Lecture 18 Reinforced Shear Design and Columns

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Lecture 18 - Reinforced Shear Design and Columns

• November 6, 2001
• CVEN 444

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Lecture Goals

• Joist Design for shear
• One way slab design
• Columns

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Example Design of Stirrups to Resist Shear
fc 4000 psi fy 60 ksi wsdl
1.2 k/ft wll 1.8 k/ft fys 40 ksi
wb 0.5 k/ft
From flexural design will use either a 3 or 4
stirrup
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Discontinuities at Bar Cutoff
Prohibits flexural bar cutoffs in zone of
flexural tension, unless 1 of the following is
satisfied.
ACI 12.10.5
(1) (2)
Extra stirrups are provided at the cutoff
points. (See Sec. 12.10.5.2 for details)
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Discontinuities at Bar Cutoff
Prohibits flexural bar cutoffs in zone of
flexural tension, unless 1 of the following is
satisfied.
ACI 12.10.5
For No 11 bars smaller Increase shear
strength is required when bars are cutoff in a
tension zone.
(3)
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Joist Design
Refer to earlier notes for general information on
joist layout.ACI Sec. 8.11 Joist
construction requirements
Flat Slab reinforcement is calculated for bending
or minimum reinforcement for shrinkage and
temperature.
(1)
GR 40 or GR 50 0.0020 Ag GR 60
0.0018 Ag
(ACI Sec 7.12.2 )
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Joist Design
Shear Design of Joist Ribs (Joist - Section 8.11)
(2)
Shear strength may be increased using shear
reinforcement or by widening the ends of the ribs
(not typical)
(a)
(b)
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Joist Design
ACI shear and moment coefficients may be used if
requirements in ACI Sec 8.3.3 are met. Ribs are
designed as T- Sections Main positive
reinforcement includes at least 2 bars.
(3)
(4)
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Joist Design
Tie beams. (a) one, if L is 15 ft. - 20 ft. (b)
two, if L is 20 ft. - 30 ft. At least 1- 4
T-B (continuous) Cover 11 and smaller
3/4 in. 14, 18 1 1/2 in.
(5)
(6)
Not exposed to weather
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One-Way Slab Design
Design of one slabs is like design of parallel
12 beams.
(Sec. 10-4 text)
Thickness of One-Way Slabs
Minimum thickness for solid one-way slabs not
supporting or attached or attached to partitions,
etc. Likely to be damaged by large deflections
ACI Table 9.5(a)
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One-Way Slab Design
Thickness of One-Way Slabs
The table calculates the minimum thickness t
( l span length in inches) (normal weight
concrete fy 60 ksi see code for
modification factors)
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One-Way Slab Design
Thickness of One-Way Slabs Table A-14 min t,
when damage to non-structural components may occur
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One-Way Slab Design
Thickness of One-Way Slabs
Fire Rating
This is equal to the number of hours for
unexposed surface to rise a set amount usually
250 o F
3.5 in. 1 hour 5.0 in.
2 hours 6.25 in. 3 hours
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Cover for Slab Reinforcement
ACI Sec. 7.71 (min. cover for corrosion
protection)
( 1.) Concrete exposed to earth or weather.
5 and smaller 1.5 in. 6 and larger 2.0
in.
( 2.) Concrete not exposed to earth or weather.
11 and smaller 0.75 in.
Min. covers for fire ratings should also be
considered.
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One-Way Slab Design
Reinforcement
Typical Reinforcement in a one-way slab
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One-Way Slab Design
Cutoffs
If requirements for use of ACI Moment
Coefficients
Figure A-5 one-way slab
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One-Way Slab Design
Cutoffs
- Figure A-5 one-way slab
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One-Way Slab Design
Need to confirm thickness is adequate for one-way
shear. Difficult to place shear reinforcement in
a slab.
Minimum area of shear reinforcement required in
slabs if
ACI Sec. 11.5.51
Usual use
ACI Eqn. 11-3
Note See Example 10-1 design of one-way slabs
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Analysis and Design of Short Columns
General Information
Vertical Structural members Transmits axial
compressive loads with or without moment transmit
loads from the floor roof to the foundation
Column
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Analysis and Design of Short Columns
General Information
Column
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Analysis and Design of Short Columns
Tie Columns - 95 of all columns in buildings
are tied
Tie spacing h (except for seismic) tie
support long bars (reduce buckling) ties provide
negligible restraint to lateral expose of core
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Analysis and Design of Short Columns
Spiral Columns
Pitch 1.375 in. to 3.375 in. spiral restrains
lateral (Poissons effect) axial load
delays failure (ductile)
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Analysis and Design of Short Columns
Elastic Behavior
Concrete creeps and shrinks, therefore we can not
calculate the stresses in the steel and concrete
due to acting loads using an elastic analysis.
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Analysis and Design of Short Columns
Elastic Behavior
An elastic analysis using the transformed section
method would be
For concentrated load, P
uniform stress over section
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Analysis and Design of Short Columns
Elastic Behavior
An elastic analysis does not work because creep
and shrinkage affect the acting concrete
compression strain as follows
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Analysis and Design of Short Columns
Elastic Behavior
The change in concrete strain with respect to
time will effect the concrete and steel stresses
as follows
Concrete stress
Steel stress
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Analysis and Design of Short Columns
Elastic Behavior
Therefore, we are not able to calculate the real
stresses in the reinforced concrete column under
acting loads over time. As a result, an
allowable stress design procedure using an
elastic analysis was found to be unacceptable.
Reinforced concrete columns have been designed by
a strength method since the 1940s.
Creep and shrinkage do not affect the strength of
the member.
Note
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Initial Behavior up to Nominal Load - Tied and
spiral columns.
1.
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Let Ag Gross Area bh
Ast area of long steel
fc concrete compressive strength
fy steel yield strength
Factor due to less than ideal consolidation and
curing conditions for column as compared to a
cylinder. It is not related to Whitneys stress
block.
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Maximum Nominal Capacity for Design Pn (max)

