Geotechnical and Geological Engineering

, Volume 37, Issue 1, pp 1–11 | Cite as

Bending Properties of Granite Beams with Various Section-Sizes in Three-Point Bending Tests

  • Xiang Fan
  • Hang LinEmail author
  • Rihong Cao
Original paper


To examine the size effects on the bending strength of rock and determine the relation between Brazilian splitting strength and bending strength, Brazilian splitting tests were performed to measure the indirect tensile strength of rock materials. Three-point bending tests were used to evaluate the bending properties of rock beam by changing the sample cross section size including height, width, and diameter. The peak load increases as section size linearly expands. An exponential relation between the peak load and the cross section area ratio is found for rectangular section with different heights and circular section with different diameters samples, whereas a linear one is observed for rectangular section with different widths samples. The measured peak load ratio for all tested samples actually differs from the theoretical one. The maximum shear stress on the cross section of the sample is linearly affected by the section height and diameter but hardly influenced by the section width. Bending strength is barely affected by section size which leads to the conclusion that no size effect is observed in the tested size range. However, the ratio of bending strength to Brazilian tensile strength is found within 3.81–4.26 for rectangular samples and 3.14–3.48 for circular samples. The obtained bending strength is higher than the Brazilian tensile strength, which is in good agreement with the previous results, and the bending strength to Brazilian tensile strength ratio is associated with the sample section size.


Bending strength Three-point bending test Cross-section size Indirect tensile strength 

List of symbols


Vertical distance, mm


Vertical load, kN


Rectangular section with different heights


Rectangular section with different widths


Circular section with different diameters


Length of sample in three-point bending test, mm


Height of rectangular cross-section, mm


Width of rectangular cross-section, mm


Support span length, mm


Height of cylindrical sample in Brazilian test, mm


Diameter of cylindrical sample, mm


Indirect tensile strength obtained from Brazilian splitting test, MPa

\(\bar{\sigma }_{t}\)

Average value of indirect tensile strength, MPa

\(\bar{\sigma }_{f}\)

Average value of bending strength, MPa


Ratio of \(\bar{\sigma }_{f}\) to \(\bar{\sigma }_{t}\)



This paper gets its funding from project (51474249, 51774322) supported by National Natural Science Foundation of China; Project (2016CX019) supported by Innovation-driven Plan in Central South University; Project (2016M602742) supported by China Postdoctoral Science Foundation; Open Fund of Key Laboratory of Bridge Engineering Safety Control by Hunan Province, Department of Education (Changsha University of Science and Technology) (15KB02); Open Fund of Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road and Traffic Safety of Ministry of Education (Changsha University of Science and Technology kfj150405); Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (SKLGP2016K009). The authors wish to acknowledge these supports.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of HighwayChang’an UniversityXi’anChina
  2. 2.School of Resources and Safety EngineeringCentral South UniversityChangshaChina
  3. 3.Key Laboratory of Bridge Engineering Safety Control by Hunan Province, Department of EducationChangsha University of Science and TechnologyChangshaChina
  4. 4.Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road and Traffic Safety of Ministry of EducationChangsha University of Science and TechnologyChangshaChina
  5. 5.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologyChengduChina

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