Comparison between Analytical Equation and Numerical Methods for Determining Shear Stress in a Cantilever Beam

Imad Al-Qasem, A. Rasem Hasan, Mohanad Abdulwahid, Isaac Galobardes


A three meter-length cantilever beam loaded with a concentrated load at its free end is studied to determine shear stresses. In the present study, three cross sections are considered: rectangle (R); I, and T. The study presents a comparison of maximum shear stresses obtained by means of two methods: classical analytical equation derived by Collingnon, and finite element method (FEM) software. Software programs ANSYS and SAP2000 were used. The results show difference between the maximum shear stresses obtained by the analytical equation and the software, being the last is always higher. The average differences for ANSYS and SAP2000, independently of the cross section, were 12.76% and 11.96%, respectively. Considering these differences, correction factors were proposed to the classical analytical formula for each cross section case to obtain more realistic results. After the correction, the average differences decrease to 1.48% and 4.86%, regardless of the cross section shape.


Shear Stress; Finite Element Methods; Analytical Equations; Comparison Analysis; Correction Factor.


Duan T. C., Li L. X. “The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models.” Latin American Journal of Solids and Structures 13 (September 2017): 1716-1737. doi:10.1590/1679-78252732.

Ghavami P. “Mechanics of Materials” (2015).

Kurrer, K. E. “The History of the Theory of Structures: From Arch Analysis to Computational Mechanics.” (2012).

Singiresu S. R. “The Finite Element Method in Engineering.4th” (2005).

Martinásek J., Valeša, J.,Kala Z. “Inelastic finite element analysis of lateral buckling for beam structures.” Procedia Engineering 172 (2017):481 – 488. doi:10.1016/j.proeng.2017.02.056.

Yeghiazarian, H., B. Yazdizadeh.“Some FEM Models for Bending and Vibration Problems of Beam.” Proceedings of the Yerevan State University, Physical and Mathematical Sciences. (2013): 38–43.[7] Thompson M., Thompson, J. “ANSYS Mechanical APDL for Finite Element Analysis.” (2017):123–130

Ruiz M., González C. “Influence of flanges on the shear-carrying capacity of reinforced concrete beams without web reinforcement.” Structural concrete 18 (March 2017): 720-732. doi:10.1002/suco.201600172.

P. Kettil, N. E. Wiberg. “Application of 3D solid modelling and simulation programs to a bridge structure.” Engineering with Computers 18 (August 2002):160-169. doi:10.1007/s003660200014.

Qasrawi, H. “Design of Normal Concrete Mixtures Using Workability-Dispersion-Cohesion Method.” Advances in Civil Engineering (2016): 1-11. doi:10.1155/2016/1035946.

EN 1992-1-1 (English): Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. (2004). doi: 10.3403/03178016u.

Love, A. E. H.“A Treatise on the Mathematical Theory of Elasticity, Edition 4th” (2011).

Galobardes I. et al. “Estimation of the modulus of elasticity for sprayed concrete.” Construction and Building Materials 53(February 2014):48-58. doi:10.1016/j.conbuildmat.2013.11.046.

Galobardes, I., Figureiredo, A. “Correlation between beam and Barcelona tests for FRC quality control for structural applications.” Proceedings of the International Conference FIBRE CONCRETE. (2015):149-158. doi 10.13140/RG.2.1.4771.6327.

Sandoval, G. F. B. et al. “Comparison between the falling head and the constant head permeability tests to assess the permeability coefficient of sustainable previous concrete.” Case Studies in Construction Materials 7 (December 2017): 317-328. doi:10.1016/j.cscm.2017.09.001.

Full Text: PDF

DOI: 10.28991/cej-030989


  • There are currently no refbacks.

Copyright (c) 2018 Mohanad Abdulwahid

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.