Class #25.1
c
1

Reinforced Concrete Structural Steel
Advantage Disadvantage Advantage Disadvantage
Shapes
Fire resistance
Maintenance
Time dependent
Strength
Weight
Stiffness
Any shape
1-3 Hr. resistance with
NO coating
Less,
No need to paint
Rigid,
Less; drift, deflection, vibrations.
Must make forms Manufactured shapes
Limited shapes
Creep due to long term load.
Shrinkage due to curing.
Low tensile strength.
Low strength/volume ratio.
Higher,
More seismic load
High tensile strength.
High strength/volume ratio.
Lower,
Less seismic load
Must add fire-proof coating
More,
Must paint for corrosion resistance
More thermal expansion and contraction
Flexible ,
More; drift, deflection, vibrations.
2

What is Reinforced Concrete?
 Definition:
 A construction material composed of:


Course Aggregate – particles > 0.25“ diameter, retained on #4 sieve.
Fine Aggregate – Sand particles < 0.25” diameter, pass #4 sieve.



Water
Cement powder
 cement paste,
 Forms a gluing paste, when mixed with proper amount of water
Reinforcement bars – steel (if no reinforcement, use ACI 318, Ch.22)
 Two Methods of Reinforced Concrete Construction:


Cast-in-Place : members are constructed at their final location;



A form (wood) or mold (steel) is built in the shape of the member,
Reinforcement bars are placed inside form (mold);
Concrete is poured into form (mold).
Pre-Cast : members are constructed off-site;


Members are transported to their final location,
Members are erected and joined to form a structure.
3

I-75, Suder Ave. ramp
McCormac, 8 th ed., p.73
4

Veterans Glass City Skyway bridge
5

Reinforced Concrete Structures
One-way slab
Load bearing
Fig. 4-1,MacGregor, masonry walls.
5 th edition, 2009,
Pearson/Prentice Hall
Gravity loads supported by columns.
Two-way slab
MacGregor, 5 th ed., Fig. 4-1
6

Reinforced Concrete Structures
 Floor slabs: One-way or Two-way;
 One-way slab :
 Takes load in only One direction,
 Slab forms top flange of T-beam joist,
 T-beam takes load in only One direction,
 Load transferred to T-beam joist,
 T-beam transfers load to girder,
 Girder transfers load to column (or wall),
 Column (or wall) transfers load to;
 Piles, Spread footings.
L
1
- one-way slab; L
2
/L
1
> 2
- two-way slab; L
2
/L
1
< 2
L
2
MacGregor, 5 th ed., Fig. 4-34
One-way slab
MacGregor, 5 th ed., Fig. 4-36
7

Reinforced Concrete Structures
 Floor slabs: One-way or Two-way;
 Two-way slab:
 ACI 318, Chapter 13,
 Transfers load in Two directions to girder or column,
MacGregor, 5 th ed., Fig. 13-2
Two-way slab MacGregor, 5 th ed., Fig. 5-22 8

Dimensions and Tolerances
 The design Engineer must:
 specify the exterior dimensions of members so that the members have;
 Adequate strength to resist loads ,
 ACI 318, Ch. 9-21.
 Adequate stiffness to prevent excessive deflections ,
 ACI 318, Sect. 9.5.
 specify the reinforcement , - size, quantity, location.
 ensure constructability of members;
 Rebars must not interfere with each other,


Need space for concrete to flow around rebars,
9
Adequate strength during – erection, curing.

Dimensions and Tolerances
 The design Engineer should specify :
 Calculations;
 3 significant digits,
 Exterior dimensions of beams, columns;
 In whole inch increments,
 Slab thickness;
 In half-inch increments,
 Rebar size, length;
Rebar diameter = 9/8”
 Bar sizes are manufactured in 1/8 in. increments,
 Length in two-inch increments, ACI 318, Sect. 7.5.
 Concrete cover;
 In half-inch increments,
10

Dimensions and Tolerances
 The design Engineer should ensure construction tolerances of:
 Exterior dimensions of beams and columns;


0.5 inch,
 Slab thickness;


0.25 inch,
 Concrete cover; ACI 318, Sect. 7.5.2.1;


0.375 inch, effective depth, d

8 inch,


0.5 inch, effective depth, d > 8 inch,
11

Material Properties
 In any beam (concrete, steel, masonry, wood):
MacGregor, 5 th ed., Fig. 1-4
 Applied loads produce
Internal resisting Couple,
 Tension and Compression forces form couple.
 Positive bending moment,
 Axial Compression forces in the top regions,
 Axial Tension forces in the bottom regions , 12

Material Properties
Cracks occur in areas of Tension ,
Beam will have sudden Brittle failure unless Steel reinforcement is present to take Tension.
MacGregor, 5 th ed., Fig. 1-4 13

