/F14 4 0 R Here I have mentioned some numerical to find slop and deflection of the beam by conjugate beam method which will make you a clear understanding of this topic.. This diagram shows the real slopes at every location along the beam (in radians). The following procedure provides a method that can be used with the conjugate-beam method to determine the displacement and deflection at a point on a beam’s elastic curve. The result of this is an area for 'd' of $-72/EI$, giving a total deflection at point B' of $-339/EI$. This conversion process for the supports in conjugate beams is shown in Figure 5.10.

This may be done by first analysing a free body diagram of member CD to find the reaction $C_y$ and shear at the hinge (remembering that the moment at C must be zero due to the presence of the hinge). The continuity of the beam allows the transfer of shear and moment, and the support reaction provided by the pin causes a step in the shear diagram at that location (a discontinuity in the shear). The conjugate-beam method is an engineering method to derive the slope and displacement of a beam. In this new conjugate beam, the 'shears' would actually be the slopes of the real beam and the 'moments' would actually be the deflections of the real beam (using the relationships shown in Figure 5.9). the beam can have a 'kink' and the hinge, meaning that the tangent slope of the beam is different on either side of the hinge. This post shows an example on how to apply it. The conjugate beam is loaded with the real beam's M/EI diagram.

Therefore, the fixed end at A becomes a free end, the hinge at C becomes a pin support below the beam at that point, and the end roller at point D remains a roller. Which method you prefer and why? Therefore, for the equivalent conjugate support we need a support that allows a non-zero shear (it provides a vertical reaction) but has zero moment (does not have a moment reaction component). It is defined as an imaginary beam of the same dimensions (length) as the original beam, but the load on the conjugate beam at any point is equal to the moment of bending at that point divided by EI. Although this occurs, the M/EI loading will provide the necessary "equilibrium" to hold the conjugate beam stable.[2]. The most difficult part about this analysis is finding the reactions in the first step. (Hint: Draw the M diagram by parts, starting from midspan toward the ends.

Draw the conjugate beam for the real beam. If we draw the moment diagram for the beam and then divided it by the flexural rigidity(EI), the 'M/EI diagram' results by the following equation. To apply the knowledge successfully structural engineers will need a detailed knowledge of mathematics and of relevant empirical and theoretical design codes. [1]

The loads applied to the beam result in reaction forces at the beam's support points. Various Structures of Shear Key. The method only accounts for flexural effects and ignores axial and shear effects. The resulting slope diagram ($\theta$) is shown in the figure. The completed shear and moment diagrams for the beam are shown in the figure just below the beam. University of Arkansas . Resources for Structural Engineers and Engineering Students. This page was last edited on 16 October 2020, at 19:53. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis. The basis for the method comes from the similarity of Eq. Here the shear V compares with the slope θ, the moment M compares with the displacement v, and the external load w compares with the M/EI diagram. Between point A and point A' ($2.62\mathrm{\,m}$ to the right of point A), the slope diagram has a parabola signified 'a' in the figure. Using the equations of statics, determine the reactions at the beams supports. Essentially, it requires the same amount of computation as the moment-area theorems to determine a beam's slope or deflection; however, this method relies only on the principles of statics, so its application will be more familiar.