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

4.2.5 Steel temperature development according to Eurocode 1993-1-2:2005

according to EN 1993-1-2 c.a varies with θ.a. It is shown described in the graph below, and the if statement to the left. For the DE to be correct, it needs to consider c.a(θ.a) at any given time.

ρ.a 7850 :

α.c 25 :

c.a θ.a 600 < 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + θ.a 735 < 66613002738 θ.a - / + θ.a 900 < 54517820 θ.a 731 - / + 650 if if if :

Φ 1.0 :

ε.m 0.7 :

ε.f 1.0 :

σ 5.67 108^/ :

t θ.g 203458 t * 1 + log10 * + :

ratio.Am.b_V 70102^* : 7000

ratio.Am_V 107102^* : 10700

k.sh 0.9 ratio.Am.b_V ratio.Am_V / * : 0.589

when you open this workbook, the plot is still working because i have overridden the c.a(θ.a) function. once you delete the definition of c.a to the left, the plot will disappear.

c.a 650 :

c.a 650

t θ.a D k.sh c.a ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* :

θ.a.init 20 :

t0 0 :

tmax 60 :

steps tmax :

res θ.a.init t0 tmax steps t θ.a D rkm9mkn :

res x θ.g 2 1 sys

critical steel temperature, failure ensues if θ.a surpasses this value

θ.a.cr 639 :

To verify the ODE, use θ.cr from examples below, and compare t(θ.a.cr) to calculated time in the examples

t.req 60 :

required time for steel structure to withstand (fire)load. After t.req, θ.a can surpass θ.a.cr and it's OK

time res 1 col :

temp res 2 col :

t.req θ.a time temp t.req ainterp :

t.req θ.a 929.11

θ.a.cr t temp time θ.a.cr ainterp :

θ.a.cr t 27.31

Examples I am trying to replicate to verify the ODE