Lecture 16 DesignTBeams

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Lecture 16 Design(T-Beams)

• February 21, 2003
• CVEN 444

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Lecture Goals

• Design of T-Beams
• Known section dimensions

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Design Procedure for section dimensions are
unknown (T- Reinforced Beams)
Assume that the material properties, loads, and
span length are all known. Estimate the
dimensions of self-weight using the following
rules of thumb a. The depth, h, may be taken as
approximate 8 to 10 of the span (1in deep per
foot of span) and estimate the width, b, as
about one-half of h. b. The weight of a
rectangular beam will be about 15 of the
superimposed loads (dead, live, etc.). Assume
b is about one-half of h. Immediate values of h
and b from these two procedures should be
selected. Calculate self-weight and Mu.
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Design Procedure for Singly Reinforced Flange
Beams when flange is in compression Known
dimensions

• Calculate controlling value for the design
  moment, Mu.
• Assume that resulting section will be tension
  controlled, et 0.005 so that can take f 0.9.

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Design Procedure for Singly Reinforced Flange
Beams when flange is in compression Known
dimensions

• Calculate d, since h is known

For one layer of reinforcement. For two layers of
reinforcement.
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Design Procedure for Singly Reinforced Flange
Beams when flange is in compression Known
dimensions

• Determine the effective width of the flange, beff
• Check whether the required nominal moment
  capacity can be provided with compression in the
  flange alone.
• and

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Design Procedure for Singly Reinforced Flange
Beams when flange is in compression Known
dimensions

• If Need to utilize
  web below flanges. Go to step 4.
• If Use design procedure
  for rectangular beams with b beff , (d
  -a/2) 0.95d
• Note f 0.9 for flexure without axial load
  (ACI 318-02 Sec. 9.3)

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Find nominal moment capacity provided by
  overhanging flanges alone (not including web
  width)
• For a T shaped section
• and

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Find nominal moment capacity that must be
  provided by the web.

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Calculate depth of the compression block, by
  solving the following equation for a.

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Find required reinforcement area, As (reqd)

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Select reinforcing bars so As (provided) As
  (reqd). Confirm that the bars will fit within
  the cross-section. It may be necessary to change
  bar sizes to fit the steel in one layer or even
  to go to two layers of steel.

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Calculate the actual Mn for the section
  dimensions and reinforcement selected. Check
  strength f Mn Mu (keep over-design within
  10 )

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Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known

• Check whether As provided is within allowable
  limits.
• As (provided) As (min)

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Minimum Area
Calculate the minimum amount of steel
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Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
Must distribute flexural tension steel over
effective flange width, be (tension)
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Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
When be (comp) gt l/10 some
longitudinal reinforcement shall be
provided in outer portions
of flange.
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Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
For l use centerline dimensions when adjacent
spans for - M _at_ support are not equal, use
average l to calculate be (tension) One scenario
when be (tension) lt be (compression)
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Design Procedure for SR Beam Unknown Dimension
Do a preliminary geometric size based on the
following
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Design Procedure for SR Beam Unknown Dimension
Assume
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Example Problem
T-Beam with unknown dimensions, hf 6
in.(slab) fc 4500 psi fy 60 ksi. Three
spans continuous beam, simply supported on walls.
Spans are (25ft, 30 ft. and 25 ft.) The beam
spacing is 14 ft center to center
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Example Problem
Using estimated values h 26 in. , b 16
in. Max Mu 300 k-ft Max - Mu 435 k-ft
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Example Problem Negative Moment
Calculate the moment term, where the bottom
section is in compression. Max Mu 435 k-ft.
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Example Problem-b Value
Determine the b1 term for the concrete
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Example Problem k value
Calculate a desired k c/d Determine the Ru
term for the concrete
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Example Problem Design
From the design of the Determine the Ru term
for the concrete
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Example Problem Design
The nominal moment is defined as The bd2
value will for design is
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Example Problem Design
Assume that the b 0.65d so that Determine
the value for b
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Example Problem Design
Determine h assuming a single layer of
reinforcement Check to see if the estimate
will work
Over-designed by 10.9 so it will work but we
would need to go back an recalculate the weight
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Example Problem Design
Calculate the actual value for k
Use the quadratic formula
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Example Problem Check
Calculate the actual value for k
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Example Problem Check
Calculate the actual value for k Calculate the
As required for the beam
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Example Problem Check
Calculate the actual value for As
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Example Problem Flange
The flange is in tension so the reinforcement,
the beff in tension must be computed according to
ACI 10.6.6
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Example Problem Flange
The size of the flange in compression is from
8.10.2 of the ACI code, the beff in compression
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Example Problem Flange
The size of the flange in compression is from
8.10.2 of the ACI code, the beff in compression
Use 82 in. for the compression flange.
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Example Problem Flange
The flange is in tension so the reinforcement,
the beff in tension must be computed according to
ACI 10.6.6
Use 33 in. for beff in tension.
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Example Problem Steel
Select the steel for the reinforcement at least
0.5 As needs to be in the beff of the beam. Use
3 8 bars and 8 5 bars, (which will give you 4
on each side.)
The As 4.85 in2 gt 4.84 in2 OK!
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Example Problem Cover
Check to the value for d
The d will work.
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Example Problem a value
Calculate the new a using the equilibrium
equations.
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Example Problem Strain
Check the strain condition for the beam
Use f 0.9
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Example Problem Mn
Calculate the moment capacity of the
beam Ultimate moment capacity of the beam.
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Example Problem Amin
Calculate the minimum amount of steel Amin
2.26 in2 lt 4.85 in2 OK
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Example Problem Summary
Summary of the beam with M 435 k-ft.
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Example Problem Positive Moment
Calculate the moment term, where the bottom
section is in compression. Max Mu 300 k-ft.
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Example Problem Capacity
Calculate the moment capacity of the beam with d
22.5 in. and hf 6 in.
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Example Problem Amin
The minimum amount of steel is Use As
6.19 in2
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Example Problem a value
So the beam can be designed as a singly
reinforced beam with the minimum amount of steel
5.91 in2.
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Example Problem Mn
Compute the moment capacity of the beam with the
minimum amount of steel 6.19 in2.
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Example Problem Summary
Use 8 8 bars As 6.32 in2. Check to see that
the steel will fit. It will not be within 10 of
the ultimate moment capacity of the beam.
However, the minimum amount steel will preside.
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Homework
Problem 5.13