How is stress due to temperature gradient loads calculated for a box girder bridge?
To clearly understand the load application for temperature gradient, I am dividing the calculation process into 2 parts:
1. Load Calculations :
Based on the input by users like H1, T1, B, etc., the software calculates the resultant axial force and moment due to the temperature gradient. To calculate the axial force as well as the moment, the section properties are not used. So, for calculating the acting axial stress/force, the area used is derived from user input of B and the difference between H (Say H1 & H2) for each part with non-linear temperature. Similarly for calculating the moment as well, the user input is used.
Beam Section Temperatures Dialog Box
2. Sectional stress calculations :
Now, once this axial force and its eccentricity is obtained, this force is applied to the said structure and once this is done, the stress output is provided at points 1, 2, 3 and 4 of the cross-section. These points of the cross-section could be noted from the section property.
This stress calculation is nothing but P/A (+/-) M/Zi, where P is the axial force calculated before, A is C/s Area of the section, M is the moment as calculated before and Zi is the I/yt, where I is Iyy of section and yt is the distance of the fibre where stress is being measured from the centroid.
A sample calculation for temperature gradient at point 1 for one such section is attached for review. The method used is recommended in Bridge Deck Behavior by E.C. Hambly.