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.
2nd floor Spandrel beam Door lintel Beam Column Joist slab Column 1st floor Supported slab Beam Foundation walls Basement Slab on grade Landing Column Stairs Wall footing Spread footing Fig. 1. Reinforced concrete building elements (MacGregor 1997, p. 5)
Roof Flat plate Upturned beam 1st floor Interior columns Drop panels Flat slab Column bracket Exterior columns Column capital Basement wall Basement floor Interior columns Slab on grade Spread footings Pedestal Fig. 2. Reinforced concrete building elements (MacGregor 1997, p. 5)
Design Codes ACI 318-95. Building Code Requirements for Reinforced Concrete มาตรฐานส าหร บอาคารคอนกร ตเสร มเหล กโดยว ธ หน วยแรงใช งาน (วสท) มาตรฐานส าหร บอาคารคอนกร ตเสร มเหล กโดยว ธ ก าล ง (วสท)
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.
f c 0.5 f c Tangent modulus at f c Initial modulus (tangent at origin) Ultimate strain varies from 0.003 to 0.004 Secant modulus at f c 0 0.001 0.002 0.003 0.004 CONCRETE STRAIN,, Fig. 3. Methods of defining modulus of elasticity of concrete (Wang and Salmon 1979, p.13)
Stress-strain Curve of Concrete Fig. 4. Stress-strain curves for concrete of various strengths (Nawy 1985, p. 46) STRAIN,,
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-high early strength Type I-normal Days Age (log scale) Years 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 methods 1. Flexural test (ASTM C78 or C293) 2. Split cylinder test (ASTM C496)
Standard Test Methods (cont d) 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, f r, is calculated from: f r M = = S 6M bh 2 where, M = moment S = section modulus b = width of specimen h = overall depth of specimen
Standard Test Methods (cont d) 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, f ct, is calculated from: f ct = 2P πld where, P = maximum load in the test l = length of specimen d = diameter of specimen
Split Cylinder Test P F 1 F 2 d l P 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 f y Neglect in design Design stress-strain curve 1 E s f y = Yield Strength, y STRAIN,, S Fig. 7. Stress-strain curve for reinforcement (Notes 1990, p.6-3)
Types of Reinforcing Steels Main ribs First mark is initial of producing mill. Second mark is bar size. Grade marking for Grade 60 Third mark is type of steel: A615-85 or A615-82(S1) A615 prior to 1985 without S1 Rail, A616-85 Rail, A616-85 Axle, A617 Low alloy, A706 (a) Grade 40 or 50 (b) Grade 60
Types and Grades of Reinforcing Steels A A OVERALL DIAMETER 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) Reinforcement location Fig. 9. Simply-supported beam (MacGregor 1997, p.113)
Concrete beam Loads on beam Stirrup Wall Stirrups Possible shear cracks at about 45E angle Wall Longitudin bar 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
Exterior column Column loads Interior column 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
Not this Use this Bar bears against concrete 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 bars Closed 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) = ว ธ หน วยแรงใช งาน Strength Design (SD) = ว ธ ก าล ง
Working Stress Design Design is based on working loads, also referred to as service loads or unfactored loads. 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 For example, M u φm n 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 (φ) Type of Loading ACI Code Sect. 9.3.2 ACI Code Appendix C Flexure, without axial load 0.90 0.80 Axial tension and axial tension with flexure 0.90 0.80 Axial compression and axial compression with flexure: a. Members with spiral reinforcement conforming to 0.75 0.70 10.9.3 b. Other reinforced members 0.70 0.65 Shear and torsion 0.85 0.75 Bearing 0.70 0.65 Plain 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.