Analysis of indeterminate structure by slope deflection. Thus, the long term deflection will be added to the short term deflection to get the total. Dec 14, 2015 apr 14, 2020 the slopedeflection method. Slope deflection method a h m 531 structures 2 slope.
Design methods two design methods are allowed by the aashtolrfd specifications. Determine the moments when each of the members that make up the structure and find the support reactions. Slope deflection method university of nebraskalincoln. Similarly for finding out a rotation, at any point of a loaded structure, the corresponding eq.
Learn how to solve statically and kinematically indeterminate beams with the slope deflection method with these structural analysis tutorials. Download as ppt, pdf, txt or read online from scribd. The one of the method for finding the deflection of the beam is the direct integration method, i. Using moment displacement relations, moments are then known. Slope deflection method strain energy method moment distribution method kanis method 2. This video lecture, part of the series structural analysis video lessons by prof. Displacement methods of structural analysis, analysis of. Draw bending moment and shear force diagrams for the plane frame.
The matter presented here is prepared by the author for their respective teaching assignments by referring the text books and reference books. The slopedeflection method relies on the use of the slopedeflection equation, which relate the rotation of an element both rotation at the ends and rigid body rotation to the total moments at either end. Slope deflection method and moment distribution method are both stiffness methods. What is the difference between slope deflection method and. Example 1 determine the moments at b and d, then draw the moment diagram. Deflection method this method takes into account only the bending deformations. F force required to produce deflection m moment required to produce rotation stiffness of beam. Introduction slopedeflection method is the second of the two classical methods presented in this course. This method follows essentially the same steps for both statically determinate and indeterminate structures. In the slope deflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. 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. Westergaard, deflection of beams by the conjugate beam method. In many ways, it can be thought of as the opposite of the force method. Deflections using energy methods conservation of energy.
Structural deflectionsvirtual workunit load method dr. Slope deflection equation for continuous beam in hindi by. The list of steps given below for the solution of deflection problems by the areamoment method may prove helpful. 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. At the wall x0 the moment felt is the maximum moment or pl, but at the end of the beam, the moment is zero because moments at the locations do not contribute to the overall moments. The rotation angles or the slope angles are measured with the formation of slope deflection equations and the use of joint and shear equilibrium conditions. Introduction to force and displacement methods of structural analysis, analysis of continuous beam and plane frame by slope deflection method and moment. Frames with sidesway version 2 ce iit, kharagpur page 3 module 3 analysis of statically indeterminate structures by the. Said gantry is subjected to vertical and horizontal forces. Devdas menon, department of civil engineering, iit madras. We will use castiglianos theorem applied for bending to solve for the deflection where m is applied.
Check out for more free structural analysis tutorials. It is the forcemoment required to be applied at a joint so as to produce unit deflectionrotation at that joint. Theorem ii the deviation of any point b relative to the tangent drawn to the elastic curve at any other point a, in a direction perpendicular to the original position of the beam, is equal to the product of 1ei multiplied by the moment of an area about b of that part of the moment diagram between points a and b. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. In this frame, nodes c, d and e are restrained from translating horizontally by the fixed end support at node b recall that we are considering all members to be axially rigid. In statically indeterminate structures, the beam axis rotates due to. In this lesson, slopedeflection equations are applied to analyse. Slope deflection method for indeterminate structure. In the force method, we first identified redundant forces for the analysis and solved for them. Banerjee, department of civil engineering, iit bombay for more courses visit. Slope deflection method frame structure structural. Class note for structural analysis 2 fall semester, 20 hae sung lee, professor dept.
That is, node displacements are treated as the unknowns, after solving the stiffness equation for displacements, member forces and reactions are obtained. This with be done later in the stiffness method and it also forms the basis of the finite element method. If i 240 in4 and e 30,000 kipsin2, compute the magnitude of the slope at. Structural analysis iii the moment area method mohrs. The slope deflection method was widely used for more than a decade until the moment distribution method was developed.
Assume a and c are pinned and b and d are fixed connected. Measurements were carried out during normal traffic. Area moment method memorial university of newfoundland. Empirical method of minimum thickness evaluation for deflection control the aci code recommends in table 9. The slope deflection method belongs to a structural analysis method for beams and frames. Slope deflection method in the slopedeflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. Conjugate beam method the conjugatebeam method was developed by h.
Moment area method to find the deflection and slope using moment area method to learn about the theorems of moment area method, click here to find the. Using the slope deflection method, determine the member end moments in the indeterminate beam shown in figure 12. In this method it is assumed that all deformations are due to bending only. The frames will sidesway the frames will be displaced to the right or left or will be displaced up or down.
