Does Bernoulli’s Hypothesis Apply to Differential Shrinkage Problems?

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Title: Does Bernoulli’s Hypothesis Apply to Differential Shrinkage Problems?

Author(s): J. Silfwerbrand

Publication: Special Publication

Volume: 246

Issue:

Appears on pages(s): 279-292

Keywords: Bernoulli’s hypothesis; differential shrinkage; strain measurements

Date: 9/1/2007

Abstract:
Differential shrinkage - shrinkage difference between an old concrete substrate and a new-cast concrete overlay - causes stresses of substantial magnitude in repaired concrete structures. Consequently, it is important to determine normal stresses in the overlay and in the substrate as well as shear stresses in the interface. The literature on differential shrinkage problems goes back to the 1950s. Most theories use Bernoulli’s hypothesis as an important assumption. Bernoulli’s hypothesis states that plane sections remain plane after bending. It facilitates the computations. In this paper, Swedish laboratory tests on overlaid concrete beams have been reconsidered to test the validity of Bernoulli’s hypothesis. Strain measurements across the beam depth support Bernoulli’s hypothesis. Still the ultimate and generally accepted theory for computing stresses and strains in composite concrete structures subjected to differential shrinkage is missing but this paper shows that Bernoulli’s hypothesis may constitute one of the foundation-stones in such a theory.