2 nd Workshop on Four Point Bending, Pais (ed.), © 2009. University of Minho. ISBN 978-972-8692-42-1 19 Shear deflection in 4PB tests A.C. Pronk & M. Huurman Delft University of Technology, Delft, ZH, The Netherlands ABSTRACT: Bending tests are normally used for the determination of (initial) stiffness mod- ulus and fatigue characteristics of asphalt mixes. In the back calculation of the stiffness modulus from deflection measurements on beams the bending theory for a slender beam is used in which deflection due to shear is ignored. The error is around 4 % depending on the height over length ratio, the width over height ratio and the Poisson ratio. For practical purposes and in view of the natural scatter in measurements this error is often accepted. However, in case of calibration of the equipment the deflection due to shear should be taken into account. In the formula for the deflection due to shear a correction coefficient is used representing the influence of the shear distribution on the deformation of the cross section during bending. In most back calculation procedures used for the interpretation of 4PB test the shear deflection is ignored. But in the few back calculations procedures which take care of deflection due to shear this coefficient is taken equal to 2/3. In this paper it is shown that for the dimensions of beams used for the characteriza- tion of asphalt properties a value of 0.85 is more appropriate. The proof is based on 3D finite element modeling in which the beam is bended in such away that no constraints are present. Or with other words the beam is bended without really touching or grabbing it. Therefore the mod- el is completely comparable to the theoretical 1D finite element model and the analytical solu- tions. 1 INTRODUCTION 1.1 Bending of a slender beam: Pure bending and shear When a beam is bent two bending phenomena will take place. The first one is the so call pure bending deflection and the second one is the deflection due to the appearance of shear forces in- side the beam. In case of a slender beam many terms in the differential equations can be neg- lected. In the analytical approach, in which the beam is considered to be one dimensional, two equations will describe the deflection profile of the beam due to a given load distribution along the beam (Timoshenko, 1921). Normally only the deflection due to pure bending is considered in practice because in the simplification of the three dimensional beam to a one dimensional ‘line’ representation, the shear load distribution at the supports is unknown and formed already for decades a mathematical challenge. By performing finite element calculations it is possible to get an estimate for the shear correction coefficient.
Shear deflection in 4PB tests
May 17, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