The slope deflection method is more preferable than flexibility method because as its calculations are easy. Sketch deflected shape of the plane frame not restrained against sidesway. The beam, which behaves elastically, carries a concentrated load at midspan. All the joints of the frame are rigid, distortion, due to axial and shear stresses, being very small, are neglected. Determine the moments at the ends of each member of the frame. Williot mohr diagram method virtual work method or unit load method the deflection. Solve the indeterminate structure using slope deflection method. Moment distribution method hardy cross method stiffness. Able to analyse plane frames restrained against sidesway by slopedeflection equations. The slope deflection method is an alternate way to analyse indeterminate structures. Empiricalmechanistic method of design is based on the mechanics of materials that relates input, such as wheel load, to an output or pavement response. Areamoment method beam deflections strength of materials. Comparison of methods for measuring deflection and vibration. Dec 04, 2012 this is a detailed example analyzing a statically indeterminate beam using slope deflection equations.
Axial deformations are neglected as they are very small. When a body is elastically deflected by any combination of loads, the deflection at any point and in any direction. Structural design and inspection deflection and slope of beams by dr. In slope deflection method we directly know unknown joints. The slope deflection method for a nonsway frame will be illustrated using the example in figure 9. This method is based on the following simplified assumptions. Analysis of statically indeterminate structures by the. Wood page 1 of 26 slope deflection method lesson objectives.
The slopedeflection equations give us the moment at either end of each element within a structure as a function of both end rotations, the chord rotation, and the fixed end moments caused by the external loads between the nodes see section 9. Beams notes, engg, sem notes edurev is made by best teachers of. Using the slopedeflection method, determine the member end moments in the indeterminate beam shown in figure 12. Castiglianos method if deflection is not covered by simple cases in table 5. The basic idea of the slope deflection method is to write the equilibrium equations for each node in terms of the deflections and rotations. I wish to thank several of my students and staff of nptel for their contribution in. Dec 05, 20 assumptions in the slope deflection method. In this lesson, slopedeflection equations are derived considering the rotation of beam axis. This document is highly rated by students and has been viewed 532 times. Analysis of indeterminate structure by slope deflection method. The deflection of the loaded beam can be obtained various methods. Conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure.
The computation of deflections in structures is also required for. Aug 20, 2017 slope deflection method for indeterminate structure. Clapeyrons theorem of three moments, strain energy method and slope deflection method. Frames without sideframes without sidesssswayway in frames axial deformations are much smaller than the bending deformations and are neglected in the analysis. Design step 6 design of bearings prestressed concrete. Sep 11, 2015 page 1 module 3 analysis of statically indeterminate structures by the displacement method version 2 ce iit, kharagpur page 2 module 3 analysis of statically indeterminate structures by the displacement method version 2 ce iit, kharagpur lesson 17 the slopedeflection method. View test prep slope deflection method from civil and eb527112 at kenya polytechnic university college. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. These methods of analysis require a solution of set of simultaneous. The slopedeflection method can be used to analyze statically determinate and indeterminate beams and frames. Computer methods matrix methods finite element method finite difference method. Note that in the solution, for spans ab and cd the shorthand slopedeflection formula along with pinnedfixed fems are used. Nptel notes pdf civil engineering 105 courses in pdf format useful for gate. A beam abc, 10m long, fixed at ends a and b is continuous over joint b and is loaded as shown in fig.
Gorbels standard, preengineered jib cranes are available in capacities from 50 pounds 23 kg to 5 tons 4536 kg. With this assumption some frames will not sidesway the frames will not be displaced to the right or left. Advanced structural analysis online course video lectures. As pointed out earlier, there are two distinct methods of analysis for statically indeterminate structures depending on how equations of equilibrium, load. The slope deflection method for beams will be illustrated using the example structure shown in figure 9. There is no point in memorizing these steps as they are not a substitute for an understanding of the principles involved. The following procedure provides a method that may be used to determine the displacement and deflection at a point on the elastic curve of a beam using the conjugatebeam method. The paper presents a comparison of deflection and vibration measurements performed on span of a steel bridge designed for tram traffic. It was assumed to obtain the data necessary to determine the span deflection and vibration. Structural analysis slope deflection method for indeterminate structure in hindi.
Analysis of two span continuous beam by slope deflection method by parag pal duration. Skew roller support beam analysis using the stiffness method. These problems are typically pretty long, so the examples are split into 3 parts each. Replacing them back into the slope deflection equations, member end moments are instantly found. After the end moments are determined, draw the shear and moment curves.
Sketch the loaded beam, the moment or mei diagrams either by parts or. Frames with sideframes with sidesssswayway in frames axial deformations are much smaller than the bending deformations and are neglected in the analysis. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4. The slope deflection method is a fun method to use when analyzing indeterminate structures. Stiffness method, which forms the basis of most computer software currentlyused for stt ltructural analilysis. Castiglianos theorem illinois institute of technology. Objective to obtain slope and deflection of beam and frame structures using slope deflection method. Nodes a and c are fixed and so do not have any degreesoffreedom dofs. Slope deflection method example structural analysis. Now here we look into another methodology which we call as the moment area method where we evaluate the slope and deflection in beams. The basic assumption used in the slope deflection method is that a typical member can flex but the shear and axial deformation are negligible. In tructural analysis i, several ce 305 s methods, including energy and computer procedures, are discussed in details. Using the slope deflection method, compute the end moments and plot the bending moment diagram.
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