Lecture 13 Analysis and Design

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Lecture 13 Analysis and Design

• February 13, 2002
• CVEN 444

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Lecture Goals

• Resistance Factors and Loads
• Design of Singly Reinforced Rectangular Beam
• Unknown section dimensions
• Known section dimensions

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Flexural Design of Reinforced Concrete Beams and
Slab Sections
Analysis Versus Design
Analysis Given a cross-section, fc ,
reinforcement sizes, location, fy compute
resistance or capacity Design Given factored
load effect (such as Mu) select suitable
section(dimensions, fc, fy, reinforcement,
etc.)
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Flexural Design of Reinforced Concrete Beams and
Slab Sections
ACI Code Requirements for Strength Design
Basic Equation factored resistance
factored load effect
Ex.
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ACI Code Requirements for Strength Design
Mu Moment due to factored loads (required
ultimate moment) Mn Nominal moment capacity
of the cross-section using nominal dimensions
and specified material strengths. f
Strength reduction factor (Accounts for
variability in dimensions, material strengths,
approximations in strength equations.
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Flexural Design of Reinforced Concrete Beams and
Slab Sections
Required Strength (ACI 318, sec 9.2)
U Required Strength to resist factored
loads D Dead Loads L Live loads W Wind
Loads E Earthquake Loads
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Flexural Design of Reinforced Concrete Beams and
Slab Sections
Required Strength (ACI 318, sec 9.2)
H Pressure or Weight Loads due to
soil,ground water,etc. F Pressure or weight
Loads due to fluids with well defined densities
and controllable maximum heights. T Effect
of temperature, creep, shrinkage, differential
settlement, shrinkage compensating.
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Factored Load Combinations
U 1.4 D 1.7 L Always check even if other
load types are present. U 0.75( 1.4 D
1.7 L 1.7 W) U 0.75( 1.4 D 1.7 L) U 0.9
D 1.3 W
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Factored Load Combinations
Similar combination for earthquake, lateral
pressure, fluid pressure, settlement, etc. U
1.05 D 1.28 L 1.4 E U 0.9 D 1.43 E U
1.4 D 1.7 L 1.7 H U 0.9 D 1.7
H U 1.4 D 1.7 L 1.4 F U 0.9 D 1.4
F U 0.75(1.4 D 1.4 T 1.7 L) U 1.4 (D
L)
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Resistance Factors, f - ACI Sec 9.3.2 Strength
Reduction Factors
1 Flexure w/ or w/o axial tension f 0.90 2
Axial Tension f 0.90 3 Axial Compression
w or w/o flexure (a) Member w/ spiral
reinforcement f 0.75 (b) Other reinforcement
members f 0.70 (may increase for very small
axial loads)
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Resistance Factors, f - ACI Sec 9.3.2 Strength
Reduction Factors
4 Shear and Torsion f 0.85 5 Bearing on
Concrete f 0.70 ACI Sec 9.3.4 f
factors for regions of high seismic risk
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Background Information for Designing Beam Sections
1.
Location of Reinforcement locate reinforcement
where cracking occurs (tension region) Tensile
stresses may be due to a ) Flexure b )
Axial Loads c ) Shrinkage effects
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Background Information for Designing Beam Sections
2.
Construction formwork is expensive - try to
reuse at several floors
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Background Information for Designing Beam Sections
3.

• Beam Depths
• ACI 318 - Table 9.5(a) min. h based on l
  (span) (slab beams)
• Rule of thumb hb (in) l (ft)
• Design for max. moment over a support to set
  depth of a continuous beam.

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Background Information for Designing Beam Sections
4.
Concrete Cover Cover Dimension between the
surface of the slab or beam and the
reinforcement
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Background Information for Designing Beam Sections
Concrete Cover Why is cover needed? a
Bonds reinforcement to concrete b Protect
reinforcement against corrosion c Protect
reinforcement from fire (over heating
causes strength loss) d Additional cover used
in garages, factories, etc. to account for
abrasion and wear.
4.
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Background Information for Designing Beam Sections

• Minimum Cover Dimensions (ACI 318 Sec 7.7)
• Sample values for cast in-place concrete
• Concrete cast against exposed to earth - 3 in.
• Concrete (formed) exposed to earth weather
  No. 6 to No. 18 bars - 2 in. No. 5 and
  smaller - 1.5 in

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Background Information for Designing Beam Sections

• Minimum Cover Dimensions (ACI 318 Sec 7.7)
• Concrete not exposed to earth or weather - Slab,
  walls, joists No. 14 and No. 18 bars - 1.5
  in No. 11 bar and smaller - 0.75 in - Beams,
  Columns - 1.5 in

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Background Information for Designing Beam Sections
5.
Bar Spacing Limits (ACI 318 Sec. 7.6) -
Minimum spacing of bars - Maximum spacing of
flexural reinforcement in walls slabs
Max. space smaller of
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Minimum Cover Dimension
Interior beam.
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Minimum Cover Dimension
Reinforcement bar arrangement for two layers.
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Minimum Cover Dimension
ACI 3.3.3 Nominal maximum aggregate size. 3/4
clear space., 1/3 slab depth, 1/5 narrowest dim.
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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)
1) For design moment Substitute
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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)
Let
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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)
Let
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Design Procedure for section dimensions are
unknown (singly 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 section dimensions are
unknown (singly Reinforced Beams)

• Select a reasonable value for r based on
  experience or start with a value of about 45 to
  55 of rbal.
• Calculate the reinforcement index,

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

• Calculate the coefficient
• Calculate the required value of

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

• Select b as a function of d. b (0.45d to
  0.65d)
• Solve for d. Typically round d to nearest 0.5
  inch value to get a whole inch value for h, which
  is approximately d 2.5 in.

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

• Solve for the width, b, using selected d value.
  Round b to nearest whole inch value.
• Re-calculate the beam self-weight and Mu based on
  the selected b and h dimensions. Go back to step
  1 only if the new self weight results in
  significant change in Mu.

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

• Calculate required As rbd. Use the selected
  value of d from Step 6. And the calculated (not
  rounded) value of b from step 7 to avoid errors
  from rounding.

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

• Select steel reinforcing bars to provide As
  (As required from step 9). 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. If you need to use two layers of
  steel, the value of h should be adjusted
  accordingly.

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Design Procedure for section dimensions are
unknown (singly Reinforced Beams)

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

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Design Procedure for section dimensions are known
(singly Reinforced Beams)
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Design Procedure for section dimensions are known
(singly Reinforced Beams)

• Calculate controlling value for the design
  moment, Mu.
• Calculate d, since h is known. d h -
  2.5in. for one layer of reinforcement. d
  h - 3.5in. for two layers of reinforcement.

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Design Procedure for section dimensions are known
(singly Reinforced Beams)

• Solve for required area of tension reinforcement,
  As , based on the following equation.
  

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Design Procedure for section dimensions are known
(singly Reinforced Beams)

• Rewrite the equation

Assume (d-a/2) 0.9d to 0.95d and solve for
As(reqd) Note f 0.9 for flexure without
axial load (ACI 318-95, Sec. 9.3)
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Design Procedure for section dimensions are known
(singly Reinforced Beams)

• Select reinforcing bars so As(provided)
  As(reqd) Confirm 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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Design Procedure for section dimensions are known
(singly Reinforced Beams)

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

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Design Procedure for section dimensions are known
(singly Reinforced Beams)

• Check whether As(provided) is within the
  allowable limits. As(provided)
  As(max) 0.75 As(bal) As(provided)
  As(min)