Reinforced Concrete Design

Lecture no. 1

Mechanics of RC

Concrete is strong in compression but week in tension. Therefore, steel bars in RC members resist the tension forces.

RC Members

Reinforced concrete structures consist of a series of individual members.

The members interact to support the loads placed on the structure.

ColumnJoist slab

2nd floor

Beam ColumnDoor lintel

Spandrelbeam

Supported slabBeam

1st floor

Foundationwalls

Slab on grade

Basement

Spread footing

Wall footing

ColumnLanding

Stairs

Fig. 1. Reinforced concrete building elements (MacGregor 1997, p. 5)

Basementwall

Spread footings Pedestal

Slab on grade

InteriorcolumnsBasement floor

ExteriorColumnbracket

Upturnedbeam

RoofFlat plate

Interiorcolumns

columns

1st floor

Drop panels Flat s lab

Column capital

Fig. 2. Reinforced concrete building elements (MacGregor 1997, p. 5)

Design Codes

ACI 318-95. Building Code Requirements for Reinforced Concrete

()

()

Types of Loadings

Dead loads Live loads Others (wind, snow, earthquake, etc.)

Dead Loads

Live Loads

Properties of Concrete

Compressive strength and modulus of elasticity (stress-strain curve)

Shrinkage, creep, and thermal expansion

Compressive Strength (fc)

The minimum specified compressive strength (fc) is the strength of concrete after 28 days of curing.

Concrete structures are designed to resist all loads during their service life based on the 28-day strength.

The tensile strength of concrete is very low, about 8% to 15% of the compressive strength.

CONCRETE STRAIN, ,

0 0.001 0.002 0.003 0.004

0.5 fc

Secant modulus at fc

Initial modulus (tangent at origin)

Tangent modulus at fcUltimate strainvaries from0.003 to 0.004

fc

Fig. 3. Methods of defining modulus of elasticity of concrete (Wang and Salmon 1979, p.13)

Stress-strain Curve of Concrete

STRAIN, ,

Fig. 4. Stress-strain curves for concrete of various strengths (Nawy 1985, p. 46)

Factors Affecting Compressive Strength

Water/cement ratio Aggregate (type, texture, and grading) Age of concrete Supplementary cementitious materials

(e.g. fly ash, silica fume) Moisture conditions during curing Temperature conditions during curing Rate of loading

Effect of Age on Compressive Strength

Type III-highearly strength

Type I-normal

Days YearsAge (log scale)

Fig. 5. Effect of age on compressive strength of moist-cured concrete (Nelson and Winter 1991, Wang and Salmon 1991, p.44)

Standard Test Methods

Compressive strength test: Cylinder 6 in diameter by 12 high (ASTM Standards C31 and C39)

Tensile strength test: 2 methods1. Flexural test (ASTM C78 or C293)2. Split cylinder test (ASTM C496)

Standard Test Methods (contd)

In the flexural test, a plain concrete beam, 6 x 6 x 30 long is loaded in flexure on a 24 span.

The flexural tensile strength or modulus of rupture, fr, is calculated from:

2

6r

M MfS bh

= =where, M = momentS = section modulusb = width of specimenh = overall depth of specimen

Standard Test Methods (contd)

In the split cylinder test, a standard 6 x 12 compression test cylinder is placed on its side and loaded in compression along a diameter.

The splitting tensile strength, fct, is calculated from:

2ct

Pfld

=where, P = maximum load in the testl = length of specimend = diameter of specimen

Split Cylinder TestP

P

F1

F2

d l

Stress on element Test procedure

Fig. 6. Split cylinder test for determining tensile strength of concrete (MacGregor 1988, p.52)

Shrinkage of Concrete

Drying shrinkage of hardened concrete increases greatly with the amount of water added to the concrete mix.

Shrinkage can be harmful if not controlled. It can (1) cause cracks in RC members, (2) induce large stresses in statically indeterminate structures, and (3) lead to loss of prestressing force.

