Introduction slopedeflection method is the second of the two classical methods presented in this course. The basis for the method comes from the similarity of eq. Aug 14, 2019 when the real beam is fixed supported, both the slope and displacement are zero. Skew roller support beam analysis using the stiffness method. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. Structural analysis iii the moment area method mohrs. The slope deflection method can be used to analyze statically determinate and indeterminate beams and frames. The number of simultaneous equations will be equal to the. Analysis of indeterminate structure by slope deflection.
In statically indeterminate structures, the beam axis rotates due to. Deflection method this method takes into account only the bending deformations. Advanced structural analysis online course video lectures by. The deflection of the beam is needed for two main reasons. 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. For example, as shown below, a pin or roller support at the end of the real beam provides zero displacement, but a non zero slope. Mohrs theorems for slope and deflection state that if a and b are two points on the deflection curve of a beam and b is a point of zero slope, then m. Slope and deflection double integration method problem 1 slope and deflection of beams duration. In the slope deflection method, the moments at the ends of the members are expressed in terms of displacements and end rotations of these ends. Essentially, it requires the same amount of computation as the momentarea theorems to determine a beams slope or deflection. Why is it necessary to compute deflections in structures.
Devdas menon, department of civil engineering, iit madras. Now, the required equation to solve for the rotation. The slope deflection method relies on the use of the slope deflection equation, which relate the rotation of an element both rotation at the ends and rigid body rotation to the total moments at either end. Castiglianos theorem illinois institute of technology.
Direct stiffness method deformations due to axial forces are not neglected. Analysis of statically indeterminate structures by the. Conjugate beam method cbmslope deflection structural. Assume a and c are pinned and b and d are fixed connected. Example 1 determine the moments at b and d, then draw the moment diagram. Nptel notes pdf civil engineering 105 courses in pdf format useful for gate acoustics and daylighting in building nptel civil engineering notes pdf advanced foundation. In the next section slopedeflection method as applied to multistoried frame is discussed. Stiffness method, which forms the basis of most computer software currentlyused for stt ltructural analilysis. Sudarshan sri siddhartha institute of tech, tumkur. English beam deflection using double integration method duration. Class note for structural analysis 2 fall semester, 20 hae sung lee, professor dept. 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.
Elastic deflection castiglianos method 1 obtain expression for all components of energy table 5. Equilibrium equations end moments are expressed in terms of unknown rotation. Able to analyze determinate beam deflection and slope by moment area method. The slopedeflection method results in a set of simultaneous equations of unknown displacements. If the deflection of a structure is more than the permissible, the structure will not look aesthetic and will cause psychological upsetting of the occupants. When a point of zero slope is known, either from symmetry or from supports, a tangent drawn at this point will frequently be useful. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Using the slope deflection method, compute the end moments and plot the bending moment diagram.
Banerjee, department of civil engineering, iit bombay for more courses visit. 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 was used for many years before the computer era. Slope deflection method in this method it is assumed that all deformations are due to bending only. Used by engineers for analysis of small structures. Now here we look into another methodology which we call as the moment area method where we evaluate the slope and deflection in beams.
Dec 05, 20 assumptions in the slope deflection method. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. Slope deflection method numerical example with support. 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. Advanced structural analysis online course video lectures. Moment area method to find slope and deflection of a beam vit chennai duration.
If the beam is designed based on the maximum allowable deflection, this is called design for stiffness. A beam abc, 10m long, fixed at ends a and b is continuous over joint b and is loaded as shown in fig. An important characteristic of the slope deflection method is that it does not become increasingly. 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. 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. Nodes a and c are fixed and so do not have any degreesoffreedom dofs. It does not involve the solution of many simultaneous equations. This video lecture, part of the series structural analysis video lessons by prof.
Slope deflection method university of nebraskalincoln. The slope deflection method for beams will be illustrated using the example structure shown in figure 9. Method aims determine the slope and deflection by using moment area method expected outcomes. In this lesson, slopedeflection equations are derived considering the rotation of beam axis. The slope as well as the deflection would be maximum at free end hence putting x 0 we get y max pl3 3ei negative sign indicates the deflection is downward slope max. Computation of deflection of structures is necessary for the following reasons. Slope deflection equation for continuous beam in hindi by. Slope deflection method devdas menon1018 structural analysis. The slope deflection method is so named as it relates the unknown slopes and deflections to the applied load on a structure. Further, since the deflection curve is smooth, the deflection equations for the same slope and deflection at the point of application of load i. Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. Able to analyse plane frames restrained against sidesway by slopedeflection equations.
In order to develop general form of slope deflection equations, we will consider the typical span ab of a continuous beam which is subjected to. Westergaard, deflection of beams by the conjugate beam method. Structural design and inspection deflection and slope of beams by dr. All the joints of the frame are rigid, distortion, due to axial and shear stresses, being very small, are neglected.
In this method it is assumed that all deformations are. Maccaulays method is a means to find the equation that describes the deflected shape of a beam from this equation, any deflection of interest can be found maccaulays method enables us to write a single equation for bending moment for the full length of the beam when coupled with the eulerbernoulli theory, we can then. This method is based on the following simplified assumptions. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4.
Computation of deflection using moment area method. 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 slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. Sep 05, 2019 conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure. The slope deflection method uses displacements as unknowns and is referred to as a displacement method. Derive slopedeflection equations for the frames undergoing sidesway. Wood page 1 of 26 slope deflection method lesson objectives. We will use castiglianos theorem applied for bending to solve for the deflection where m is applied.656 413 10 1224 1358 398 1242 516 623 1053 1229 856 112 102 648 1394 313 1043 1098 538 417 921 1153 1070 1064 1456 1032 841 642 225 1517 536 1322 968 896 909 1214 160