a28c1ff5-e7b3-4941-938a-acac115e571a 37 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 :

4.22 μ θ 39.19 1 0.9674 μ 3.833^* / 1 - ln * 482 + (:

4.22 x q 39.19 1 0.9674 x n^* / 1 - ln * 482 + (:

y x q ≡ x solve maple 500048371100482 - y + (* 3919 / exp + (* / ln n / exp