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The stress distribution of a temperature gradient is calculated as E α T. Users may analytically solve for axial force (P) by integrating this expression over the section, accounting for the web and flange areas. To solve for M3, integrate the moment of stresses about the neutral axis. CSI Software derives temperature-gradient response by following these formulations. First, the software assumes a linear gradient with two unknowns, including neutral-axis value and gradient slope. Integration procedures yield a set of polynomial expression for P and M3. Simultaneous solution then yields exact expressions for axial force and moment.
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