Transcription of Chapter 4a – Development of Beam Equations - Memphis
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Chapter 4a – Development of Beam Equations - Memphis
Chapter 4a Development of beam Equations Learning Objectives To review the basic concepts of beam bending To derive the stiffness matrix for a beam element To demonstrate beam analysis using the direct stiffnessmethod To illustrate the effects of shear deformation in shorterbeams To introduce the work-equivalence method for replacingdistributed loading by a set of discrete loads To introduce the general formulation for solving beamproblems with distributed loading acting on them To analyze beams with distributed loading acting onthemChapter 4a Development of beam Equations Learning Objectives To compare the finite element solution to an exactsolution for a beam To derive the stiffness matrix for the beam element withnodal hinge To show how the potential energy method can be usedto derive the beam element Equations To apply Galerkin s residual method for deriving thebeam element equationsCIVL 7/8117 Chapter 4 - Development of beam Equations - Part 11/39 Development of beam EquationsIn this section, we will develop the stiffness matrix for a beam element, the most common of all structural element
The local transverse nodal displacements are given by vi and the rotations by ϕi. The local nodal forces are given by fiy and the bending moments by mi. 3. Forcesare positive in the positive y direction. Beam Stiffness At all nodes, the following sign conventions are used on the element level: 1. Momentsare positive in the counterclockwise ...
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