Lecture 17 Shear Design

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Lecture 17 Shear Design

• July 16, 2003
• CVEN 444

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Lecture Goals

• Shear beam example for a beam
• Shear design for slab
• Slab design example

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Example Design of Stirrups to Resist Shear
From flexural design
fc 4000 psi fy 60 ksi wsdl
1.2 k/ft wll 1.8 k/ft fys 40 ksi wb
0.5 k/ft
will use either a 3 or 4 stirrup
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Example Design of Stirrups to Resist Shear
Consider the pattern loading on the beam and
determine the envelope of absolute maximum shear
along the beam for a symmetric beam with
uniformly distributed loads, a straight line
drawn between the maximum at the end and midspan
is adequate.
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Example Design of Stirrups to Resist Shear
The maximum shear is where,
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Example Design of Stirrups to Resist Shear
The maximum shear is Note
Multiply by 1.15 for end moments _at_ face of 1st
internal support when using ACI shear coefficient
1.15 Vumax (section 8.3)
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Example Design of Stirrups to Resist Shear
The wall is an interior section so the
coefficient is 1.0. For shear the reduction
factor, f, is 0.75.
How do you get maximum shear the center?
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Example Design of Stirrups to Resist Shear
There is no pattern load for dead loads Vdl 0
_at_ center
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Example Design of Stirrups to Resist Shear
There is a pattern load for live loads at the
center of the beam
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Example Design of Stirrups to Resist Shear
Compute the Vu max at the center
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Example Design of Stirrups to Resist Shear
The shear envelope can be constructed using the
values of two maximum at the two location end and
the center.
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Example Design of Stirrups to Resist Shear
Calculate the equation of the line to bound the
shear force and
The slope of the shear forces.
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Example Design of Stirrups to Resist Shear
Calculate the equation of the line to bound the
shear force and
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Example Design of Stirrups to Resist Shear
Calculate the capacity of the concrete
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Example Design of Stirrups to Resist Shear
Calculate 0.5 of Vc to check to see if shear
reinforcement is needed.
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114.8 k gt 0.5Vc Need shear reinforcement
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Example Design of Stirrups to Resist Shear
Determine the stirrup spacing requirement, Av
for the calculations
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The area, Av, is twice the area of the bars Ab
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Example Design of Stirrups to Resist Shear
The minimum spacing (11.5.5.3 ACI)
3
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Example Design of Stirrups to Resist Shear
The allowable maximum spacing
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The maximum spacing is 13.1 in.
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Example Design of Stirrups to Resist Shear
Check the maximum allowable steel shear force
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Example Design of Stirrups to Resist Shear
Check the maximum allowable steel shear force
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Reinforcements can be used for shear
reinforcement. The beam does not need to be
redesigned.
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Example Design of Stirrups to Resist Shear
Strength requirement is given as
Instead of solving for s, we can plot the Vc
Vs, where
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Example Design of Stirrups to Resist Shear
Using this technique (ACI 11.3.1), various Av and
spacing s can be used. The maximum V is
determined at the distance,d from the wall.
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Example Design of Stirrups to Resist Shear
The shear force are
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Example Design of Stirrups to Resist Shear
This is one possibly form to check
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Example Design of Stirrups to Resist Shear
There always going to be a shear reinforcement
close to the support. Use the minimum spacing, 4
in., so that the first stirrup has 4 in. Spacing
can be computed as
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Example Design of Stirrups to Resist Shear
If we are using 8 4 stirrups _at_ 7 in. spacing,
(7 in. is less than 7.92 in.) So,
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Example Design of Stirrups to Resist Shear
Compute the location of the point and
find Compute Vn
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Example Design of Stirrups to Resist Shear
Compute the next spacing
Use s 9 in., which is find for 4 bar. Trying
to fit the reinforcement inside the beam.
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Example Design of Stirrups to Resist Shear
If we are using 6 4 stirrups _at_ 9 in. spacing, 9
in. is less than 11.3 in. So,
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Example Design of Stirrups to Resist Shear
Compute the location of the point and
find Compute Vn
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Example Design of Stirrups to Resist Shear
Use a 3 bar for
Use s 12 in., because the smax is 13.1 in.
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Example Design of Stirrups to Resist Shear
If we are using 8 3 stirrups _at_ 12 in. spacing,
12 in. is less than 13.1 in. So,
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Example Design of Stirrups to Resist Shear
Compute the location of the point and find This
is at the middle of the beam. Under Vc/2 no
stirrups are need other than the minimum.
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Example Design of Stirrups to Resist Shear
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Example Design of Stirrups to Resist Shear
There is a mistake for the problem! What is the
error?
The spacing of the 3 bar is 12 in. and the max
spacing between bars is 11.7 in., so go back and
redesign. Easy way would be to use 4 instead of
3 bars.
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Example Design of Stirrups to Resist Shear
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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)
(ACI Sec 7.12.2 )
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Joist Design
Shear Design of Joist Ribs (Joist - Section 8.11)
(2)
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Joist Design
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Joist Design
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One-Way Slab Design
Design of one slabs is like design of parallel
12 beams.
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 tmin,
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
3.50 in. 1 hour 5.00 in.
2 hours 6.25 in. 3 hours
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Cover for Slab Reinforcement
ACI Sec. 7.7.1 (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 10.9 text one-way slab (ref. ACI
Committee 315 ACI Detail Manual 1980)
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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. 11.5.5.1
ACI Eqn. 11-3
Usual use
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One-Way Slab Example
The cross section of a continuous one-way solid
slab in a building is shown. The slabs are
supported by beams that span 24 ft. Between
simple supports. The dead load on the slabs is
that due to self-weight plus 60 psf The live
load is 120 psf. Design the continuous slab and
draw a detailed section. Given fc 3 ksi, fy
40 ksi.
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One-Way Slab Example
Determine the thickness of the slab.
Minimum thickness of interior bay
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One-Way Slab Example
Use h 6 in.
Dead weight
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One-Way Slab Example
Determine the load on the floor
For slab design r is seldom gt 0.01. Use c/d 0.2
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One-Way Slab Example
Find the coefficient of the moment diagram
The maximum moment is
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One-Way Slab Example
Find the design d for a one-foot strip
If b 12-in. then d 3.46-in., which for c/d
0.2, so d 5-in., the slab is OK.
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One-Way Slab Example
Find the coefficient of the shear
The maximum shear is
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One-Way Slab Example
Check the shear capacity of the slab
Use h 6-in., d 5-in. and wu 0.354 k/ft
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One-Way Slab Example
Minimum about of steel is (use ACI 7.12 )
Moment capacity of the slab (12-in. beam)
Assume
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One-Way Slab Example
Compute the moments
Moment capacity of the beam
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One-Way Slab Example
Compute the moments
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One-Way Slab Example
Check the assumption
Assumption will work!
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One-Way Slab Example
Use 4 bar Ab 0.2 in2 The maximum spacing ACI
7.6.4
maximum spacing
The spacing on the first location
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One-Way Slab Example
Select 15 in. for the spacing to calculate the
provided area.
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One-Way Slab Example
Actual spacing.
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One-Way Slab Example
Summary