# Analisis Momen by kukuhkurniawands

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RESPONSE OF MEMBER
SUBJECTED TO FLEXURE
Iswandi Imran

Section Subjected to

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Moment Curvature Response

Compability Conditions

Concrete Strain at any level y :
ε c = ε cen − φy
Steel Strain at any level y = the strain at
surrounding concrete:
ε s = ε cen − φy
ε p = ε cen − φy + Δε p

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Equibrium Conditions

∫
Ac
f c dA c + ∫
As
f s dA s + ∫
Ap
f p dA p = N

∫
Ac
f c ydA c + ∫
As
f s ydA s + ∫
Ap
f p ydA p = − M
Note :
• Tensile stresses are taken as positive
• Tensile force (N) is taken as positive
• Moment M is positive if it causes tensile stresses on bottom face

Determining Sectional Forces
Using layer-by-layer Evaluation

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Stress Block Factors
Stress-block factors α1 and β1 are determined so that the magnitude and
location of the resultant force are the same in the equivalent uniform
stress distribution as in the actual distribution :
c

∫ f bdy = α           f β1cb
'
c              1 c
o
c

∫ f bydy
c

y=        o
c
= c − 0.5β1c
∫ f bdy
0
c

For a parabolic stress-strain curve and a constant width b:
2
ε 1⎛ε                       ⎞
α 1 β1 = t' − ⎜ t'                  ⎟
εc 3⎜εc
⎝
⎟
⎠
4 − ε t / ε c'
β1 =
6 − 2ε t / ε c'

Rectangular Stress – Block
Factors

Effective embedment
zone = 2*7.5 db

∈t / ∈’c       0.25           0.50      0.75           1.00    1.25    1.50    1.75    2.00

α1             0.336          0.595     0.779          0.888   0.928   0.900   0.810   0.667

β1             0.682          0.700     0.722          0.750   0.786   0.833   0.900   1.000

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Comparison of Calculated and Observed
Moment-Curvature Response

Comparison of Short-Term and Long-
Term Moment-Curvature Response

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Elastic Uncracked Response
Compability                                               Stress – Strain Rel
ε c = ε cen − φy                                          f c = E c ε cf
ε s = ε cen − φy                                          f s = E c ε sf
ε p = ε cen − φy + Δε p                                   f p = E p ε pf

Where :
ε cf = ε c − ε co
ε sf = ε s − ε so
ε pf = ε p − ε po

Equilibrium
N = ∫ f c dAc + ∫ f s dAs + ∫ f p dAp
Ac                As                   Ap

N − N0                                          Es      Ep
ε cen =              ;                Atrans = Ac +           As +    Ap
Ec Atrans                                       Ec      Ec
N 0 = ∫ E p Δε p dAp − ∫ Ecε co dAc − ∫ Esε so dAs − ∫ E pε po dAp
Ap                          Ac                   As                   Ap

−M =
Ac
∫f   c   ydAc +   ∫f
As
s   ydAs +     ∫f
Ap
p   ydAp

M − M0
φ=
Ec I trans
M 0 = − ∫ E p Δε p ydAp + ∫ Ecε co ydAc + ∫ Esε so ydAs + ∫ E pε po ydAp
Ap                           Ac                     As                Ap

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Thermal Stress

Suggested Temperature Distribution for
Bridge Sections (from Priestley)

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Fatigue Resistance

Suggested S-N Curve

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Compatibility Conditions for
Bonded and Unbonded Beam

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Moment-Curvature Response

Comparison of Long-Term and
Short-term M-N Interaction Diagrams

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at Midheight of Column

Moments, Curvatures and
Deformations of Slender Wall Panel

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