Title: Lecture 12 Analysis and Design
1Lecture 12 Analysis and Design
- February 10, 2003
- CVEN 444
2Lecture Goals
- Resistance Factors and Loads
- Design of Singly Reinforced Rectangular Beam
- Unknown section dimensions
- Known section dimensions
3Flexural 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.)
4Flexural Design of Reinforced Concrete Beams and
Slab Sections
ACI Code Requirements for Strength Design
Basic Equation factored resistance
factored load effect
Ex.
5ACI 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.
6Flexural 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
7Flexural 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.
8 Factored Load Combinations
U 1.2 D 1.6 L Always check even if other
load types are present. U 1.2(D F
T) 1.6(L H) 0.5 (Lr or S or R) U 1.2D
1.6 (Lr or S or R) (L or 0.8W) U 1.2D 1.6
W 1.0L 0.5(Lr or S or R) U 0.9 D 1.6W
1.6H U 0.9 D 1.0E 1.6H
9Resistance Factors, f - ACI Sec 9.3.2 Strength
Reduction Factors
1 Flexure w/ or w/o axial tension The strength
reduction factor, f, will come into the
calculation of the strength of the beam.
10Resistance Factors, f - ACI Sec 9.3.2 Strength
Reduction Factors
2 Axial Tension f 0.90 3 Axial
Compression w or w/o flexure (a) Member w/
spiral reinforcement f 0.70 (b) Other
reinforcement members f 0.65 (may increase
for very small axial loads)
11Resistance Factors, f - ACI Sec 9.3.2 Strength
Reduction Factors
4 Shear and Torsion f 0.75 5 Bearing on
Concrete f 0.65 ACI Sec 9.3.4 f
factors for regions of high seismic risk
12Background 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
13Background Information for Designing Beam Sections
2.
Construction formwork is expensive - try to
reuse at several floors
14Background 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.
15Background Information for Designing Beam Sections
4.
Concrete Cover Cover Dimension between the
surface of the slab or beam and the
reinforcement
16Background 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.
17Background 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
18Background 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
19Background 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
20Minimum Cover Dimension
Interior beam.
21Minimum Cover Dimension
Reinforcement bar arrangement for two layers.
22Minimum Cover Dimension
ACI 3.3.3 Nominal maximum aggregate size. 3/4
clear space., 1/3 slab depth, 1/5 narrowest dim.
23Example - Singly Reinforced Beam
Design a singly reinforced beam, which has a
moment capacity, Mu 225 k-ft, fc 3 ksi, fy
40 ksi and c/d 0.275 Use a b 12 in. and
determine whether or not it is sufficient space
for the chosen tension steel.
24Example - Singly Reinforced Beam
From the calculation of Mn
25Example - Singly Reinforced Beam
Compute k and determine Ru
26Example - Singly Reinforced Beam
Calculate the bd 2 and by selecting c/d 0.275 f
0.9
27Example - Singly Reinforced Beam
Calculate d, if b 12 in.
Use d 22.5 in., so that h 25 in.
28Example - Singly Reinforced Beam
Calculate As for the beam
29Example - Singly Reinforced Beam
Chose one layer of 4 9 bars Compute r
30Example - Singly Reinforced Beam
Calculate rmin for the beam
The beam is OK for the minimum r
31Example - Singly Reinforced Beam
Check whether or not the bars will fit into the
beam. The diameter of the 9 1.128 in.
So b 12 in. works.
32Example - Singly Reinforced Beam
Check the height of the beam.
Use h 25 in.
33Example - Singly Reinforced Beam
Find a
Find c
34Example - Singly Reinforced Beam
Check the strain in the steel
Therefore, f is 0.9
35Example - Singly Reinforced Beam
Compute the Mn for the beam
Calculate Mu
36Example - Singly Reinforced Beam
Check the beam Mu 225 k-ft12 in/ft 2700 k-in
Over-designed the beam by 6
Use a smaller c/d ratio
37Homework
Problem 5.4, 5.5