a28c1ff5-e7b3-4941-938a-acac115e571a 43 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

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

1012 -^3.833 θ 1 3.833 θ 21 mat 463434921 mat

y n sol 500048371100482 - y + (* 3919 / exp + (* / ln n / exp :

x 3.833 θ 1 5000 1 1000 - 2 2 mat 2 1 sys

x c 10 x ≤ (x 4634 ≤ (& cases :

x 3.8 sol x c * 350 2 350 1 - 2 2 mat 2000 0.25 2000 1 - 2 2 mat 3 1 sys

Check x 0.75 1.25 0.76 range : j 1 x rows range sol j el x j el 3.833 θ eval : for x sol augment 31 line :

Check 11 mat 0.75 511.3323 0.76 508.365 0.77 505.3601 0.78 502.3114 0.79 499.2122 0.8 496.0546 0.81 492.8301 0.82 489.5286 0.83 486.1388 0.84 482.6473 0.85 479.0386 0.86 475.2942 0.87 471.3918 0.88 467.3043 0.89 462.9981 0.9 458.4309 0.91 453.5483 0.92 448.2786 0.93 442.5244 0.94 436.1484 0.95 428.949 0.96 420.6104 0.97 410.5978 0.98 397.8898 0.99 380.1182 1 349.1342 1.01 274.2328 123.119 i * + 1.02 357.6325 123.119 i * + 1.03 381.5327 123.119 i * + 1.04 395.7043 123.119 i * + 1.05 405.6736 123.119 i * + 1.06 413.2895 123.119 i * + 1.07 419.4005 123.119 i * + 1.08 424.4668 123.119 i * + 1.09 428.7666 123.119 i * + 1.1 432.4806 123.119 i * + 1.11 435.7329 123.119 i * + 1.12 438.6126 123.119 i * + 1.13 441.1853 123.119 i * + 1.14 443.5014 123.119 i * + 1.15 445.5999 123.119 i * + 1.16 447.5116 123.119 i * + 1.17 449.2617 123.119 i * + 1.18 450.8705 123.119 i * + 1.19 452.355 123.119 i * + 1.2 453.7294 123.119 i * + 1.21 455.0056 123.119 i * + 1.22 456.1939 123.119 i * + 1.23 457.3031 123.119 i * + 1.24 458.3407 123.119 i * + 1.25 459.3134 123.119 i * + 512 mat 11 mat