Lecture 20 Bar Development

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Lecture 20- Bar Development

• March 3, 2003
• CVEN 444

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Lecture Goals

• Bar Cut-off Points
• Spice

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Determining Locations of Flexural Cutoffs
Given a simply supported beam with a distributed
load.
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Determining Locations of Flexural Cutoffs
Note Total bar length Fully effective length
Development length
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Determining Locations of Flexural Cutoffs
ACI 12.10.3 All longitudinal tension bars must
extend a min. distance d (effective depth of
the member) or 12 db (usually larger) past the
theoretical cutoff for flexure (Handles
uncertainties in loads, design approximations,etc.
.)

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Determining Locations of Flexural Cutoffs
Development of flexural reinforcement in a
typical continuous beam. ACI 318R-02

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Bar Cutoffs - General Procedure
Determine theoretical flexural cutoff points for
envelope of bending moment diagram. Extract the
bars to satisfy detailing rules (from ACI Section
7.13, 12.1, 12.10, 12.11 and 12.12) Design extra
stirrups for points where bars are cutoff in zone
of flexural tension (ACI 12.10.5)
1. 2. 3.
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Bar Cutoffs - General Rules
All Bars Rule 1. Rule 2.
Bars must extend the longer of d or 12db past the
flexural cutoff points except at supports or the
ends of cantilevers (ACI 12.11.1)
Bars must extend at least ld from the point of
maximum bar stress or from the flexural cutoff
points of adjacent bars (ACI 12.10.2 12.10.4 and
12.12.2)
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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Simple Supports At least one-third of the
  positive moment reinforcement must be extend 6
  in. into the supports (ACI 12.11.1).
• Continuous interior beams with closed stirrups.
  At least one-fourth of the positive moment
  reinforcement must extend 6 in. into the support
  (ACI 12.11.1 and 7.13.2.3)

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Continuous interior beams without closed
  stirrups. At least one-fourth of the positive
  moment reinforcement must be continuous or shall
  be spliced near the support with a class A
  tension splice and at non-continuous supports be
  terminated with a standard hook. (ACI 7.13.2.3).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Continuous perimeter beams. At least one-fourth
  of the positive moment reinforcement required at
  midspan shall be made continuous around the
  perimeter of the building and must be enclosed
  within closed stirrups or stirrups with 135
  degree hooks around top bars. The required
  continuity of reinforcement may be provided by
  splicing the bottom reinforcement at or near the
  support with class A tension splices (ACI
  7.13.2.2).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Beams forming part of a frame that is the primary
  lateral load resisting system for the building.
  This reinforcement must be anchored to develop
  the specified yield strength, fy, at the face of
  the support (ACI 12.11.2)

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 4.

• Stirrups
• At the positive moment point of inflection and at
  simple supports, the positive moment
  reinforcement must be satisfy the following
  equation for ACI 12.11.3. An increase of 30 in
  value of Mn / Vu shall be permitted when the ends
  of reinforcement are confined by compressive
  reaction (generally true for simply supports).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 4.
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Bar Cutoffs - General Rules
Negative Moment Bars Rule 5.

• Negative moment reinforcement must be anchored
  into or through supporting columns or members
  (ACI Sec. 12.12.1).

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Bar Cutoffs - General Rules
Negative Moment Bars Rule 6.

• Structural Integrity
• Interior beams. At least one-third of the
  negative moment reinforcement must be extended by
  the greatest of d, 12 db or ( ln / 16 ) past the
  negative moment point of inflection (ACI Sec.
  12.12.3).

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Bar Cutoffs - General Rules
Negative Moment Bars Rule 6.

• Structural Integrity
• Perimeter beams. In addition to satisfying rule
  6a, one-sixth of the negative reinforcement
  required at the support must be made continuous
  at mid-span. This can be achieved by means of a
  class A tension splice at mid-span (ACI
  7.13.2.2).

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Moment Resistance Diagrams
Moment capacity of a beam is a function of its
depth, d, width, b, and area of steel, As. It is
common practice to cut off the steel bars where
they are no longer needed to resist the flexural
stresses. As in continuous beams positive moment
steel bars may be bent up usually at 45o, to
provide tensile reinforcement for the negative
moments over the support.
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Moment Resistance Diagrams
The nominal moment capacity of an
under-reinforced concrete beam is To determine
the position of the cutoff or bent point the
moment diagram due to external loading is drawn.
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Moment Resistance Diagrams
The ultimate moment resistance of one bar, Mnb
is The intersection of the moment resistance
lines with the external bending moment diagram
indicates the theoretical points where each bar
can be terminated.
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Moment Resistance Diagrams
Given a beam with the 4 8 bars and fc3 ksi and
fy50 ksi and d 20 in.
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Moment Resistance Diagrams
The moment diagram is
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Moment Resistance Diagrams
The moment resistance of one bar is
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Moment Resistance Diagrams
The moment diagram and crossings
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Moment Resistance Diagrams
The ultimate moment resistance is ?. The moment
diagram is drawn to scale on the basis A bar can
be terminated at a, two bars at b and three bars
at c. These are the theoretical termination of
the bars.
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Moment Resistance Diagrams
It is necessary to develop part of the strength
of the bar by bond. The ACI Code specifies that
every bar should be continued at least a distance
d, or 12db , which ever is greater, beyond the
theoretical points a, b, and c. Section 12.11.1
specify that 1/3 of positive moment reinforcement
must be continuous.
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Moment Resistance Diagrams
Compute the bar development length is
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Moment Resistance Diagrams
Two bars must extend into the support and moment
resistance diagram Mur must enclose the external
bending moment diagram.
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Example Cutoff
For the simply supported beam with b10 in. d
17.5 in., fy40 ksi and fc3 ksi with 4 8 bars.
Show where the reinforcing bars can be
terminated.
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Example Cutoff
Determine the moment capacity of the bars.
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Example Cutoff
The minimum distance is
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Example Cutoff
The minimum amount of bars are As/3 or two bars
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Example Cutoff
Determine the location of the bar intersections
of moments.
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Example Cutoff
Determine the location of the bar intersections
of moments.
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Example Cutoff
The resulting moment-resistance diagram is