Definition of conjugate beam method?
The conjugate beam method is used to find the deflection of beams under any loading pattern. The first step is to draw the moment diagram for the beam as actually loaded. Construct the M/EI diagram by dividing the value of M at every point along the beam by EI at that point. If the beam is of constant cross section, EI will be constant along the length of the beam, and the M/EI diagram will have the same shape as the moment diagram. If the beam cross section varies along the length of the beam, the moment of interia, I, will change. In that case the M/EI diagram will not look the same as the moment diagram. The M/EI diagram now acts as the load to the conjugate beam from which you can draw the shear and moment diagram. From the shear diagram, you can read off the deflections at any point of the beam, and from the moment diagram, you can read off the beam's rotation at any point along the beam.
In conjugate beam method, when solving a conjugate beam, in which direction are we supposed to take reactions?
The reactions are always determined in the same manner. The RESULTANT direction of the reaction depends on the summation of moments about THAT reaction. It could be up or down. You ASSUME a direction in the beginning. If the answer is negative, all that means is that you assumed the wrong direction. Cross out the assumed directions and pencil in the correct direction. Keep this in mind, you're not converting the beam into a "conjugate" beam; you're using another method to solve the problem, "Conjugate Beam Theory". Only the method changes.
What is difference between real beam and conjugate beam?
REAL BEAM : The Beam which is designed for slopes and deflections, which is the original beam to be constructed.CONJUGATE BEAM : The IMAGINARY beam used in conjugate beam method for designing of the original beam for slopes and deflections.The Beam is drawn…with the same dimensions as that of the original beam but with M/EI diagram of real beam as the load on conjugate beamchanging the support conditions ( like fixed support of real beam is free end in the conjugate and intermediate support in real to internal hinge in conjugate etc…)Shear Force of conjugate beam is Slope of the real beam.Bending moment of the conjugate beam is the Deflection of the real beam.so…basically conjugate beam is used in conjugate beam method for finding slopes and deflections of real beam by calculating support reactions, shear force, bending moment of the conjugate beamThis method is used for beams with varying cross section or with internal hingesNOTE : The change in the support reactions of conjugate beam can be found in google . The Conjugate beam method is a Important and Long method in finding the slopes and deflections. I have just mentioned only a rough idea about the method.Pleasure…!!!
How do I use a conjugate beam method to the analysis of a given real beam?
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. Thats my assumption to me for use conjugate beam method to the analysis of a given real beam.Slope on real beam = Shear on conjugate beamDeflection on real beam = Moment on conjugate beamproperties of Conjugate BeamEngr. Christian Otto Mohr :The length of a conjugate beam is always equal to the length of the actual beam.The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.A simple support for the real beam remains simple support for the conjugate beam.A fixed end for the real beam becomes free end for the conjugate beam.The point of zero shear for the conjugate beam corresponds to a point of zero slope for the real beam.The point of maximum moment for the conjugate beam corresponds to a point of maximum deflection for the real beam.Supports of Conjugate BeamKnowing that the slope on the real beam is equal to the shear on conjugate beam and the deflection on real beam is equal to the moment on conjugate beam, the shear and bending moment at any point on the conjugate beam must be consistent with the slope and deflection at that point of the real beam. Take for example a real beam with fixed support; at the point of fixed support there is neither slope nor deflection, thus, the shear and moment of the corresponding conjugate beam at that point must be zero. Therefore, the conjugate of fixed support is free end. Beam Deflections - Conjugate Beam Method Example 1- Structural Analysis Conjugate Beam Method | Beam Deflection
What are the advantages of conjugate beam over other beams?
Conjugate beam is actually an imaginary beam which is used for the analysis of real beam so practically there's no advantage of conjugate beam over the other beams because it wouldn't make any sense as the concept of conjugate beam is itself a derived concept from a real beam. But the uses are,They are used to find the slope and deflection of the real beam for which the conjugate beam is formed. The slope of real beam at any section is the shear force of the conjugate beam at that particular section. The deflection of real beam at a section is the bending moment of the conjugate beam at the particular section. The support conditions of conjugate beam differ from the real beam to achieve the slope amd deflection
Definition of a conjugate?
con‧ju‧gate /v. ˈkɒndʒəˌgeɪt; adj., n. ˈkɒndʒəgɪt, -ˌgeɪt/ Pronunciation Key - Show Spelled Pronunciation[v. kon-juh-geyt; adj., n. kon-juh-git, -geyt] Pronunciation Key - Show IPA Pronunciation verb, -gat‧ed, -gat‧ing, adjective, noun –verb (used with object) 1. Grammar. a. to inflect (a verb). b. to recite or display all or some subsets of the inflected forms of (a verb), in a fixed order: One conjugates the present tense of the verb “be” as “I am, you are, he is, we are, you are, they are.” 2. to join together, esp. in marriage. –verb (used without object) 3. Biology. to unite; to undergo conjugation. 4. Grammar. to be characterized by conjugation: The Latin verb esse does not conjugate in the passive voice. –adjective 5. joined together, esp. in a pair or pairs; coupled. 6. Botany. (of a pinnate leaf) having only one pair of leaflets. 7. Grammar. (of words) having a common derivation. 8. Bibliography. (of two leaves in a book) forming one sheet. 9. Mathematics. a. (of two points, lines, etc.) so related as to be interchangeable in the enunciation of certain properties. b. (of an element) so related to a second element of a group that there exists a third element of the group that, multiplying one element on the right and the other element on the left, results in equal elements. c. (of two complex numbers) differing only in the sign of the imaginary part. 10. Chemistry. a. of or noting two or more liquids in equilibrium with one another. b. (of an acid and a base) related by the loss or gain of a proton: NH 3 is a base conjugate to NH4+. NH4+ is an acid conjugate to NH3. c. Also, con‧ju‧gat‧ed. (of an organic compound) containing two or more double bonds each separated from the other by a single bond. –noun 11. one of a group of conjugate words. 12. Mathematics. a. either of two conjugate points, lines, etc. b. Also called conjugate complex number. either of a pair of complex numbers of the type a + bi and a − bi, where a and b are real numbers and i is imaginary
Can you help in explaining beam method and shell method in Ansys?
These both method are generally use to create mesh in ANSYS.The BEAM METHOD: It is 1D method. This method is generally used to analyse the structural elements who are linear and simple in Geometry. Singular bars, connecting road can be analysed primarily as per the BEAM METHOD.The SHELL METHOD: It is more in-depth and concrete method to analyse any elements. It is suitable for complicated geometry at a greater degree. It uses elements like tetrahedron, pyramids, quadrilateral elements to create meshes. This method leads us to better results as it encounters the most intricate parts of the geometry.