Material Properties



Strong in Compression,
Weak in Tension , f t


0 .
05

0 .
10
 f c
'
 Cracks occur in Concrete when:
Tensile Stress in Concrete

Tensile Strength of
 Tensile Stress can be due to:
 Loads
 Restrained shrinkage during curing
 Temperature changes
Concrete
14

Material Properties
 f c
'
 Nominal strength ( n ) is based upon
 f c
'
D esign Strength ≥ Required Strength

Reduced Nominal Strength ≥ Factored Up Load
 n ≥ U
 f c
'
In order to validate a specified , concrete plant must have;


Strength test records

12 months old,
A sample standard deviation, s s
 established from 30 consecutive compressive strength tests
15  2 cylinders tested per test

Material Properties
 In order to validate a specified
 f c
'
; f
'
A Required Average Compressive Strength, , must be obtained;
 For f c
' 
5000 psi
 Use the larger value computed from Eq. (5-1) and Eq. (5-2); f f cr
'
' cr

 f c
' 
1 .
34 s s f c
' 
2 .
33 s s

500
Eq. (5-1)
Eq. (5-2)
 Eq. (5-1) is based on a probability of 1-in-100 that the average of f c
'
3 consecutive tests may < specified.
 Eq. (5.2) is based on a probability of 1-in-100 that an individual test
16 f c
' may be more than 500 psi below specified.

Material Properties
 In order to validate a specified
 f c
'
; f
'
A Required Average Compressive Strength, , must be obtained;
 For f c
' 
5000 psi
 Use the larger value computed from Eq. (5-1) and Eq. (5-3); f f cr
'
' cr

 f
0 .
c
' 
1 .
34 s s
90 f c
' 
2 .
33 s s
Eq. (5-1)
Eq. (5-3)
 Eq. (5-1) is based on a probability of 1-in-100 that the average of f c
'
3 consecutive tests may < specified.
 Eq. (5.3) is based on a probability of 1-in-100 that an individual test
17
0 .
90 f c
' may be < specified.

Material Properties
 Standard Cylinders;
 
ApC
 max Compr
 Concrete samples taken per ASTM C172,
6”
 Concrete samples molded, cured per ASTM C31,
 Concrete strength tested per ASTM C39;

6”x12” cylinders,
 Fill cylinder with concrete,
12”


Allow concrete to harden in cylinder,
 24 hours, 60 ˚ 
80 ˚F, no moisture loss,
Strip the cylinder mold,

 
ApC
Place cylinder in a curing room (100% humidity) or water tank at 72 ˚F,
 max Compr
 After 28 days,


Load 2 cylinders in compression at rate of 35 psi/sec.
Record failure load, calculate failure stress.
18

Cracking & Failure Mechanisms
P
Concrete (and all Brittle materials) fail on the plane of
Max Normal Tension Stress

ApC
Apply a Normal Stress in Compression
– concrete Compression Cylinder Test :
 Will have Tension cracks parallel to applied load,
 on plane of
 max Tension
ApC

ApC
 
ApC
 max Compr
 max Tension
 max T
Plane of max Tension 
ApC
  max Compr
P 19

Apply a Normal Stress in Compression – Split Cylinder Test :
Ductile Material fails by Buckling .
Concrete
Brittle Material fails on plane of max
NORMAL ( Tension ) Stress,
 max Tension

Steel
Ductile on Mohr Circle from applied stress

ApC
Plane of max
Tension

ApC
Brittle
90
˚
 max
2x90
˚
  min

ApC 90
˚
 tension
Tension


Compression
  max

ApC
2

ApC
20

Apply a Normal Stress in Tension :
Ductile Material fails on plane of
 max Tension
 max
From to failure stress = 2x45˚=90˚ on Mohr Circle
Brittle Material fails on plane of
 max
 max
Steel
Tension
Ductile
Tension acts on plane perpendicular to applied Tension load.
 max
 min

0
Compression
2x45 ˚
  max
Tension

ApT

 max
45
˚
45 ˚
45
˚

  max

ApT
2
90 ˚
Cast Iron
Plexiglass
Brittle
45 ˚
Plane of

ApT Tension

Brittle concrete fails on plane of max normal (tension) Stress.
Failure stress located at: 2x90˚=180˚on Mohr Circle
 tension
Concrete
Brittle
 tension
90
˚
  min

ApC
Neutral Axis
2x90
˚
  max
2x45 ˚
 Shear Stress
ApC

2
 max
 slightTens ion

Plane of max
Tension
Principal
Stress
22

Cracking & Failure Mechanisms

ApC
(MacGregor, 5 th ed., Fig. 3.13)
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43)
-
-
(0) Overall Cracking Process ; individually, cement paste & aggregate each have brittle, linear stress-strain curves, 
ApC during a cylinder compression test,
friction between test machine head-plates and cylinder ends,
prevents lateral expansion at cylinder ends,
-
-
this restrains vertical cracking near cylinder ends , this strengthens conical regions near cylinder ends, vertical cracks at mid-height of cylinder do not enter conical regions.
But, in the concrete mixture, the cement paste & aggregate together produce a non-linear stress-strain curve, that appears slightly ductile, due to the gradual micro-cracking within the mixture and redistribution of stress throughout
23 the concrete mixture.

