f72125a9-0abc-4843-bd91-7e3741ff4ed0 13 4 5 decimal

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

Set of two equations with two unknowns to be solved:

Data:

Dane geometryczne:

Dane odkszłceniowe:

Dane materiałowe:

h 500 mm * :

ε.s 2 :

f.ck 35 MPa * :

α.cc 1 :

E.s 200 GPa * :

b 200 mm * :

ε.c 1 :

f.yk 500 MPa * :

γ.c 1.5 :

A.s1 3.41 2 * cm 2^* :

a.1 30 mm * :

γ.s 1.15 :

Rozciąganie z minusem

Dane siłowe:

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M 100 kN * m * :

b

ε.c

h 2 / -

N 0 :

N.c

M

d h a.1 - :

N

z.0

z σ

y

x

ε

f.cd f.ck α.cc * γ.c / :

f.yd f.yk γ.s / :

z

h 2 /

ε.s

N.s

Equillibrium

a.1

A.s1

ε.s ε.c ΣF.x N ε.s N.s + ε.s ε.c N.c - :

ε.s ε.c ΣM.y M ε.s N.s h 2 / a.1 - (* + ε.s ε.c N.c ε.s ε.c z.Nc * - :

Curvature and position of neutral fiber

ε.s ε.c κ ε.s ε.c + h a.1 - / :

ε.s ε.c z.0 h 2 / a.1 - ε.s ε.s ε.c κ / - (:

11 z.0 0.015 m * -

Stress-strain (steel)

x shape x abs x 1 - abs - 1 + 2 / :

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

ε σ.s 1 - 0 ε.sa ε.sa 1 + 41 mat 001141 mat f.yd MPa / * ε linterp MPa * :

ε.sa f.yd E.s / : ‰ 2.17

ε σ.s f.yd ε ε.sa / shape * :

x ‰ * σ.s MPa /

Stress-strain (steel) - simplified ε σ.s 0 ε 0 ≤ E.s ε * ε 0 ε.sa ltlt f.yd cases :

ε.s N.s ε.s σ.s A.s1 * :

1 ‰ * N.s kN 136.4

Stress-strain (concrete)

N.cmax f.ck b * h * : kN 3500

N.smax f.yd A.s1 * : kN 297

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

ε σ.c 1 - 0 ε.c3 ε.c3 1 + 41 mat 001141 mat f.cd MPa / * ε linterp MPa * :

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

ε σ.c f.cd ε ε.c3 / shape * :

x ‰ * σ.c MPa /

1 ‰ * σ.c 1.3333 107^* Pa *

Moment of order 0 ε.c M.c.0 ε σ.c ε 0 ε.c int :

x ‰ * M.c.0 MPa ‰ * /

Resultant force ε.s ε.c N.c b ε.c / h 2 / ε.s ε.c z.0 + (* ε.c M.c.0 * :

1 ‰ * x ( ‰ * N.c kN /

1 (‰ * 1 ‰ * N.c kN 313.3333

1 (‰ * 1 ‰ * z.0 mm 15 -

Moment of order 1 ε.c M.c.1 ε σ.c ε * ε 0 ε.c int :

x ‰ * M.c.1 MPa ‰ 2 ^ * /

Position of resultant force

ε.c ζ ε.c M.c.1 ε.c M.c.0 / 1 ε.c / * :

1 ‰ * ζ 0.6667

2/3 for triangular region

3 ‰ * ζ 0.6258

10 ‰ * ζ 0.5423

1/2 for rectangular region (ε>>ε.c3)

ε.s ε.c z.Nc ε.s ε.c z.0 h 2 / ε.s ε.c z.0 - (ε.c ζ * - :

z

1 ‰ * 1 ‰ * z.Nc mm 191.6667 -

1 ‰ * 1 ‰ * z.0 mm 15 -

v 0.2 2 0.4 range (‰ * : 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 101 mat

i 1 v length range j 1 v length range vE1 i j el v i el v j el ΣF.x : vE2 i j el v i el v j el ΣM.y : 21 line for for

vE1 kN 35 - 140 - 255 - 374 - 495 - 617 - 740 - 864 - 987 - 1094 - 1371 - 171 - 280 - 393 - 509 - 628 - 748 - 868 - 974 - 5118 - 106 - 205 - 310 - 419 - 532 - 647 - 764 - 867 - 842652 - 142 - 239 - 342 - 449 - 559 - 671 - 772 - 116655 - 86 - 177 - 274 - 375 - 481 - 588 - 686 - 1461013837 - 121 - 212 - 309 - 409 - 513 - 607 - 17513578970 - 156 - 248 - 344 - 443 - 535 - 2041681165123 - 104 - 191 - 283 - 378 - 467 - 233200152912255 - 138 - 226 - 318 - 404 - 261231186130649 - 88 - 173 - 261 - 344 - 1010 mat

vE2 kN m * 11811610589704928517 - 39 - 12513613813212311094775940130145154157155149139128114991351511641721761751711651561441391561711821901941951931881801441601761902012082122142132081501651811962092192262312322301551691862022162282372442492491601741902072222352462552622641661791952122272422542652732771010 mat