<p>Some definitions</p>

23228790-1d1e-4460-b376-673a137e24cc 466 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Combinet biaxial bending and tension/compression of rectangular concrete section

4 - appVersion 0.99.7030.1435

ε σ.c 0 ε 0 ≤ 1000 ε * 250 ε * - 1 + (* f.cd * ε 0.2 % * < f.cd cases :

Concrete constitutive equation

Concrete design strenght

f.cd 35 MPa * :

Steel constitutive

ε σ.s E.s ε * :

Steel Young's modulus

E.s 210 GPa * :

Secion width

B 14 cm * :

Section height

H 14 cm * :

barre x y # ϕ 25 mm * 25 mm * 112 mm * 115 mm * 115 mm * 112 mm * 115 mm * 25 mm * 112 mm * 25 mm * 115 mm * 112 mm * 54 mat :

Rebar matrix

<p>Some definitions</p>

x.s barre 2 barre rows 11 submatrix :

y.s barre 2 barre rows 22 submatrix :

r.b x.s y.s augment :

num barre 2 barre rows 33 submatrix :

dia barre 2 barre rows 44 submatrix :

i 1 num length range num i el ≠ A.s i el num i el π 4 / * dia i el (2^* : A.s i el if for

x.s mm 251151152541 mat

y.s mm 251152511541 mat

A.s mm 2^113.1 113.1 113.1 113.1 41 mat

Rebar #

n.b barre rows 1 - : 4

arm 1 :

External actions

Axial force

N.Ed 0 kN * :

Bending mom X

M.x.Ed 20 - (kN * m * :

Bending mom Y

M.y.Ed 20 - (kN * m * :

Solution by discretization

There are 3 variables:

Axial deformation (trial)

eG 1.9465 - (103 -^* :

Curvature X (trial)

Xx 0.0698195 - m / :

Curvature X (trial)

Xy 0.0698195 - m / :

nx 14 :

ny 14 :

Element #

dx B nx / : mm 10

dy H ny / : mm 10

Element dimension

i j Clear j 1 nx range i 1 ny range yg i j el dy 2 / dy i 1 - (* + : xg i j el dx 2 / dx j 1 - (* + : a i j el dx dy * : 31 line for for A a sum : Sx yg i j el a i j el * i 1 yg rows sum j 1 yg cols sum : Sy xg i j el a i j el * i 1 xg rows sum j 1 xg cols sum : yG Sy A / : xG Sx A / : 12 mat j 1 nx range i 1 ny range y i j el yg i j el yG - : x i j el xg i j el xG - : 12 mat ε i j el eG Xx y i j el * + Xy x i j el * + : σ i j el ε i j el σ.c : N i j el a i j el σ i j el * : Mx i j el y i j el a i j el * σ i j el * : My i j el x i j el a i j el * σ i j el * : 61 line for for 71 line

yg mm 55555555555551515151515151515151515151525252525252525252525252525353535353535353535353535354545454545454545454545454555555555555555555555555555656565656565656565656565657575757575757575757575757585858585858585858585858585959595959595959595959595951051051051051051051051051051051051051051151151151151151151151151151151151151151251251251251251251251251251251251251251351351351351351351351351351351351351351413 mat

xg mm 515253545556575859510511512513551525354555657585951051151251355152535455565758595105115125135515253545556575859510511512513551525354555657585951051151251355152535455565758595105115125135515253545556575859510511512513551525354555657585951051151251355152535455565758595105115125135515253545556575859510511512513551525354555657585951051151251355152535455565758595105115125135515253545556575859510511512513551525354555657585951051151251351414 mat

a mm 2^1001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001413 mat

A cm 2^196

Area

Coords baricentro

xG mm 70

yG mm 70

y mm 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 65 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 55 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 45 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 35 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 25 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 15 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 55555555555551515151515151515151515151525252525252525252525252525353535353535353535353535354545454545454545454545454555555555555555555555555555656565656565656565656565651413 mat

x mm 65 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 515253545556565 - 55 - 45 - 35 - 25 - 15 - 5 - 51525354555651414 mat

ε 0.01 0.01 0.01 0.01 000000 0.01 0.01 0.01 0000000 0.01 0.01 00000000 0.01 00000000000000000000000000000000000000000000000000000000000000000000 0.01 - 00000000 0.01 - 0.01 - 0000000 0.01 - 0.01 - 0.01 - 000000 0.01 - 0.01 - 0.01 - 0.01 - 00000 0.01 - 0.01 - 0.01 - 0.01 - 0.01 - 1410 mat

