The Deflection Analysis on Cantilever Beam with Load Point Applied at Free End Using Double Integration Method

Abstract

This study analyzes the deflection behavior of a cantilever beam subjected to a concentrated load at its free end using the double integration method. The objective is to derive and validate the deflection equation of the beam based on classical beam theory (Pytel & Kiusalaas, 2012). The methodology involves applying the Euler-Bernoulli beam equation and performing successive integrations with appropriate boundary conditions to determine the deflection function (Gere & Goodno, 2012). The results indicate that the maximum deflection occurs at the free end and is directly proportional to the magnitude of the applied load and the cube of the beam’s length, and inversely proportional to the flexural rigidity (Hibbeler, 2017). The analytical solution obtained is consistent with standard beam deflection formulas, confirming the accuracy and reliability of the double integration approach (Pytel & Kiusalaas, 2011). This method provides a fundamental and systematic procedure for structural analysis in engineering mechanics (Gere & Goodno, 2012).

Keyword: Beam Deflection, Cantilever Beam, Double Integration Method, Structural Analysis