
-
7/27/2019 rcc-lec-01
48/59
Example: Ax ial Load vs . Moment
In teract ion DiagramColumn Analysis
-1000
-500
0
500
1000
1500
2000
0 100 200 300 400 500 600
M (k-ft)
P(
k)
Use a series of c
values to obtain the
Pn verses Mn.
Example: Axial Load vs Moment
-
7/27/2019 rcc-lec-01
49/59
Example: Axial Load vs. Moment
In terac t ion Diagram
Column Analysis
-800
-600
-400
-200
0
200
400
600
800
1000
1200
0 100 200 300 400 500
fMn (k-ft)
fPn
(k)
Max. compression
Max. tension
Cb
Location of the linearlyvarying f.
-
7/27/2019 rcc-lec-01
50/59
-
7/27/2019 rcc-lec-01
51/59
-
7/27/2019 rcc-lec-01
52/59
-
7/27/2019 rcc-lec-01
53/59
-
7/27/2019 rcc-lec-01
54/59
ACI Design Aids for Columns
-
7/27/2019 rcc-lec-01
55/59
g
Design Example 8.3
-
7/27/2019 rcc-lec-01
56/59
g p
-
7/27/2019 rcc-lec-01
57/59
Bar splicing in Columns
-
7/27/2019 rcc-lec-01
58/59
p g
Assignment No 1: (Total Marks100 each question carries 50 marks
-
7/27/2019 rcc-lec-01
59/59
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 loadmoment 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,17 2012.