σ MPa 3535353535353535 33.18 35353535353535 33.18 23.35 353535353535 33.18 23.35 4.99 3535353535 33.18 23.35 4.99 035353535 33.18 23.35 4.99 00353535 33.18 23.35 4.99 0003535 33.18 23.35 4.99 000035 33.18 23.35 4.99 00000 33.18 23.35 4.99 000000 23.35 4.99 0000000 4.99 00000000000000000000000000000000000149 mat

N kN 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.32 2.34 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.32 2.34 0.5 3.5 3.5 3.5 3.5 3.5 3.5 3.32 2.34 0.5 0 3.5 3.5 3.5 3.5 3.5 3.32 2.34 0.5 00 3.5 3.5 3.5 3.5 3.32 2.34 0.5 000 3.5 3.5 3.5 3.32 2.34 0.5 0000 3.5 3.5 3.32 2.34 0.5 00000 3.5 3.32 2.34 0.5 000000 3.32 2.34 0.5 0000000 2.34 0.5 00000000 0.5 0000000000000000000000000000000000000001410 mat

Mx kN m * 0.23 - 0.23 - 0.23 - 0.23 - 0.23 - 0.23 - 0.23 - 0.19 - 0.19 - 0.19 - 0.19 - 0.19 - 0.19 - 0.19 - 0.16 - 0.16 - 0.16 - 0.16 - 0.16 - 0.16 - 0.15 - 0.12 - 0.12 - 0.12 - 0.12 - 0.12 - 0.12 - 0.08 - 0.09 - 0.09 - 0.09 - 0.09 - 0.08 - 0.06 - 0.01 - 0.05 - 0.05 - 0.05 - 0.05 - 0.04 - 0.01 - 0 0.02 - 0.02 - 0.02 - 0.01 - 000 0.02 0.02 0.01 0000 0.05 0.04 0.01 0000 0.06 0.01 00000 0.02 000000000000000000000000000147 mat

My kN m * 0.23 - 0.19 - 0.16 - 0.12 - 0.09 - 0.05 - 0.02 - 0.02 0.05 0.23 - 0.19 - 0.16 - 0.12 - 0.09 - 0.05 - 0.02 - 0.02 0.04 0.23 - 0.19 - 0.16 - 0.12 - 0.09 - 0.05 - 0.02 - 0.01 0.01 0.23 - 0.19 - 0.16 - 0.12 - 0.09 - 0.05 - 0.01 - 00 0.23 - 0.19 - 0.16 - 0.12 - 0.08 - 0.04 - 000 0.23 - 0.19 - 0.16 - 0.12 - 0.06 - 0.01 - 000 0.23 - 0.19 - 0.15 - 0.08 - 0.01 - 0000 0.23 - 0.18 - 0.11 - 0.02 - 00000 0.22 - 0.13 - 0.02 - 000000 0.15 - 0.03 - 0000000 0.03 - 00000000000000000000000000000000000149 mat

N.int.CLS N sum : N 184709.26

M.x.int.CLS Mx sum : N mm * 6546063.68 -

M.y.int.CLS My sum : N mm * 6546063.6841 -

ε.G χ.x χ.y x y ε ε.G y yG - (χ.x * + x xG - (χ.y * + :

N.int.As i Clear arm A.s i el eG Xx Xy x.s i el y.s i el ε σ.s * i 1 n.b sum * 21 line :

N.int.As N 184920.93 -

M.x.int.As i Clear arm A.s i el y.s i el yG - (* eG Xx Xy x.s i el y.s i el ε σ.s * i 1 n.b sum * 21 line :

M.x.int.As N mm * 13431775.41 -

M.y.int.As i Clear arm A.s i el x.s i el xG - (* eG Xx Xy x.s i el y.s i el ε σ.s * i 1 n.b sum * 21 line :

M.y.int.As N mm * 13431775.41 -

Equazioni di equilibrio

Ed, CLS, As are all idependent. You can solve either of the triplet from setting/solving an otherwise equality system [U, V, W]

U 1.23456789 :

eq N.Ed N.int.CLS - N.int.As - kN / M.x.Ed M.x.int.CLS - M.x.int.As - kN m * / M.y.Ed M.y.int.CLS - M.y.int.As - kN m * / 31 mat : 0.212 0.022 - 0.022 - 31 mat

V 2 sqrt :

W π :

New N.Ed N.int.CLS - N.int.As - U - 0 ≡ kN / M.x.Ed M.x.int.CLS - M.x.int.As - V - 0 ≡ kN m * / M.y.Ed M.y.int.CLS - M.y.int.As - W - 0 ≡ kN m * / 31 mat :

init N.Ed ? ≡ M.x.Ed ?? ≡ M.y.Ed ??? ≡ 31 mat :

eq norme 0.214