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Class #27.2

Class #27.2. Civil Engineering Materials – CIVE 2110 Concrete Material Stress vs. Strain Curves Steel Reinforcement Fall 2010 Dr. Gupta Dr. Pickett. 1. Stress-Strain Curve for Compression. Slightly ductile shape of Stress-Strain curve A descending branch exists after is reached

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Class #27.2

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  1. Class #27.2 Civil Engineering Materials – CIVE 2110 Concrete Material Stress vs. Strain Curves Steel Reinforcement Fall 2010 Dr. Gupta Dr. Pickett 1

  2. Stress-Strain Curve for Compression Slightly ductile shape of Stress-Strain curve A descending branch exists after is reached Due to redistribution of load to un-cracked regions with less stress, (MacGregor, 5th ed., Fig. 3-26) 2

  3. Stress-Strain Curve for Compression Strength of Reinforced Concrete structures controlled by, Size of members, Shape of members, Stress-Strain curves of; - concrete, - reinforcement. Five properties of Stress-Strain curves; (1) - Initial slope, Ec (2) - Ascending parabola (3) - Strain at max stress, (4) - Descending parabola (5) - Strain at failure (Fig. 3-18, MacGregor, 5th ed.) 3

  4. Stress-Strain Curve for Compression (1) - Initial Slope, Ec ; ACI 318, Sect. 8.5, 8.6 sensitive to Eaggregate , Ecement . For normal weight concrete; For other weight concrete; Defined as the slope of a line drawn from As water increases, Ec decreases, because cement paste becomes more porous, there is less aggregate. (MacGregor, 5th ed., Fig. 3.17) 4

  5. Stress-Strain Curve for Compression Lightweight Concrete ; ACI 318, Sect. 8.5, 8.6 sensitive to Eaggregate . For all parameters involving Each parameter shall be multiplied by a modification factor for sand-lightweight conc. for all-lightweight concrete If splitting tensile strength, fct , is specified, then This accounts for the reduced capacity of lightweight concrete due to aggregate failure; Such as: Shear strength Splitting resistance Concrete-rebar bond For normal weight concrete the average splitting tensile strength is; (MacGregor, 5th ed., Fig. 3.26) 5

  6. Stress-Strain Curve for Compression (2) – Ascending Parabola; Curve becomes steeper as increases. • (3) – Strain ( ) at ; • Strain at max stress increases as increases. • (4) – Slope of descending branch; • Less steep than ascending branch, • Slope increases as increases. • (5) – Strain ( ) at failure; • Decreases with increases in • (4 and 5) – depend on; • Specimen size; Load, type, rate 6 (Fig. 3.18, MacGregor, 5th ed.,)

  7. Stress-Strain Curve for Tension Tensile strength of concrete: Determined by one of 2 tests: (1) Flexure (Modulus of Rupture) test, (2) Split Cylinder test, fct P H P B 8” 8” 8” • (1) Flexure (Modulus of Rupture) test; • Load until failure due to cracking on tension side, • ASTM C78 or ASTM C293, • H = 6”, B = 6” L = 30” 3” 3” P V 0 -P M 0 7

  8. Stress-Strain Curve for Tension • (2) Split Cylinder test, fct ; • Load in compression along long side, • ASTM C496, • a standard 6”x12” cylinder is placed on side, • Outside surface area, • Load is resisted by only half of surface area, 8 (MacGregor, 5th ed., Fig. 3.9)

  9. Stress-Strain Curve for Tension Concrete always cracks on plane of Split Cylinder Test Bi-Axial Stress 2x90˚ Tension Compression 9

  10. Stress-Strain Curve for Tension Tensile strength of concrete: Determined by one of 2 tests: (1) Flexure (Modulus of Rupture) test, (2) Split Cylinder test, H P P B • Tensile strength from Split Cylinder test is less than that from Flexure (modulus of Rupture) test because; • In Flexure test, only bottom of beam reaches • In Split Cylinder test, majority of cylinder reaches 10

  11. Stress-Strain Curve for Tension Results from various Split Cylinder tests vs. are plotted in Fig. 3.10 The mean Split Cylinder strength is: ACI 318, Sect. R8.6.1 states; The mean Modulus of Rupture strength is: ACI 318, Sects. 8.6.1 & 9.5.2.3 state, for deflection calculations: (MacGregor, 5th ed., Fig. 3.10) 11

  12. Stress-Strain Curve for Tension Tensile strength of concrete: From: • Concrete tensile failure is BRITTLE. • Same factors affect as ; • Water/Cement ratio, • Type of Cement, • Type of Aggregate, • Curing Moisture conditions, • Curing Temperature, • Age, • Maturity, • Loading rate. Etinitial = linear (MacGregor, 5th ed., Fig. 3-21) From: 0  12

