Conjugate beam method objectives in this course you will learn the following computation of deflection using conjugate beam method. Home university of southern california dissertations and theses analysis of rigid frames by the conjugate beam method. 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. A simple support for the real beam remains simple support for the conjugate beam.
Thats my assumption to me for use conjugate beam method to the analysis of a given real beam. For example, building codes specify limits on deflections as well as stresses. Geometry of the structure, including shape and flexural rigidity of member. Conjugatebeam method p ei m ei pl actual beam conjugate beam 0 0 y. The deflection will depend on the following factors. The conjugate method many have asked how westside developed the conjugate system and why. However, the bending moment at the fixed end is 4000 inlb and is thus the maximum moment. This video lecture, part of the series structural analysis video lessons by prof. In writing this article i solely aim to provide a reliable source of information which outlines how to use the westsidebarbell conjugate method.
Jul 24, 2017 conjugatebeam method mathematical equivalence slopedeflection loadshearmoment ei m ei m. Beam deflections conjugate beam method example 1 structural. Then, apply the last 3 guiding rules to compute and report the requested solutions. 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. Nov 18, 2012 introduction and explanation of the conjugate beam method for calculating beam deflections. Matrix methods and computer applications have in effect made many of the older classical methods of structural analysis redundant. 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.
Problem 656 beam deflection by conjugate beam method. Reciprocity and conjugation fidelity in double phase. A continuous beam with a pin support satisfies these criteria. If you have watched this lecture and know what it is about, particularly what civil engineering topics are discussed, please help us by commenting on this video with your suggested description and title. Effective teaching and learning of the conjugate beam method.
Conjugate beam a ei m b l p ab ei m ei ml 2 ei m ei ml 2 ei pl 16 2 ei pl 4 ei pl 16 2 point load. So, lets create a conjugate beam with the same geometry as the real beam but treating the curvatures as the loads. Bending moment at any section in a conjugate beam gives in the actual. Beam rotations and deflections using conjugate beam method in this tutorial, i go over the theory of conjugate beam method which is a method. Hi, this is module 4 of mechanics materials part 4. Introductory example applying the conjugate beam method to calculate deflections in a cantilever beam with changing flexural rigidity aka. A comparison of two set of equations indicates that if m ei is the loading on an imaginary beam, the resulting shear and moment in the beam are the slope and. A conjugate beam is a fictitious beam that corresponds to the real beam and loaded with mei diagram of the real beam. Aug 17, 2015 beam rotations and deflections using conjugate beam method in this tutorial, i go over the theory of conjugate beam method which is a method. I created another tutorial that has a title that starts with the word derivation this video isnt going viral. How to use a conjugate beam method to the analysis of a given. Solutions of a simple beam deflection problem using a variety. This method uses equilibrium equations in conjugate beam, instead of using moment area diagram in real beam. I started training full time in powerlifting in late 1969 after returning from the army.
Before i begin its important for me to clarify what i aim to accomplish through writing this article. Excessive deflection of a beam not only is visually disturbing but also may cause damage to other parts of the building. Conjugatebeam method mathematical analogy slopedeflection loadshearmoment ei m ei m dx d. The load on the conjugate beam is the mei diagram of the loads on the actual beam. Hence the equations for rotation and deflections at point b from the two conjugate beams loaded with equivalent mei diagrams is given by. Introduction and explanation of the conjugate beam method for calculating beam deflections. Deflections using conjugate beam method determine the slope and deflection at point b of the beam shown in fig, 3. The slope and deflection at any section in a real simply supported beam are given by the shear and bending moment at that section in the conjugate beam, and the elastic curve of the real beam is. The conjugate beam is free at both the ends as the real beam is fixed supported. This is the same problem that was covered in the previous moment area theorem method example. Real beam conjugate beam a ei m ei m b 12 0, 24 2 2 2 0. Sep 08, 2016 i think to conjugate beam method is difficult but we can calculate from loads that worked at the beam to knowing safety with engineering mechanica. Some example conversions from real beams to conjugate beams are shown in figure 5. Aug 11, 2015 about video lecture a sample problem showing how to calculate beam slopes and deflections using the conjugate beam method.
Beam rotations and deflections using conjugate beam method. Analysis of rigid frames by the conjugate beam method. The conjugate beam method provides a different way to find slopes rotations and deflections of determinate beams. This video shows the steps for calculating slope in a beam using the conjugate beam method. Lets see how the conjugate beam method works for the familiar free standing beam problem in which a constant density of 10 lbft acts on a 10 foot beam as shown in. The purpose of this text is to develop students fundamental understanding of the principles of structural analysis in the modern engineering office. The westside conjugate system is the best of two advanced training systems.
Solutions of a simple beam deflection problem using a variety of methods. This video illustrates an example of applying conjugate beam method in determining slope and deflection of a simply supported beam. Conjugate beam method example 1 simply supported beam with. For instance consider a simply supported beam subjected to a uniformly distributed load as shown in figure 5. First, you must know the support of both real and conjugate beams, and then you transform the support of the real beam to the support of the conjugate beam, and draw it. There are different established methods in mechanics of materials for determining deflections of beams. Second, you plot the mei of real beam on the conjugate beam. Extensive glass breakage in tall buildings can be attributed to excessive deflections large deflections in buildings are unsightly and unnerving and can cause cracks in ceilings and walls. Conjugate beam analogy the conjugate beam method analogy relies simply on the similarities between the governing equations. What is the value of t in 7 it vq for determining the largest horizontal shear stress anywhere on the cross section. Matrix methods, and structural analysis software such as sap2000 are the tools that most engineers use in.
Arthur gunn puts an incredible spin on a creedence clearwater revival classic american idol 2020. Deflections conjugate beam eciv 320 structural analysis i. Applied to the double phase conjugate mirror dpcm this invariant can be rewritten as an equality between the ratio of the conjugation fidelity of the two ports of the dpcm and the ratio of the transmission in intensity of the two beams. View notes deflections conjugate beam from ce 358 at university of southern california.
A fixed end for the real beam becomes free end for the conjugate beam. Abstract the method of model formulas is a recently published method. A conjugate beam is an imaginary beam with imaginary support conditions and imaginary loading meant to find slope and deflection in a real beam. Conjugate beam method with internal hinge civil engineering. Aug 31, 2014 53 top structural analysis civil engineering multiple choice questions and answers pdf. From the shear force diagram, we find v 0 at x 25 and, thus the maximum bending moment is 2250 inlb at x25. No matter which established method is used, one rightfully. Advantages of method of model formulas versus those of conjugate beam method. The conjugate beam method is an engineering method to derive the slope and displacement of a beam. Todays learning outcome is to use the double integration method to determine the equation for the deflection of a beam. Assume the following beam cross section experiences a shear force. The length of a conjugate beam is always equal to the length of the actual beam. This video provides an extended overview to the force method aka flexibility method, compatibility method, method of superposition, method of consistent deformations and a guided example. Unlike the moment area method and the conjugate beam method, it can be used to find the deflections of trusses, beams or frames or, in fact any mechanical system.
745 1426 476 896 1044 250 434 459 1028 345 371 1364 996 1404 517 382 1424 662 1508 593 979 1011 179 1043 1005 931 1315 601 185 398 274 870 532 405 235 1355 1489 1329 47 1295