Behavior Under Axial by kukuhkurniawands

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Behavior under Axial Forces

Iswandi Imran, PhD

Observed Response of Bar
Encased in Concrete

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Concrete and Reinforcement

Member Subjected to Axial
Forces

Compatibility                      Equilibrium
Δ
ε        =
∫ fdA = N
c
L
ε   s    = ε   c
A

ε        = ε         + Δε        Ac f c + As f s + Ap f p = N
p            c          p

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Calculation of Strain
Difference

Time Dependent Effect

ε c = ε cf + ε sh + ε cth
ε s = ε sf + ε sth
ε p = ε pf + ε pth

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Creep and Relaxation

Eci
Ec ,eff =
1 + Φ (t , ti )
f ci
ε cf (t , ti ) =
Ec ,eff
fp
E p ,eff =                Ep
f pi

Stress-Strain Relationship
⎡ 2ε cf ⎛ ε cf ⎞ 2 ⎤
f c = f c' ⎢      −⎜
⎜      ⎟ ⎥ if ε cf < ε cr
⎟
⎢ ε co ⎝ ε co ⎠ ⎥
⎣                  ⎦
⎡    f cr         ⎤
f c = α1'α 2 ⎢                 ⎥ if ε cf > ε cr
⎢1 + 500ε cf
⎣                 ⎥
⎦

f s = Esε sf if ε sf < ε sy
f s = f sy
y   if ε sff > ε sy
y

⎡              0.975            ⎤
f p = E pε pf ⎢0.025 +                        ⎥ ≤ 1860 MPa ⇒ Low − relaxation
⎢
⎣           (
1 + (118ε pf )10
0.10
⎥
⎦)
⎡              0.970            ⎤
f p = E pε pf ⎢0.030 +                        ⎥ ≤ 1860 MPa ⇒ Stress − Re lieved
⎢
⎣           (
1 + (121ε pf )       )
6 0.167
⎥
⎦

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Linear Elastic Response
Equilibrium                                Strain Relationship

N = Ac f c + As f s + A p f p               ε c = ε cf + ε sh + ε cth
Compatibility                               ε s = ε sf + ε sth
εs = εc
ε p = ε pf + ε pth
ε p = ε c + Δε p
N − ε c Relationship
Constitutive Relationship
f c = Ec ε cf
f s = E s ε sff                                           N − N0
εc =
f p = E p ε pf                                            Ec Atrans
Es     Ep
Atrans = Ac +      As + Ap
Ec     Ec
No = ApEpΔε p −(AcEcεsh + AcEcεcth + As Esεsth + ApEpε pth)

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