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A simply-supported beam (or a simple beam , for short), has the following boundary conditions: w(0)=0 . Because the beam is pinned to its support, the beam cannot experience deflection at the left-hand support.
The boundary condition indicates whether the beam is fixed (restrained from motion) or free to move in each direction. For a 2-dimensional beam, the directions of interest are the x-direction (axial direction), y-direction (transverse direction), and rotation.
We now turn our attention to the solution of the beam de ection, Eq. (5.11). This is the fourth-order linear inhomogeneous equation which requires four boundary conditions. There are four types of boundary conditions, de ned by (M M ) w0= 0 (5.22a) (V V ) w= 0 (5.22b) For the sake of illustration, we select a pin-pin BC for a beam loaded by the ...
A simply supported beam (one resting on only two supports) or a simply cantilevered beam are examples of such determinate beams; in the former case there is one reaction force at each support, and in the latter case there is one transverse force and one moment at the clamped end.
This method entails obtaining the deflection of a beam by integrating the differential equation of the elastic curve of a beam twice and using boundary conditions to determine the constants of integration.
The integrations needed to determine beam deflections require the enforcement of the appropriate displacement and rotation boundary conditions (BCs). It is important that we be able to recognize these boundary conditions as we work through this analysis and be able to check our work in the end.
Linear Elastic Beam Theory. Basics of beams. Geometry of deformation. Equilibrium of “slices”. Constitutive equations. Applications: Cantilever beam deflection. Buckling of beams under axial compression. Vibration of beams.
