Formulation of the Internal Stress Equations of Pinned Portal Frames Putting Shear Deformation into Consideration
Okonkwo V. O1, Onyeyili I. O2, Aginam C. H.3, Chidolue C. A4
1Okonkwo V. O, Department of Civil Engineering, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.
2Onyeyili I. O, Department of Civil Engineering, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.
3Aginam C. H., Department of Civil Engineering, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.
4Chidolue C. A, Department of Civil Engineering, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.
Manuscript received on October 26, 2013. | Revised Manuscript received on November 02, 2013. | Manuscript published on November 05, 2013. | PP: 8-15 | Volume-3 Issue-5, November 2013 . | Retrieval Number: D1822093413/2013©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this work the internal stress equations for pinned portal frames under different kinds of loading was formulated using the equilibrium method. Unlike similar equations in structural engineering textbooks these equations considered the effect of deformation due to shearing forces. This effect was captured in a dimensionless constant α, when α is set to zero, the effect of shear deformation is removed and the equations become the same as what can be obtained in any structural engineering textbook. An investigation into the effect of shear deformation on the internal stresses and its variation with the ratios of second moment of areas of the horizontal and vertical members of the frame ( 𝑰𝟐 𝑰𝟏 ) and the ratio of height to length of the portal frame ( 𝒉 𝑳 ) showed that the effect of shear deformation is generally small and can be conveniently neglected in manual calculations except for pinned portal frames under concentrated horizontal forces where the effect was considerable.
Keywords: Flexural rigidity, Pinned Portal frames, shear deformation, stiffness matrix