Article 7.4 Thermal Gradients
By Dean Van Landuyt
Changing atmospheric conditions create differential temperatures through the cross-section of bridge superstructures. Solar radiation causes the temperature of the deck to rise but since concrete is a poor heat conductor, lower portions of the cross-section experience less heat gain through the day. The most severe condition occurs when a sunny, windless day follows a few days of cold weather. This is known as a positive thermal gradient. A negative thermal gradient occurs when a rainy, cold front interrupts a few days of hot weather. The negative thermal gradient is usually smaller and has less effect on structural design than the positive gradient.
The non-linear nature of the gradient causes internal, self-equilibrating stresses to develop as plane sections must remain plane.1 These stresses are compounded if the structure is statically indeterminate. For a continuous structure, a positive thermal gradient will cause a theoretically weightless beam to camber such that the interior piers are no longer in contact with the beam. Since the beam is not weightless, it remains in contact with the interior piers causing moments to develop in the beam. These restraint-induced moments can be quite large and result in increases in post-tensioning in order to meet code requirements for allowable stresses. This phenomenon is particularly severe in short, stiff spans.
There have been a few reported instances of thermal related cracking in some of the first segmental bridges.2 As a result, the AASHTO Guide Specification for Design and Construction of Segmental Concrete Bridges 2nd Edition, 1999 (Sections 6.4 and 7.2.2) requires that thermal gradients be accounted for. The values are based on a 1983 study by Potgieter and Gamble derived from meteorological data and a heat flow program and adopted in the 1985 NCHRP report 276 "Thermal Effects in Concrete Bridge Superstructures".3 AASHTO LRFD Bridge Design Specifications 2nd Edition, 1998 has similar thermal gradient requirements.
A few laboratory and actual field studies have been conducted to determine the shape and magnitude of thermal gradients. One study by Roberts et al.4 and another by Davis et al.5 have essentially verified the shape of the code positive gradients. However they reach different conclusions about the magnitudes. Both studies found the code negative gradients inaccurate. Roberts also recommends that thermal gradients not be included for ultimate load checks because the formation of plastic hinges relieves restraint induced deformations.6 Of course designers should follow the code as the report suggestions have not yet been adopted.
References
1Roberts, C.L., Breen, J.E., and Kreger, M.E., Measurement Based Revisions for Segmental Bridge Design and Construction Criteria (Center for Transportation Research, The University of Texas at Austin, 1993), 165.
2Ibid., 163.
3Ibid., 174.
4Ibid., 203.
5Davis, R.T., Thompson, M.K., Wood, B.A., Breen, J.E., and Kreger, M.E., Measurement-Based Performance Evaluation of a Segmental Concrete Bridge (Center for Transportation Research, The University of Texas at Austin, 1999), 217.
6Roberts et al., op. cit., 173 & 203.
