a28c1ff5-e7b3-4941-938a-acac115e571a 39 4 5 decimal

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

θ 500 °C * :

4.25 t Δθ.a k.sh c.a ρ.a * / A.m V / * t h.net * Δt * :

b 170 mm * :

h 360 mm * :

A.m 4 b * 2 h * + : 1.4 m *

Section is IPE360

A.m.b 2 b h + (* : 1.06 m *

4.26a k.sh 0.9 A.m.b V / A.m V / / * : 0.68

V 7270 mm 2^* :

3.2a/b/c/d c.a θ K / 873.15 < 425 7.73 101^/ θ K / * + 1.69 103^/ θ K / (2^* - 2.22 106^/ θ K / (3^* + θ K / 1008.15 < 66613002738 θ K / - / + θ K / 1173.15 < 54517820 θ K / 731 - / + 650 if if if J kg K * / * :

c.a J kg K * / 1038.42

ρ.a 7850 kg m 3^/ * :

3.1 t h.net t h.net.c t h.net.r + :

3.2 t h.net.c α.c t Θ.g K / Θ.m K / - (* :

α.c 25 W m 2^K * / * :

3.4 t Θ.g 203458 t min / * 1 + log10 * + (°C * :

Θ.m 20 °C * :

3.3 t h.net.r Φ ε.m * ε.f * σ * t Θ.r K / (4^Θ.m K / (4^- (* :

Φ 1.0 K 3^* :

ε.m 0.8 :

ε.f 1.0 :

σ 5.67 108^/ W m 2^K 4^* / * :

t Θ.r t Θ.g :

Problem 1: How can I solve the differential equation 4.25 with respect to θa(t)? I want to be able to calculate the development of temperature in a steel member as a function of time.

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Problem 2: How can I solve the following equation 4.22 with respect to μ0 using the built in solvers in Smath? Below I have solved the equation manually. Is there a way to do that with a solver in Smath?

4.22 θ.a.cr 39.19 1 0.9674 μ.0 3.833^* / 1 - ln * 482 + (°C * :

4.22 solved by μ0 manually μ.0 1 e θ.a.cr K / (482 - 273.15 - 39.19 /^1 + / 0.9674 / 3.833 nthroot :

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4.25 t Δθ.a k.sh c.a ρ.a * / A.m V / * t h.net * Δt * :

k.sh c.a ρ.a * / A.m V / * 9 min * h.net * UnitsOf min * 60

t θ.a t diff k.sh c.a ρ.a * / A.m V / * t h.net * ≡

Differential equation?

0 min * θ.a 500 ≡

θ 500 °C * :

Is this the initial value for Q.a?

θ Δ°C / 773.15

k.sh c.a ρ.a * / A.m V / * 1 min * h.net * UnitsOf Hz

What about units?

t θ.a D k.sh c.a ρ.a * / A.m V / * t min * h.net * min * :

00 D 6.0242 1016 -^*

from 0 to 10 min

t0 0 :

tmax 10 :

res θ °C / 01020 t θ.a D Rkadapt :

Solving ODE

res 0 773.15 0.5 775.7785 1 781.6638 1.5 789.7927 2 799.7463 2.5 811.2734 3 824.2007 3.5 838.3992 4 853.7679 4.5 870.2249 5 887.7023 5.5 906.1421 6 925.4947 6.5 945.7165 7 966.7691 7.5 988.6181 8 1011.2328 8.5 1034.5853 9 1058.6503 9.5 1083.4044 10 1108.8263 212 mat

First column time in 'minutes, second temperature in 'K

res