RF-CONCRETE Surfaces

RF-CONCRETE Surfaces

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2.7.10.8 最终截面性质

The curvature for both crack states c (cracked/uncracked) is calculated as follows:

κc,ϕ1 = ksh,c,ϕ1 · mϕ1 - nϕ1 · ec,ϕ1E · Ic,ϕ1 

  • uncracked state:

κl,ϕ1 = 1.158 · 30 · 103 - -100 ·103 · 1.4 · 10-311 · 109 ·6.816 · 10-4 = 4.655 · 10-3 

  • cracked state:

κII,ϕ1 = 1.353 · 30 · 103 - -100 ·103 · -41.5 · 10-311 · 109 ·2.193-4 = 14.499 · 10-3 

The strain for both crack states is determined as follows:

εc,ϕ1 = nϕ1E · Ac,ϕ1 

  • uncracked state:

εl,ϕ1 = -100 · 10311 · 109 · 0.206 = - 4.413 · 10-5 

  • cracked state:

εIl,ϕ1 = -100 · 10311 · 109 · 0.087 = - 10.449 · 10-5 

Thus, it is possible to determine the mean strain.

εϕ1 = ζϕ1 · εII,ϕ1 + 1 - ζϕ1 · εI,ϕ1 =       = 0.835 · -10.449 · 10-5 + 1-0.835 · -4.413 · 10-5 = -9.459 · 10-5 

The mean curvature is determined as follows:

κϕ1 = ζϕ1 · κII,ϕ1 + 1 - ζϕ1 · κI,ϕ1 =       = 0.835 · 14.449 · 10-3 + 1-0.835 · 4.655 · 103 = 12.885 · 10-3 

With the mean curvature and the longitudinal strain, you can calculate the final cross-section properties while taking account of shrinkage, creep, and tension stiffening.

Ideal cross-section area

Aϕ1 = nϕ1E · εϕ1 = -100 · 10311 · 109 · -9.459 · 10-5 = 958.59 cm2 

Ideal moment of inertia to the ideal center of the cross-section

Iϕ1 = II,ϕ1 ·III,ϕ1ζϕ1 · II,ϕ1 · kdh,II,ϕ1 + 1 - ζϕ1 · III,ϕ1 · kdh,I,ϕ1=      = 6.816 · 10-4 · 2.193 · 10-40.836 · 6.816 · 10-4 · 1.353 + 1 - 0.836 · 2.193 · 10-4 · 1.158=18 391.50 cm4 

Eccentricity of centroid

eϕ1 = mϕ1 - κϕ1 · E · Iϕ1nϕ1 =30 · 103 - 12.855 · 10-3 · 11 ·109 · 1.839 ·10-4-100 ·103 = -39 mm 

Ideal moment of inertia to the geometric center of the cross-section

I0,ϕ1 = Iϕ1 + Aϕ1 · eϕ12 = 1.839 · 10-4 + 0.096 · -0.03932 = 33 207 cm4 

Poisson's ratio is determined as follows:

ν = 1 - maxd{1,2} ζd · νinit = (1 - max 0.0836) · 0.2 = 0.0328 

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