Cracking & Failure Mechanisms
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43)

ApC

0

0 .
3 f c
'
(1) No-Load Bond Cracking during curing;
- cement paste shrinks,
- shrinkage restrained by non-shrinking aggregate,
- shrinkage causes tension in the concrete,
No-Load Bond Cracks occur along interface between cement paste and aggregate,

- stress-strain curve remains nearly linear up to
ApC

0 .
3 f c
'
ApC
24

Cracking & Failure Mechanisms
0 .
5 f c
'
0 .
3 f c
'
0 .
75 f c
'
(MacGregor, 5 th ed., Fig. 3.1)
25 f c
'

Cracking & Failure Mechanisms

ApC

0 .
3

0 .
5 f c
'
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43)
(2) Stable Crack Initiation ;
Bond Cracks occur from one aggregate to another piece of aggregate,
- cracks are stable,
- cracks will propagate only if load is increased,
- additional load is redistributed to un-cracked portions,
- causes gradual curving of stress-strain curve.

ApC
26

Cracking & Failure Mechanisms

ApC

0 .
5

0 .
75 f c
'
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43)
(3) Stable Crack Propagation ;
Mortar Cracks occur between Bond Cracks,
- cracks develop parallel to the compressive load, due to

- crack do not grow during constant load,
- cracks propagate only with increasing load,
- stress-strain curve continues to curve.
- the onset of this stage is called the Discontinuity Limit .

ApC
27

Cracking & Failure Mechanisms

ApC

0 .
75 f c
'
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43)
(4) Un-Stable Crack Propagation ;
Mortar Cracks lengthen with constant load,
- additional cracks form,
- few undamaged portions remain to carry additional load,
- cracks propagate without increasing load,
- this is an unstable condition,
- stress-strain curve becomes very non-linear,
- eventually, stress-strain curve begins to flatten,
- failure will occur.

ApC
- The onset of this stage is called Critical Stress at

ApC

0 .
75 f c
'
28

Cracking & Failure Mechanisms

ApC

0 .
75 f c
'
Concrete cracking process;
4 stages :
(MacGregor, 5 th ed., pp. 41-43))
(4) Un-Stable Crack Propagation ;
Critical Stress;

ApC

0 .
75 f c
'
significant lateral strains caused by large amount of micro cracks,
- volumetric strain increases, significantly,
- causes outward force on lateral confining reinforcement,
- spirals,
- lateral ties,

ApC
- confining reinforcement becomes in Tension,
- confining Steel restrains concrete expansion and disintegration,
- puts column in a state of Triaxial Compressive Stress.
29

Uni-Axial vs. Bi-Axial Loadings
Concrete always cracks on plane of

MaxTension
So far, discussion has involved
Uni-Axial loading;
Uni-Axial compression, points A or A’
Uni-Axial tension, points B or B’
(MacGregor, 5 th ed., Fig. 3.12)
30

Uni-Axial vs. Bi-Axial Loadings
Bi-Axial Compression; from points A-CA’
- Delays the formation of - Bond Cracks
- Mortar Cracks
- Stable crack propagation - longer time
- higher load
Due to Bi-Axial Compression; failure at point C ≈
1 .
07 f c
'
(MacGregor, 5 th ed., Fig. 3.12)
31

Tri-Axial Loadings
Tri-axial Compression ;
- Compared to uni-axial compression;
- higher compressive strength,
- more ductile,
 
Failure
4 .
3

3
(MacGregor, 5 th ed., Fig. 3.16)
-
In columns:
Uni-axial compression causes outward force on lateral confining reinforcement,
- spirals
- ties
- confining Steel restrains concrete expansion and disintegration,
- reinforcement becomes in Tension, as it restrains concrete expansion
- puts column into 32
Triaxial Compression
(MacGregor, 5 th ed., Fig. 3.15)

Cracking & Failure Mechanisms
Confining reinforcement ;
saved Olive View Hospital from complete collapse;
saved building in Philippines from complete collapse;
33

Cracking & Failure Mechanisms
Confining reinforcement ;
double spiral reinforcement used in bridge piers by CALTRANS,
- puts column into a state of
Triaxial
Compressive
Stress.
34