  13. Steel Reinforcement in Concrete In any beam (concrete, steel, masonry, wood): Applied loads produce Internal resisting Couple, Tension and Compression forces form couple. In a concrete beam: - Cracks occur in areas of Tension, - Beam will have sudden Brittle failureunlessSteel reinforcement is present to take Tension. MacGregor, 5th ed. Fig. 1-4 13

  14. Brittle concrete fails on plane of max normal (tension) Stress. Failure stress located at: 2x90˚=180˚on Mohr Circle Concrete Brittle Mohr’s Circle Method – Failure Modes 90˚ Neutral Axis 2x90˚ Plane of max Tension 2x45˚ Shear Stress Normal Stress Principal Stress 14

  15. Steel Reinforcement in Concrete Steel Reinforcement: Hot-Rolled deformed bars (rebars) Welded wire fabric ASTM A 615: - made from steel billets - most commonly used ASTM A 706: - made from steel billets - for seismic applications - better - ductility - bendability - weldability Reinforcement Bars (Rebars): ASTM specs specify; - diameter, cross-sectional area - sizes in terms of 1/8 inch - #4 rebar, diameter = 4/8 in. - metallurgical properties - mechanical properties - Grade  min. Tensile Yield Strength - Grade 60, Yield Strength = fy = 60 ksi 15

  16. Steel Reinforcement in Concrete Reinforcement Bars (Rebars): (MacGregor, 5th ed., Table 3-4) Upper Limit on 16

  17. Steel Reinforcement in Concrete (MacGregor, 5th ed., Fig. 3-30) Rebars in metric units: - just numerical conversions of US customary sizes. - #36  - Grade 420,  Rebars in US customary units: - Grade 60,  - # 11  17

  18. Steel Reinforcement in Concrete Reinforcement Bars (Rebars): (MacGregor, 5th ed., Table A-1) 18

  19. Steel Reinforcement in Concrete Reinforcement Bars (Rebars): (MacGregor, 5th ed., Table A-1M) 19

  20. Steel Reinforcement in Concrete Reinforcement Bars (Rebars): - modulus of Elasticity, ES = 29,000,000 psi ACI 318, Sect. 8.5.2 - for rebars with fy > 60,000 psi must use fy = ES x ( ) ACI 318, Sect. 3.5.3.2 (MacGregor, 5th ed., Fig. 3-31) 20

  21. Steel Reinforcement in Concrete Reinforcement Bars (Rebars): - at temperatures > 850˚F fy and fultimate drop significantly - concrete cover over the rebars helps to delay loss loss during fires (MacGregor, 5th ed., Fig. 3-34) 21

  22. Steel Reinforcement in Concrete Fatigue Strength of rebars: - Bridge decks subjected to large number of load cycles - Stress Range, Sr = - Fatigue failure may occur if at least one stress is tensile and Sr > 20 ksi - Fatigue failure will not occur if; (MacGregor, 5th ed., Fig. 3-33) - Fatigue strength reduced at: 22 Bends, Welds

  23. Fatigue Strength of rebars: - Stress Range, Sr = Steel Reinforcement in Concrete Example: Fatigue Failure possible; Example: Fatigue Failure not possible; 23

  24. Welded-Wire Reinforcement: - used in: Walls, Slabs, Pavements. - due to cold-working process used in drawing the wire strain-hardening occurs, so wire is BRITTLE. - Plain wire; ASTM A82; A185; ACI 318, Sect. R3.5.3.6  fy = 60,000 psi - mechanical anchorage in concrete provided by - cross-wires - Deformed wire; ASTM A496; A497; ACI 318, Sect. R3.5.3.7  fy = 60,000 psi - mechanical anchorage in concrete provided by - cross-wires - deformations Steel Reinforcement in Concrete 24

  25. Welded-Wire Reinforcement: - Wire diameter = 0.125”  0.625” - Wire area  increments of 0.01 in2 . - Plain wire; W - Deformed wire: D - ACI 318, Sect. 3.5.3.5 D-4  wire size  D-31 area = 0.04 in2 area = 0.031 in2 . - Steel Reinforcement in Concrete (MacGregor, 5th ed., Table A-2a) 25

  26. Welded-Wire Reinforcement: - Wire area  increments of 0.01 in2 . - Wire center-center spacing  a x b , inches - Plain wire; W - Steel Reinforcement in Concrete (MacGregor, 5th ed., Table A-2b) 26

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