A re ned shear deformation theory for exure of (exure的再保险ned剪切变形理论).pdf
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8(2011) 183 – 195
∗
A Hyperbolic Shear Deformation Theory (HPSDT) taking
into account transverse shear deformation effects, is used for Department of Applied Mechanics, Govern-
the static flexure analysis of thick isotropic beams. The dis- ment College of Engineering, Aurangabad-
placement field of the theory contains two variables. The 431005, Maharashtra State – India
hyperbolic sine function is used in the displacement field in
terms of thickness coordinate to represent shear deformation.
The transverse shear stress can be obtained directly from the
use of constitutive relations, satisfying the shear stress-free
Received 20 Dec 2010;
boundary conditions at top and bottom of the beam. Hence, In revised form 21 Dec 2010
the theory obviates the need of shear correction factor. Gov-
∗ Author email: ghugal@rediff
erning differential equations and boundary conditions of the
theory are obtained using the principle of virtual work. Gen-
eral solutions of thick isotropic simply supported, cantilever
and fixed beams subjected to uniformly distributed and con-
centrated loads are obtained. Expressions for transverse dis-
placement of beams are obtained and contribution due to
shear deformation to the maximum transverse displacement
is investigated. The results of the present theory are com-
pared with those of other refined shear deformation theories
of beam to verify the accuracy of the theory.
hyperbolic sh
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