In Timoshenko beam theory the shear strain mentioned as (dw/dx)+Ф for mathematical convenience . Why can't we use with (dw/dx)-Ф?

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Victor J. Аdlucky

Hi Raja Sekhar,

Very clear derivation of Timoshenko beam equations is given at https://en.wikipedia.org/wiki/Timoshenko_beam_theory#Boundary_conditions

(Show: Derivation of quasistatic Timoshenko beam equations).

Khaled Megahed

As Ф is negative around axis y, see the attached figure