Lecture 22 Shear Design

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Lecture 22 - Shear Design

• March 6, 2002
• CVEN 444

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Lecture Goals

• Shear design

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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
Table 5.13.1
Simple formula More detailed Note
Eqn 11.3
Eqn 11.6
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Shear Strength Provided by Concrete
Bending and Axial Compression
Simple formula
Nu is positive for compression and Nu/Ag are in
psi.
Eqn 11.4
Eqn 11.8
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Shear Strength Provided by Concrete
Bending and Axial Compression
More detailed
Nu is positive for compression and Nu/Ag are in
psi.
Use Mm in Eqn 11.6 with no limits
Eqn 11.8
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Shear Strength Provided by Concrete
Bending and Axial Tension
Simple formula
Design shear reinforcement for all shear.
Nu is negative for tension and Nu/Ag are in psi.
Eqn 11.9
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Lightweight ConcreteShear Strength Provided by
Shear Reinforcement
Minimum Shear Reinforcement (11.5.5)
Except
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Lightweight ConcreteShear Strength Provided by
Shear Reinforcement
Vc for lightweight concrete 11.2 fct -splitting
tensile strength
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Lightweight ConcreteShear Strength Provided by
Shear Reinforcement
(provides additional 50 psi of shear strength)
Note
for stirrups
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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. 12.12 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. 7.11 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
When
The support reaction introduces compression into
the end regions of the member. No concentrated
load occurs with in d from face of support .
1.
2.
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Location of Maximum Shear for Beam Design
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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