A Beam is a Structural Member Designed to Resist Primarily Transverse Loads Elemontary beam theory Transverse Loads are Transported to Supports by Flexural Action ,10 Compressive stress 7aaoea Plane Beam Terminology (a) (b) (e) gww 802anh9a866 1 1 FEM – Chapter 4 Flexure elements Elementary beam theory (a) Simply supported beam subjected to arbitrary (negative) distributed load.(b) Deflected beam element. (c) Sign convention for shear force and bending moment. 1. The beam is loaded only in the y direction. 2. Deflections of the beam are small in comparison to the characteristic dimensions of the beam. 3. The material of the beam is linearly elastic, isotropic, and homogeneous. 4. The beam is prismatic and the cross section has an axis of symmetry in the plane of bending. Beam cross sections:(a) and (b) satisfy symmetry conditions for the simple bending theory, (c) does not satisfy the symmetry requirement. The ramifications of assumption 4 are illustrated in Figure, which depicts two cross sections that satisfy the assumption and one cross section that does not. Both the rectangular and triangular cross sections are symmetric about the xy plane and bend only in that plane. On the other hand, the L-shaped section possesses no such symmetry and bends out of the xy plane, even under loading only in that plane. With regard to the figure, assumption 2 can be roughly quantified to mean that the maximum deflection of the beam is much less than dimension h. A generally applicable rule is that the maximum deflection is less than 0.1h