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A simple support (pin or roller) is equivalent to a point force on the beam which is adjusted in such a way as to fix the position of the beam at that point. A fixed support or clamp, is equivalent to the combination of a point force and a point torque which is adjusted in such a way as to fix both the position and slope of the beam at that point.
The maximum elastic deflection on a beam supported by two simple supports, loaded at a distance from the closest support, is given by: [1] = / where F {\displaystyle F} = force acting on the beam L {\displaystyle L} = length of the beam between the supports
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
A stiffer beam (high modulus of elasticity and/or one of higher second moment of area) creates less deflection. Mathematical methods for determining the beam forces (internal forces of the beam and the forces that are imposed on the beam support) include the "moment distribution method", the force or flexibility method and the direct stiffness ...
This beam has the same length as the real beam and has corresponding supports as listed above. In general, if the real support allows a slope, the conjugate support must develop shear; and if the real support allows a displacement, the conjugate support must develop a moment. The conjugate beam is loaded with the real beam's M/EI diagram.
Simply supported beam with a constant 10 kN per meter load over a 15m length. Take the beam shown at right supported by a fixed pin at the left and a roller at the right. There are no applied moments, the weight is a constant 10 kN, and - due to symmetry - each support applies a 75 kN vertical force to the beam. Taking x as the distance from ...
If, in addition, the support at A is changed to a roller support, the number of reactions are reduced to three (without H A), but the beam can now be moved horizontally; the system becomes unstable or partly constrained—a mechanism rather than a structure.
Releasing the vertical reaction for A allows the beam to rotate to Δ. Likewise for part (c). Δ is typically taken as positive upwards. Part (d) of the figure shows the influence line for shear at point B. Using the beam sign convention and cutting the beam at B, we can deduce the figure shown.