Lecture 16 Shear Design

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Lecture 16 Shear Design

• July 14, 2003
• CVEN 444

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Lecture Goals

• Class Project
• Shear
• Shear Design

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Class Project
The structural floor plan of a three-story
(ground floor, two suspended floors, and a roof)
office building is shown on the next page. The
roof covers the hole used for the elevator shaft
and stairwells. The new building will be located
in Houston, Texas. The floor systems consist of
one-way pan joists slabs supported in one
direction by beams located on column lines A
through F. In addition, beams are located on
column lines 1 and 4 as part of the lateral force
resisting system.
0.75L
0.75L
0.75L
0.75L
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Class Project
The design loads for the floor (in addition to
the self-weight) include a superimposed dead load
(SDL) of 20 psf to account for moveable
partitions, ceiling panels, etc. and a
superimposed live load (LL) to be determined from
ASCE 7-95. In addition, a 0.5 kip/ft. wall load
is applied around the building perimeter. The
design loads for the roof (in addition to the
self-weight) include a superimposed dead load
(SDL) of 10 psf.
0.75L
0.75L
0.75L
0.75L
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Class Project
Overview of Required Design

• Design the continuous beams of the first floor on
  column lines D and E of the second suspended
  floor assuming that they support the one-way pan
  joist floor system (3 parts).
• Design the slab of the second suspended floor as
  a one-way pan joist system supported in one
  direction on column lines A through F (3 parts).
• Design and detail the columns for all three
  stories for the location where column lines E and
  2 intersect (1 part).
• Design the roof system as a two-way slab without
  beams (1 part).
• Design the footing for the column on column lines
  E and 2 (1 part).

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Class Project
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Class Project
The Joist detail for section 1-1
The beam detail for section 2-2
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Class Project
Team Performance It is expected that all
assignments related to the project will be done
in teams. Each assignment must contain
computations that are initialed by the
calculators (or originators) and initialed by the
checker(s). Members of the team will rotate
between calculation and checking tasks. It is
recommended that two persons calculate for each
assignment (i.e., In a four-person team, two
persons should provide calculation services on
odd numbered assignments and checking services on
even number assignments. In a three-person team,
each person should rotate so that they are
checking every third assignment.) Those not
performing calculations are responsible for
checking them and must be afforded ample time to
thoroughly check the calculations. If revisions
are necessary, those performing the calculations
must make the corrections. Each sheet must be
initialed by the originator and checker. A cover
sheet with the signature of each team member must
be included with each assignment. Assignments
that are not signed or initialed by all team
members will not be accepted.
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Class Project
Peer Evaluation Peer evaluation is a common
practice in the engineering community. Critical
evaluation is a necessary component of improving
the engineering profession. It is generally
believed that honors and awards granted by peers
are the highest possible honors. After all, it
is our peers who know best what is required to do
an adequate, good, or outstanding job. Your
individual project grade will depend on an
evaluation by your peers at the end of the
semester. The evaluation form will have a format
similar to the one provided on the back of this
sheet. Evaluation forms will also be collected
during the middle of the semester for an
unofficial assessment of group performance.
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Class Project
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Uncracked Elastic Beam Behavior
Look at the shear and bending moment diagrams.
The acting shear stress distribution on the beam.
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Uncracked Elastic Beam Behavior
The acting stresses distributed across the
cross-section.
The shear stress acting on the rectangular beam.
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Uncracked Elastic Beam Behavior
The equation of the shear stress for a
rectangular beam is given as
Note The maximum 1st moment occurs at the
neutral axis (NA).
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Uncracked Elastic Beam Behavior
The ideal shear stress distribution can be
described as
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Uncracked Elastic Beam Behavior
A realistic description of the shear distribution
is shown as
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Uncracked Elastic Beam Behavior
The shear stress acting along the beam can be
described with a stress block
Using Mohrs circle, the stress block can be
manipulated to find the maximum shear and the
crack formation.
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Inclined Cracking in Reinforced Concrete Beams
Typical Crack Patterns for a deep beam
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Inclined Cracking in Reinforced Concrete Beams
Flexural-shear crack - Starts out as a flexural
crack and propagates due to shear
stress. Flexural cracks in beams are vertical
(perpendicular to the tension face).
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Inclined Cracking in Reinforced Concrete Beams
For deep beam the cracks are given as The shear
cracks Inclined (diagonal) intercept crack
with longitudinal bars plus vertical or inclined
reinforcement.
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Inclined Cracking in Reinforced Concrete Beams
For deep beam the cracks are given as The shear
cracks fail due two modes - shear-tension
failure - shear-compression failure

