Prestressed Concrete Hashemite University The Hashem ite University Departm ent of Civil Engineering Lecture Lecture 4 4 – – Materials Materials Dr. Hazim Dwairi Dr Hazim Dwairi Dr Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Concrete Uniaxial Concrete Uniaxial com pression com pression Stress f’ c Stage IV 75% Stage III 50% Stage II 30% Stage I Strain 0.003 Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 1
Prestressed Concrete Hashemite University Concrete Concrete Uniaxial Uniaxial com pression com pression • Before application of any load, micro Before application of any load, micro- -crack crack exit in the zone between the mortar matrix exit in the zone between the mortar matrix it i it i th th b t b t th th t t t i t i & aggregate due to drying of cement paste & aggregate due to drying of cement paste • Stage I: Stage I: � From From 0 0% to % to 30 30% . % . � Linear stress Linear stress- -strain relationship. strain relationship. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Concrete Concrete Uniaxial Uniaxial com pression com pression • Stage II: Stage II: � From � F From 30 30 30% 30% to % to 50 50% . 0% % . � Micro Micro – –cracks increase in length, width, and number, cracks increase in length, width, and number, however, a stable system of micro- however, a stable system of micro -cracks exists. cracks exists. � Beginning of non Beginning of non- -linearity of stress linearity of stress- - strain relationship strain relationship • Stage III: Stage III: � From From 50 F 50%to 50 50%t %t 75 %to75 75% 75% . % . � Cracks in the matrix. Cracks in the matrix. � Unstable crack system in the matrix. Unstable crack system in the matrix. � Non Non- -linear stress linear stress- -strain relationship. strain relationship. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 2
Prestressed Concrete Hashemite University Concrete Concrete Uniaxial Uniaxial com pression com pression • Stage IV: Stage IV: � From � F From 75 75% to failure. % to failure. % % f il f il � Rapid propagation of the cracks in the matrix and Rapid propagation of the cracks in the matrix and transition zone. transition zone. � Rapid increase in the strain. Rapid increase in the strain. � Crack system is continuous Crack system is continuous • Critical stress • Critical stress Critical stress : if concrete is subjected to Critical stress : if concrete is subjected to : if concrete is subjected to : if concrete is subjected to a sustain load equivalent to 75 a sustain load equivalent to 75% of % of f’ f’ c , it , it will fail after a certain time. will fail after a certain time. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete • Cracks affect the lateral strains and as a Cracks affect the lateral strains and as a result volume of concrete increases result volume of concrete increases especially after especially after 75 75% of % of f’ f’ c . The increase of . The increase of the volume causes an outward pressure the volume causes an outward pressure on the ties. on the ties. ε 3 Stress Stress ε 1 ε v 75%f’ c 30%f’ c Proportional Limit Axial Strain Volumetric Strain Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 3
Prestressed Concrete Hashemite University Relationship between short Relationship between short- -and and long term loading long term loading Stress t=20min. 100% 100% t=100min. 80% t=7days t= ∞ Creep Strain 0.003 0.004 0.008 Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Relationship between short Relationship between short- -and and long term loading long term loading • Due to progressive micro Due to progressive micro- -cracking at cracking at sustained loads, a concrete will fail at sustained loads, a concrete will fail at t i t i d l d l d d t t ill f il ill f il t t lower stress than induced by short lower stress than induced by short – –time time loading. loading. – Normal rate of loading is Normal rate of loading is 35 35psi/sec ( psi/sec (0 0. .24 24MPa/sec) MPa/sec) – Time to reach max. load ≈ Time to reach max. load ≈ 1. .5 5 to to 2 2 minutes minutes Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Dr. Hazim Dwairi 4
Prestressed Concrete Hashemite University Modulus of Elasticity Modulus of Elasticity = initial modulus E i = E secant stiffness E i E c c • • ACI ACI : : = 1 . 5 ' E 0 . 043 w f ( MPa ) c c = ' 4700 f ( MPa ) c 0.4f’ c • EU code : = + ' 1 / 3 E 9 . 5 ( f 8 ) (GPa) c c w = + ' 1 / 3 9 . 5 ( )( f 8 ) (GPa) c 2400 • Canadian code = 1 . 5 ' 2 E 0 . 043 w f (kg/m ) c c Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Creep Creep Strain Unloading Elastic Recovery Creep Recovery Creep strain ε c loading Permanent Elastic strain Deformation ε t= ∞ Time t o t Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Dr. Hazim Dwairi 5
Prestressed Concrete Hashemite University Creep Creep t o Creep Coefficient for Normal Concrete h=150mm and RH = 80% 1 3.4 7 2.4 28 1.8 90 1.5 365 1.1 σ ( t ) [ [ ] ] [ [ ] ] ε = + = ε + c o ( ( t ) ) 1 C ( ( t t ) ) 1 C ( ( t t ) ) c c t t 1 1 o o t t 1 1 o o E E ( ( t ) ) c o For t o =1 For t 1 & t= ∞ , C & t= ∞ , C t =2 2 to to 4 4 ( (2 2. .35 35 recommended) recommended) depending on the quality of concrete, ambient depending on the quality of concrete, ambient temperature, and humidity, as well as the temperature, and humidity, as well as the dimensions of the element considered. dimensions of the element considered. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Creep Creep OR OR C = C K K K K K K K t U t a h th s f f e • C C t : the ratio of creep strain to initial elastic strain : the ratio of creep strain to initial elastic strain • C C u : ultimate creep coefficient ( : ultimate creep coefficient (1 1. .3 3 to to 4 4. .15 15) ) 0 . 6 t • K K t : time under load coefficient = ; t in days : time under load coefficient = ; t in days + 0 . 6 10 t − • K K a : the age when loaded coefficient = : the age when loaded coefficient = 01 . 18 1 . 25 t o − • K K h : the humidity coefficient = : the humidity coefficient = ff ff 1 1 . 27 27 0 0 . 0067 0067 H H (%) (%) • K K th th : the min. thickness of member coefficient : the min. thickness of member coefficient • K K s s : the slump coefficient : the slump coefficient • K K e : air content coefficient : air content coefficient Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 6
Prestressed Concrete Hashemite University Shrinkage Shrinkage • Drying of concrete in air results in Drying of concrete in air results in shrinkage, and if the change in volume is shrinkage, and if the change in volume is restrained, stresses develop. restrained, stresses develop. • The restraint may be caused by the The restraint may be caused by the reinforcing steel, supports, or by the reinforcing steel, supports, or by the difference in volume change. difference in volume change. • Branson, B Branson,1977 B 1977 1977 1977, recommend the following , recommend the following d th d th f ll f ll i i relationships for the shrinkage strain as a relationships for the shrinkage strain as a function of time for RH= function of time for RH=40 40% % Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Shrinkage Shrinkage a) Moist - cured concrete at any time (t) after 7 days: ( ( ) ) t ε = ε + SH , t SH , u 35 t − ε = × 6 800 10 mm/mm if no local data a vailable SH , u b) Steam-cured after age of 1 to 3 days: ( ( ) ) t ε ε = ε ε + SH SH , t SH SH , u 55 t RH correction : < ≤ = − 40% RH 80% k 1 . 4 0 . 01 RH SH < ≤ = − 80 % RH 100 % k 3 0 . 03 RH SH Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Dr. Hazim Dwairi 7
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