# A COMPARISON BETWEEN THE CLASSICAL BEAM THEORIES BASED ON EQUIVALENT SINGLE LAYER AND MURAKAMI’S ZIGZAG THEORY.

## Palavras-chave:

Laminated Composite Materials, Euler-Bernoulli Beam Theory, Timoshenko Beam Theory, Equivalent Single Layer Theory, Murakami’s ZigZag Theory## Resumo

The necessity for better properties materials has made advances in the composition of

structural elements such as composite beams introduced in the fields of civil, marine, aerospace

and mechanical engineering, which requires better material properties. However, the rapid

increase in using composite materials required improvements in the kinematics of classical

beam theories made to describe the mechanical properties of composited laminated beams. This

paper presents a comparison between the Euler-Bernoulli Theory (EBT) and Timoshenko Beam

Theory (TBT), applying in laminated composited beams associated with multilayer composite

analysis theories: Equivalent Single Layer (ESL) and Murakami’s ZigZag Theory (MZZ). The

work reported here shows examples of different beam configuration and loading, subject to

both theories. It was possible to compare the results with the exact solution derived by Pagano

[1]. Defining the length/thickness relation in which these theories are valid. EBT presents

precise results for low thickness beams; however, it presents low precision in the interlaminar

stress analysis. To contour this limitation and get better results in the stress field this paper used

the equilibrium equations of the elasticity theory. Meanwhile, TBT presents more accurate

results for thicker laminate beams, and the effects of transverse shear deformation are more

relevant in these cases. This article recognizes that TBT is more precise than EBT in all

comparisons presented and can represent the mechanical properties with certain precision and

simplicity.