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Shear Strength of RC Beams without Web
Reinforcement
Total Resistance vcz vay vd (when no
stirrups are used)
vcz - shear in compression zone va - Aggregate
Interlock forces vd Dowel action from
longitudinal bars Note vcz increases from (V/bd)
to (V/by) as crack forms.
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Strength of Concrete in Shear (No Shear
Reinforcement)
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Strength of Concrete in Shear (No Shear
Reinforcement)
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Strength of Concrete in Shear (No Shear
Reinforcement)
(3) Shear span to depth ratio, a/d (M/(Vd))

Deep shear spans more detail design required
Ratio has little effect
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Strength of Concrete in Shear (No Shear
Reinforcement)
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Strength of Concrete in Shear (No Shear
Reinforcement)
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Function and Strength of Web Reinforcement
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Function and Strength of Web Reinforcement

• Uncracked Beam Shear is resisted uncracked
  concrete.
• Flexural Cracking Shear is resisted by vcz,
  vay, vd

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Function and Strength of Web Reinforcement

• Flexural Cracking Shear is resisted by
  vcz, vay, vd and vs

Vs increases as cracks widen until yielding of
stirrups then stirrups provide constant
resistance.
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Designing to Resist Shear
Shear Strength (ACI 318 Sec 11.1)
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Designing to Resist Shear
Shear Strength (ACI 318 Sec 11.1)
Nominal shear resistance provided by concrete
Nominal shear provided by the shear reinforcement
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Shear Strength Provided by Concrete
Bending only
Simple formula More detailed Note
Eqn 11.3
Eqn 11.5
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Shear Strength Provided by Concrete
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Typical Shear Reinforcement
Stirrup - perpendicular to axis of members
(minimum labor - more material)
ACI Eqn 11-15
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Typical Shear Reinforcement
Bent Bars (more labor - minimum material) see
reqd in 11.5.6
ACI 11-5.6
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Stirrup Anchorage Requirements
Vs based on assumption stirrups yield
Stirrups must be well anchored.
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Stirrup Anchorage Requirements
Refer to Sec. 12.13 of ACI 318 for development of
web reinforcement. Requirements

• each bend must enclose a long bar
• 5 and smaller can use standard hooks 90o,135o,
  180o
• 6, 7,8( fy 40 ksi )
• 6, 7,8 ( fy gt 40 ksi ) standard hook plus a
  minimum embedment

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Stirrup Anchorage Requirements
Also sec. 7.10 requirement for minimum stirrups
in beams with compression reinforcement, beams
subject to stress reversals, or beams subject to
torsion
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Design Procedure for Shear
(1) Calculate Vu (2) Calculate fVc Eqn 11-3 or
11-5 (no axial force) (3) Check
If yes, add web reinforcement (go to 4)
If no, done.
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Design Procedure for Shear
Provide minimum shear reinforcement
(4)
Also (Done)
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Design Procedure for Shear
(5)
Check
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Design Procedure for Shear
(6)
Solve for required stirrup spacing(strength)
Assume 3, 4, or 5 stirrups
from 11-15
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Design Procedure for Shear
(7) Check minimum steel requirement (eqn 11-13)
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Design Procedure for Shear
(8) Check maximum spacing requirement (ACI
11.5.4)
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Design Procedure for Shear
(9) Use smallest spacing from steps 6,7,8
Note A practical limit to minimum stirrup
spacing is 4 inches.
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Location of Maximum Shear for Beam Design
Non-pre-stressed members
Sections located less than a distance d from face
of support may be designed for same shear, Vu, as
the computed at a distance d.
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Location of Maximum Shear for Beam Design
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Location of Maximum Shear for Beam Design