2.
r Reduction factor to account for
accidents/bending r 0.80 ( tied ) r 0.85 (
spiral )
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Reinforcement Requirements (Longitudinal Steel
Ast)
3.
Let
- ACI Code 10.9.1 requires
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Behavior, Nominal Capacity and Design under
concentric Axial loads
3.
Reinforcement Requirements (Longitudinal Steel
Ast)
- Minimum of Bars ACI Code 10.9.2
min. of 6 bars in circular arrangement w/min.
spiral reinforcement. min. of 4 bars in
rectangular arrangement
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Behavior, Nominal Capacity and Design under
concentric Axial loads
3.
Reinforcement Requirements (Lateral Ties)
ACI Code 7.10.5
3 bar if longitudinal bar 10 bar
4 bar if longitudinal bar 11 bar 4
bar if longitudinal bars are bundled
size
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Behavior, Nominal Capacity and Design under
concentric Axial loads
3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing
16 db ( db for longitudinal bars )
48 db ( db for tie bar )
least lateral dimension of column
s s s
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Behavior, Nominal Capacity and Design under
concentric Axial loads
3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing Arrangement,
At least every other longitudinal bar shall have
lateral support from the corner of a tie with an
included angle 135o. No longitudinal bar
shall be more than 6 in. clear on either side
from support bar.
1.)
2.)
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Examples of lateral ties.
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Reinforcement Requirements (Spirals )
ACI Code 7.10.4
3/8 f (3/8 f smooth bar, 3 bar dll or
wll wire)
- size
1 in. 3 in.
- clear spacing
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Reinforcement Requirements (Spiral)
Spiral Reinforcement Ratio, rs
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Behavior, Nominal Capacity and Design under
concentric Axial loads
Reinforcement Requirements (Spiral)
ACI Eqn. 10-6
where
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Behavior, Nominal Capacity and Design under
concentric Axial loads
4.
Design for Concentric Axial Loads
(a) Load Combination
Gravity
Gravity Wind
and
Etc.
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Behavior, Nominal Capacity and Design under
concentric Axial loads
4.
Design for Concentric Axial Loads
(b) General Strength Requirement
f 0.7 for tied columns f 0.75 for spiral
columns
where,
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Behavior, Nominal Capacity and Design under
concentric Axial loads
4.
Design for Concentric Axial Loads
(c) Expression for Design
defined
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Behavior, Nominal Capacity and Design under
concentric Axial loads
or
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Behavior, Nominal Capacity and Design under
concentric Axial loads
when rg is known or assumed
when Ag is known or assumed
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Example Design tied Column for concentric Axial
Load
Design tied column for concentric axial load Pdl
150 k Pll 300 k Pw 50 k fc 4500 psi fy
60 ksi Design a square column aim for rg 0.03.
Select longitudinal transverse reinforcement.
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Behavior under Combined Bending and Axial Loads
Usually moment is represented by axial load times
eccentricity, i.e.
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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.
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Behavior under Combined Bending and Axial Loads
Axial Load and Moment Interaction Diagram -General
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Behavior under Combined Bending and Axial Loads
Resultant Forces action at Centroid
( h/2 in this case )
Moment about geometric center
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Example Axial Load vs. Moment Interaction Diagram