Properties of Reinforcing Steels

Yield strength (stress-strain curve) Modulus of elasticity

Stress-strain Curves of Steel

STRAIN, ,S

fy

Es

1

Design stress-strain curve

Neglect in design

,y

Fig. 7. Stress-strain curve for reinforcement (Notes 1990, p.6-3)

fy = Yield Strength

Types of Reinforcing Steels

Main ribs

Grade markingfor Grade 60

First mark is initial

Second mark is bar size.

Third mark is type of steel:A615-85 or A615-82(S1)A615 prior to 1985 without S1Rail, A616-85Rail, A616-85Axle, A617Low alloy, A706

(a) Grade 40 or 50 (b) Grade 60

of producing mill.

Types and Grades of Reinforcing Steels

A A

OVERALLDIAMETER

Fig. 8. Overall bar diameters (Manual of Standard Practice 1976, p.6-2)

Placing Reinforcing Steels in Concrete Members

(a) Deflected shape

(b) Moment diagram

(c) Reinforcementlocation

Fig. 9. Simply-supported beam (MacGregor 1997, p.113)

Concretebeam

Wall

Loads on beam

StirrupsPossible shear cracksat about 45E angle

Wall

Stirrup

Longitudinbar

Fig. 10. Reinforcement of simple beam

(a) Deflected shape

(b) Moment diagram under uniformly distributed load

(c) Straight bar reinforcement

(d) Straight and bent bar reinforcement

Fig. 11. Reinforcement of continuous beam (MacGregor 1997, p.114)

(a) Deflected shape

(b) Moment diagram

(c) Reinforcement location

Fig. 12. Reinforcement of cantilever beam (MacGregor 1997, p.113)

Fig. 13. Reinforcement of cantilever retaining wall

Exteriorcolumn column

Interior

Columnloads

C A D

B

Fig. 14. Reinforcement of combined footings

Column

Footing

Soil pressure loads

Fig. 15. Reinforcement of single footing

Not this Use this

Fig. 16. Tension bars at inside of corner

Bar bearsagainst concrete

Use thisNot this

Fig. 17. Tension bars in stair landings

(a) Buckled column bars (b) Column ties (c) Column spinals

Fig. 18. Compression reinforcement in columns

Added compression barsClosed

ties

Tension bars

(a) Double reinforced beam (b) Two piece tie (c) Cap stirrup

Fig. 19. Compression reinforcement in beams

Design Procedures Working Stress Design (WSD) =

Strength Design (SD) =

Working Stress Design

Design is based on working loads, also referred to as service loads or unfactoredloads.

In flexure, the maximum elastically computed stresses cannot exceed allowable stresses or working stresses of 0.4 to 0.5 times the concrete and steel strengths.

Strength Design

Design is based on factored loads in such combinations as are stipulated in the code.

The computed load effects (Mu, Vu, Tu) must be no greater than the resistance of the member at every section.

Strength Design

Load effects Resistances

u nM MFor example,

Moments calculated from a combination of factored loads (U)

Strength reduction factor

Nominal moment resistance based on properties of member section

Combination of Factored Loads

U = 1.4D + 1.7L U = 0.75(1.4D+1.7L+1.7W) U = 0.75(1.4D+1.7W)

D = dead load, L = live load, W = wind load

Strength Reduction Factors ()Type of Loading ACI Code

Sect. 9.3.2 ACI Code

Appendix CFlexure, without axial load 0.90 0.80Axial tension and axial tension with flexure 0.90 0.80Axial compression and axial compressionwith flexure:

a. Members with spiralreinforcement conforming to10.9.3

b. Other reinforced members

0.75

0.70

0.70

0.65

Shear and torsion 0.85 0.75Bearing 0.70 0.65Plain concrete 0.65 0.55

Analysis versus Design

Analysis: Given a cross section, concrete strength, reinforcement size, location, and yield strength, compute the resistance or capacity.

Design: Given a factored load effect such as Mu, select a suitable cross section, including dimensions, concrete strength, reinforcement, and so on.