Prob 71 solving indeterminate structure by method of consistent deformation. Moment distribution method offers a convenient way to analyse statically indeterminate beams and rigid frames. In the slopedeflection method, equations are written down for the equilibrium of all the joints in the structure. In the slopedeflection method, the moments at the ends of the members are expressed in terms of displacements and end rotations of these ends. 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. Frames with sidesway part 4, video lectures, the moment distribution method. Using momentdisplacement relations, moments are then known. The slopedeflection and moment distribution methods were extensively used for many years before the computer era. Generalized slopedeflection and moment distribution. Of course, the relative rather than the actual values of k can be used in computations. All of the required curvature diagrams are shown in figure 9. Moment distribution has an arithmetical solution in which a number of successive corrections are applied to an initial set of assumed moments.
Slope and deflection calculator for cantilever with moment. From the 1930s until when computers began to be widely used in the design and analysis of structures, the moment distribution method was the most widely used method in practice. Frames with sidesway civil engineering ce notes edurev, ppt, important questions, pdf, the moment distribution method. Equilibrium equations end moments are expressed in terms of unknown rotation. Analysis of statically indeterminate beams and frames. Lo, shihching, analysis of continuous space frames by threedimensional momentdistribution and slopedeflection methods. It is comparatively easier than slope deflection method. The slopedeflection method uses displacements as unknowns and is referred to as a displacement method. Prob 75 deflection of pinjointed truss by unit load method. The moment distributed to or resisted by a rigidly connected end k of a member equals the distribution factor for that end times the. In moment distribution method,the sum of distribution factors of all the members meeting at. Able to analyze determinate beam deflection and slope by moment area method. Class note for structural analysis 2 fall semester, 20 hae sung lee, professor. The slopedeflection method and a beam analysis code are implemented to analyze a large number of continuous beams of equal spans length.
Momentarea method the moment area method is a semigraphical procedure that utilizes the properties of the area under the bending moment diagram. This method is based on the following simplified assumptions. Analyze two span continuous beam abc by slope deflection method. Bending moment and deflection are symmetrical quantities steps involved in moment distribution method. Example 1 determine the moments at b and d, then draw the moment diagram. Two standard methods, mosoentdistribution l and slopedeflection 2 have been extenied by the author to solve continuous space frezaes. Slopedeflection method overview sa27 slopedeflection equations. Slope deflection method for indeterminate structure. The application of the hardy cross method of moment. Slope deflection method structural analysis 2 fixed.
The slope deflection method was widely used for more than a decade until the moment distribution method was developed. The beam, which behaves elastically, carries a concentrated load at midspan. Calculate fixed end moments due to applied loads following the same sign convention and procedure, which was adopted in the slopedeflection method. In this unit, the sign conventions used are same as those for slope deflection method. It means joints rotate as a whole and the angles between the tangents to the elastic curve meeting at that joint do not change due to rotation. Double integration method and moment area method are basically used to determine deflection and slope at any section of a loaded beam when beam will be loaded with a single load. Module ii analysis of continuous beam and simple portals by kanis method, analysis of two pinned and fixed arches with dead and live loads, suspension cable with two pinned stiffening girders. For the love of physics walter lewin may 16, 2011 duration. An important characteristic of the slopedeflection method is that it does not become increasingly. After the end moments are determined, draw the shear and moment curves. Maney method in this method, joints are considered rigid. Method aims determine the slope and deflection by using moment area method expected outcomes.
Analysis of continuous space frames by threedimensional moment. Solved example on indeterminate structure by method of. What is the difference between slope deflection method and. If i 240 in 4 and e 30,000 kipsin 2, compute the magnitude of the slope at joint b. Moment distribution method momentdistribution method. Pdf the momentdistribution method for statically indeterminate. Generalized slopedeflection and moment distribution methods for the analysis of viaducts and multi. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4. Slope deflection method and moment distribution method are both stiffness methods. Then, each fixed joint is sequentially released and the fixedend moments which by the time of release are. Part 3 sa31 support settlement sa32 frame analysis sa33 analysis of a building frame using slopedeflection method sa44 8. Both momentdistribution and slopedeflection methods can be applied to similar. In this method, if the slopes at the ends and the relative displacement of the ends are known, the end moment can be found in terms of slopes, deflection, stiffness and length of the members. Moment distribution method was first introduced by hardy cross in.
Problem 72 solution of indeterminate structure continuous beam by consistent deformation. Basic idea of slope deflection method the basic idea of the slope deflection method is to write the equilibrium equations for each node in terms of the deflections and rotations. Slope deflection method study notes for civil engineering. Solving indeterminate beam by method of consistent deformation. Slope deflection method analysis of indeterminate structures by displacement method hindi structural analysis 2 slope deflection method playlist. Beams of various span numbers and loading distribution are. These analyses are called threedimensional hotnentdistribution and slopedeflection laethods it is interesting to icnow that as a byproduct of. In the moment distribution method, every joint of the structure to be analysed is fixed so as to develop the fixedend moments.
Introduction structural analysis method for beams and frames introduced in 1914 by george a. Displacement method of analysis slope deflection method. Analysis of continuous space frames by threedimensional. That is, node displacements are treated as the unknowns, after solving the stiffness equation for displacements, member forces and reactions are obtained. Problem 82 solution of indeterminate frame by using moment distribution method. The structure is thus reduced to a determinate structure. Part 2 sa29 fixedend moments sa30 slopedeflection equations. Basically, in the slope deflection method, the end moments are computed using the slopes and deflection at the ends. Wood page 4 of 26 notation within the slopedeflection method.
The first, the generalized slopedeflection method, is developed from a consideration of the flexural properties of the curved or bent structural member. Using the moment area method to construct the slopedeflection equation we can determine each relative rotation component using the moment area theorem. By application of the second areamoment theorem, determine the tangential deviation at the point where the beam deflection is desired and at any other points required. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. While macaulays method is basically used to determine deflection and slope at any section of a loaded beam when beam will be loaded with multiple loads. In the book, the theory and practice of modern framed structures, written by j. Analyse continuous beam by the momentdistribution method. This video lecture, part of the series structural analysis video lessons by prof. This paper introduces two new methods of structural analysis for the singlestorey, multibay frame. When a point of zero slope is known, either from symmetry or from supports, a tangent drawn at this point will frequently be useful. Assume a and c are pinned and b and d are fixed connected. Now, the required equation to solve for the rotation. Calculate deflection and slope of simply supported beam for many load cases.
Moment distribution and slope deflection springerlink. The relationship between the applied moment m and the rotation. It is, however, restricted in its application here to those linear structures in which the connecting eaves joints are only able to. Analyse a frame shown in figure below by slope deflection method. The momentdistribution method for statically indeterminate beams. The application of the hardy cross method of moment distribution. In the slopedeflection method the rotations of the joints are treated as unknowns. In the previous lesson we discussed the slopedeflection method. Analyse the frame as shown in figure below by moment distribution method. Prob 61 calculate slope and defelction of cantilever by macaulays method.