f72125a9-0abc-4843-bd91-7e3741ff4ed0 11 2 5 decimal

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Set of two equations with two unknowns to be solved:

Data:

h 500 :

ε.s 2 :

f.ck 35 :

α.cc 1 :

E.s 200 :

b 200 :

ε.c 1 :

f.yk 500 :

γ.c 1.5 :

A.s1 3.41 2 * :

a.1 30 :

γ.s 1.15 :

Rozciąganie z minusem

Odkształcenia maksymalne to 0.175% dw betonie oraz 0.212% dla stali. Zależności są liniowe.

Dane siłowe:

M 101.33 :

N 63.92 - :

General connections:

d h a.1 - :

f.cd f.ck α.cc * γ.c / :

f.yd f.yk γ.s / :

x y ξ x abs x abs y abs + / :

x y ξ

x y x.c x y ξ d * :

Stress-strain (steel)

ε.sa f.yd E.s / : 2.17

Stress-strain (steel) - simplified y σ.s f.yd ε.sa / y * y 0 ε.sa ltlt f.yd y 0 ≥ 0 cases :

x σ.s

Stress-strain (concrete)

ε.c3 f.ck 55 ≤ 1.75 zdefiniuj inaczej if : 1.75

ε.cu2 f.ck 55 ≤ 3.5 zdefiniuj inaczej if : 3.5

n f.ck 55 ≤ 2 zdefiniuj inaczej if : 2

Stress-strain (concrete) - simplified x σ.c f.cd ε.c3 / x * x 0 ε.c3 ltlt f.cd x 0 ≥ 0 cases :

x σ.c

Integral (concrete) ε.c σ.c.int ε σ.c ε 0 ε.c int :

x σ.c.int ε.c x * σ.c.int f.cd ε.c * /

Position of compression force (concrete) ε.c σ.c_x.int ε σ.c ε * ε 0 ε.c int :

x σ.c_x.int ε.c x * σ.c_x.int f.cd ε.c * / x σ.c.εc3 x σ.c.fcd 2 1 sys

Position of compression force (concrete) x x_b x σ.c_x.int x σ.c.int x * / :

x x_t 1 x x_b - :

Compression coefficients

Coefficient before force value (concrete/area) x ω x σ.c.int x σ.c x * / :

ε.c ω 0.5029

x y N.c x ω x σ.c * x y x.c * b 100 / * :

Force in concrete for given strains - example ε.c ε.s N.c 2101.0740740741

Force in steel for given strains - example y N.s y σ.s A.s1 * :

ε.s N.s 2728

Equations to be solved:

x y N.c y N.s - N - 0 ≡

M y N.s h 2 / a.1 - (* (- x y N.c x x_t * x y x.c * (- 0 ≡

Those equations I have to solve somehow to receive x (strain in concrete) and y (strain in steel). Can anyone help with that?

x y f x y N.c y N.s - N - 0 ≡ M y N.s h 2 / a.1 - (* (- x y N.c x x_t * x y x.c * (- 0 ≡ 21 mat :

x y 21 mat x y f x y 21 mat roots : #

N 1000 :

x y N.c y N.s - N - 1 ≡ M y N.s h 2 / a.1 - (* (- x y N.c x x_t * x y x.c * (- 0 ≡ 21 mat x 1 ≡ y 0 ≡ 21 mat FindRoot #

x 1000 :

y 1000 :

x y N.c y N.s - N - 7001.4493

M y N.s h 2 / a.1 - (* (- x y N.c x x_t * x y x.c * (- 1.9408 106^* -

Solving quaternion

α 0.5 :

β 1.5 :

........ constrains ....... seeds .. result p q + r - 0 ≡ p 2^q 2^+ r 2^+ 1 ≡ α p * β r * + 0 ≡ 31 mat p 1 ≡ q 1 ≡ r 1 ≡ 31 mat FindRoot 0.59 0.7887 - 0.1968 - 31 mat

0.1961 0.7845 - 0.5883 - 31 mat

j 1015 -^:

........ constrains ....... seeds .. result P Q + R - 0 ≡ P 2^Q 2^+ R 2^+ 1 ≡ α P * β R * + 0 ≡ 31 mat P j ≡ Q j ≡ R j ≡ 31 mat FindRoot 0.5871 - 0.7828 0.1957 31 mat

0.5884 - 0.7845 0.1961 31 mat