Thermal Stress Temperature change Coefficient of thermal expansion Concrete stiffness Cracking stress
Concrete Thermal Contraction = = Coefficient of thermal expansion ~ 5*10-6 / o F = Difference in concrete temperature (T) and the concrete setting temperature (T set ) = T set - T T= Variation of the average concrete temperature after placement. Assume this variation tracks closely to the 24-hour ambient air temperature cycle (after a 72 hour period). T set = 0.95(T conc + T H )
Concrete Thermal Contraction (con’t) T conc = Concrete placement temperature at construction ( o F). Assume this value (approx. 80 o F) = Change in concrete temperature due to heat of hydration = H u = Total heat of hydration per gram (kJ/g) = 0.007 (T conc ) – 3x10 -5 (T conc ) 2 –0.0787 C= amount of cement (grams) per m 3 = Degree of hydration (estimate to be approximately 0.15-0.2) c p = Specific heat of cement = 1.044 kJ/g = Density of concrete ~ 2400 kg/m 3
Typical creep curve for cement paste. a Microstrain Time after loading Creep strain Elastic recovery Creep recovery Irreversible creep Concrete unloaded Elastic strain
Burger Model Constant Stress (Creep) time Strain
Creep of cement under simultaneous loading & drying. 62 sh =free shrinkage; bc =basic creep (specimen loaded but not drying); dc =drying creep; cr =total creep strain; tot =total strain (simultaneous loading & drying) b Free shrinkage (no load) Basic creep (no drying) Loading and drying Microstrain Time sh bc dc cr tot
Spring-Loaded Creep Frame CCCCCCCCCC 6 X 3 IN. PLUG (CONCRETE) C = 6 X 12 IN. TEST CYLINDERS 6 X 3 IN. PLUG (CONCRETE) UPPER JACK PLATE LOAD BARS LOWER JACK PLATE UPPER LOAD PLATE LOWER LOAD PLATE UPPER BASE PLATE SPRINGS LOWER BASE PLATE
Determination of Creep where crp = Creep strain v = Shrinkage strain (ASTM C 157) e = Frame strain F s = Force in concrete (F) E c = Modulus of elasticity of concrete (F/L -2 ) A c = Specimen cross sectional area (L 2 )
Effects of Paste Properties Effect of age of loading on the creep strain. Effect of w/c ratio on the shrinkage strain.
Mechanisms of Creep and Shrinkage Creep It is a complex process involving slipping of surfaces past one another within the structure of C-S-H. It is a function of pore structure and ease of slippage of C-S-H particles. As the space between particles becomes less and less the degree of creep becomes less and less. Drying Shrinkage Moisture loss is driven by the ambient relative humidity. As moisture escapes from the capillaries, menisci are created and capillary stresses are developed. As more moisture is evaporated, smaller and smaller menisci are created. This action creates stress and causes slippage between C-S-H particles.
This method is based upon a method proposed by Branson and Christiason (2.3) and was developed by ACI Committee 209 (2.4) In 1982, ACI Special Publication 76 (2.5) gives an updated but not significantly changed version of this method. This method uses the as the creep coefficient. ACI Committee 209 Method
Shrinkage – ACI The shrinkage strain at t days after the end of initial curing is where = ultimate shrinkage strain = 415 to 1070 micro-strain = 0.9 to 1.10 and f = 20 to 130 days In the absence of specific data for local aggregate and conditions Committee 209 suggests that With = product of applicable correction factors The equations for the correction factors are given in Table A
The creep coefficient at t days after loading is given by where = ultimate creep coefficient = 1.30 to 4.15 = 0.40 to 0.80 d = 6 to 30 days In the absence of specific data for local aggregates and conditions Committee 209 suggests that where = product of applicable correction factors The equations for the correction factors are given in Table A Creep – ACI 209
The concrete strength at t days is given by with suggested values of a = 4.0 days = 0.85 for most cured ordinary Portland cement concrete. The modulus of elasticity E c at t days is given by which is often taken as when E and f’ c are in MPa Strength and Modulus of Elasticity
NotesCorrection Factors CreepShrinkage Loading Age Relative Humidity Average h=average 1.14 - 0.00092 h 1.23 - 0.0015 h during 1st year Thicknessthickness in mm for 1st yr. of 150 < h < 300 loading 1.10 - 0.00067 h 1.17 - 0.0014 h ultimate value ultimate value Concrete s= slump in mm 0.82 + 0.00264s 0.89 +.00161s Composition c= cement content - kg/m 3 0.75 +.00061c Table A ACI Creep and Shrinkage Correction Factors