**Appendix F**

The bending moment *M*B,pp for RT and 300 ◦C is given by

$$\begin{array}{lcl} \mathcal{M}\_{\mathsf{B,pp}} = \int\_{-\left(\frac{\mathsf{b}}{2} - z\_{0} - t\right)}^{\frac{\mathsf{b}}{2} + z\_{0}} \int\_{\frac{\mathsf{b}}{2} - y\_{0} - t}^{\frac{\mathsf{b}}{2} - y\_{0}} \sigma\_{\mathsf{B,pl}}(T = RT) y dydz \\ & + \int\_{-\left(\frac{\mathsf{b}}{2} - z\_{0}\right)}^{\left(\frac{\mathsf{b}}{2} - z\_{0}\right)} \int\_{\frac{\mathsf{b}}{2} - y\_{0}}^{\frac{\mathsf{b}}{2} - y\_{0}} \sigma\_{\mathsf{B,pl}}(T = T\_{1}) y dydz \\ & + \int\_{-\left(\frac{\mathsf{b}}{2} - z\_{0}\right)}^{\left(\frac{\mathsf{b}}{2} - z\_{0}\right)} \int\_{\mathcal{Y}^{\mathsf{b},\mathsf{q}}}^{\mathsf{b}\_{\mathsf{P}} \mathsf{q}} \sigma\_{\mathsf{B,el}}(T = T\_{1}) y dydz \\ & - \int\_{-\left(\frac{\mathsf{b}}{2} - z\_{0}\right)}^{\left(\frac{\mathsf{b}}{2} - z\_{0}\right)} \int\_{\mathcal{Y}^{\mathsf{b},\mathsf{q}}}^{\mathsf{b}\_{\mathsf{P}}} \sigma\_{\mathsf{B,el}}(T = T\_{1}) y dydz \\ & - \int\_{-\left(\frac{\mathsf{b}}{2} - z\_{0}\right)}^{\left(\frac{\mathsf{b}}{2} - z\_{0}\right)} \int\_{-\left(\frac{\mathsf{b}}{2} + y\_{0}\right)}^{\mathsf{b}\_{\mathsf{P}}} \sigma\_{\mathsf{B},\mathsf{p}}(T = T\_{1}) y dydz, \end{array} \tag{A9}$$

with elastic bending stress *σ*B,el, plastic bending stress *σ*B,pl, the upper plasticization fiber position *y*pl,u, and the lower plastification fiber position *y*pl,l assuming partial cross-sectional plasticity. For the 600 ◦C case with full plastification, the integral is expressed as

$$\begin{array}{lcl} \mathcal{M}\_{\mathsf{B},\mathsf{fp}} = \int\_{-\left(\frac{b}{2} - z\_{0} - t\right)}^{\frac{b}{2} + z\_{0}} \int\_{\frac{b}{2} - y\_{0} - t}^{\frac{b}{2} - y\_{0}} \sigma\_{\mathsf{B},\mathsf{p}l}(T = \mathsf{RT}) y dydz \\ & + \int\_{-\left(\frac{b}{2} - z\_{0}\right)}^{\left(\frac{b}{2} - z\_{0} - t\right)} \int\_{\mathcal{Y}m}^{\frac{b}{2} - y\_{0}} \sigma\_{\mathsf{B},\mathsf{p}l}(T = T\_{1}) y dydz \\ & - \int\_{-\left(\frac{b}{2} - z\_{0}\right)}^{\left(\frac{b}{2} - z\_{0} - t\right)} \int\_{-\left(\frac{b}{2} + y\_{0}\right)}^{y\_{\mathsf{M}}} \sigma\_{\mathsf{B},\mathsf{p}l}(T = T\_{1}) y dydz. \end{array} \tag{A10}$$

Using the first degree Taylor approximation on the integrals, the bending moment can be solved.
