Christian Otto Mohr The length of a conjugate beam is always equal to the length of the actual beam. Calculate the slope at the ends and the deflection at the middle. Both methods were developed by Christian Otto Mohr, although the Conjugate Beam Method is often attributed to others. This course consist each and every terms related to conjugate beam method. Slope on real beam = Shear on conjugate beam Deflection on real beam = Moment on conjugate beam Properties of Conjugate Beam Engr. 2. A simple support for the real beam remains simple support for the conjugate beam. 1. The elastic load method is simpler than the conjugate beam method in that . Assume I = 400 in4, and E = 29(103) ksi. Using the conjugate beam method, determine the slope at support A and the deflection under the concentrated load of the simply supported beam at B shown in Figure 7.17a. With this configuration, the beam is allowed to rotate at its two ends but any vertical movement there is inhibited.

E = 29,000 ksi and I = 800 in. The Conjugate Beam Method is a variation of the Moment-Area Method that allows beam slopes and deflections to be calculated purely from the calculation of shear forces and bending moments of the beam with (in some cases) modified support conditions. Notice that this beam must be divided into three sections to accommodate the real and virtual moment expressions and the variation in the moment of inertia CIVL 3121 Virtual Work for Beams 3/4 A fixed end for the real beam becomes free end for the conjugate beam. Conjugate Beam Method Updated June 11, 2019 Page 2 Figure 1: Simple supported beam with point rotation. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. (0.000667 and -0.89 mm). (3), (4), and (5) will now be compared to another case, namely the simply supported beam loaded with a point load, shown in Figure 2. Chapter-5 Deflection of Beam Page- 7 (ix) A simply supported beam with a continuously distributed load the intensity of which at any point ‘x’ along the beam is x sin x ww L ⎛⎞π = ⎜⎟ ⎝⎠ (i) A Cantilever beam with point load at the free end. Simply supported beam. Conjugate beam is defined as the imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI. 7.17.

The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. We will use double integration method here to determine the deflection and slope of a simply supported beam carrying a point load at the midpoint of the beam.

it only applies to simply supported beams. It is simply supported over a span of 6 m.
A simply supported beam is 4 m long and has a load of 200 kN at the middle.
With the help of conjugate beam method we can determine slope and deflection of beam which is related to shear force and bending moment. The expressions for q A, D B, and q C in Eqs. This method was introduced as a way to avoid using complex tangential A simply supported beam is made from a hollow tube 80 mm outer diameter and 40 mm inner diameter. P-654, find the value of EIδ at 2 ft from R2. Example: Determine the displacement at points D on the beam shown below. … It features only two supports, one at each end. Because the conjugate beam is simply an extenuation of the elastic load method, it is necessary to first describe its predecessor. 4. The simply supported beam is one of the most simple structures.

Solution (M/EI) diagram. Conjugate beam method Last updated March 21, 2019 (0) real beam, (1) shear and moment, (2) conjugate beam, (3) slope and displacement.

A simple support for the real beam remains simple support for the conjugate beam. A pinned support and a roller support. The flexural stiffness is 300 MNm2. This course is about third method of deflection of beam that is conjugate beam method. Fig. Problem 654 For the beam in Fig. The length of a conjugate beam is always equal to the length of the actual beam.

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