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