Arce 302structural analysis lecture notes, fall 2009 ansgar neuenhofer. Moment method the areamoment method of determining the deflection at any specified point along a beam is a semi graphical method utilizing the relations between successive derivatives of the deflection y and the moment diagram. The given beam in figure 74a is statically indeterminate of degree 1. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. This method considers the deflection as the primary unknowns, while the redundant forces were used in. We require two equations to solve the two unknown rotations. Civil engineering solved examples for slope and deflection. Galib muktadir presented by tanni sarker student id. The information on this website is provided without warantee or guarantee of the accuracy of the contents. Method of analyzing indeterminate structure force method in 530314 primary unknowns forces and moments. The slopedeflection method for beams will be illustrated using the example structure shown in figure 9. Structural design and inspection deflection and slope of beams by dr.
Wood page 1 of 26 slope deflection method lesson objectives. Slope deflection method examples purdue engineering. Elastic deflection castiglianos method 1 obtain expression for all components of energy table 5. The procedure to compute a deflection component of a beam is similar to that for a truss begin by applying a unit virtual load q at the point where the deflection is to be computed apply a unit couple at the point where slope is to computed a d bc x p real load l deflections lets examine the following beam and use virtual work to. 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. Work examples on slopedeflection method of analysis. Using momentdisplacement relations, moments are then known. The modulus of elasticity and the moment of inertia of the beam are 29,000 ksi and 8000 in 4, respectively fig. Before macaulays paper of 1919, the equation for the deflection of beams could not be found in closed form. Solved example on strength of doubly reinforced concrete beam. Example 1 determine the moments at b and d, then draw the moment diagram. Introduction slopedeflection method is the second of the two classical methods presented in this course.
Nodes a and c are fixed and so do not have any degreesoffreedom dofs. The slopedeflection equations are not that lengthy in comparison. Slope deflection method university of nebraskalincoln. Different equations for bending moment were used at. The deflection of a beam must often be limited in order to provide integrity and stability of a structure or machine, or. The deflection of the beam is needed for two main reasons. Determine the deflection and slope at specific points on beams and shafts, using various analytical methods including. Slope deflection examples bending beam structure scribd. You will also learn and apply macaulays method to the solution for beams with a combination of loads. The slope deflection equations for final moment at each end are. If the beam is designed based on the maximum allowable deflection, this is. Momentarea method step by step explanation and solved example deflection and slope.
Enforcing the equilibrium equations at each joint or node. The structure is thus reduced to a determinate structure. To prevent any attached brittle materials from cracking 2. Beams example 2, example 2, 2, the 2 2ndnnddnd possibility of solution 1. General background slope deflection method is known as the displacement method and the stiffness method. When a point of zero slope is known, either from symmetry or. Using moment displacement relations, moments are then known. Assume a and c are pinned and b and d are fixed connected. Use slope deflection equations to find the resultant end moments for the continuous beam shown in figure 74a. Ce3401 linear structural analysis slope deflection method 8. It does not involve the solution of many simultaneous equations. Able to analyze determinate beam deflection and slope by moment area method. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. An important characteristic of the slopedeflection method is that it does not become increasingly complicated to apply as the number of unknowns in the problem increases.
Analysis of statically indeterminate structures by the. Slope deflection examples free download as word doc. Momentarea method step by step explanation and solved. We have provided illustrated solved examples on calculation of slope and deflection of cantilever, simply supported beams and frames by diffferent methods like double integration, macaulays method and unit load method. 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. The center column keeps ridge point c from displacing vertically. A modified equation for the slopedeflection method is used in some special cases of end spans to reduce the computations.
Macaulays method is a means to find the equation that describes the deflected shape of a beam. Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. This method takes into account only the bending deformations. All the steps of these examples are very well explained and it is expected that after going through these solved examples the students will improve their.
This tutorial goes through a slope deflection method example problem that is 4 degrees statically indeterminate and 1 degree kinematically indeterminate. Pdf new modification for slope deflection equation in. Using the slopedeflection method, determine the end moments of the beam shown in figure 11. Using the slope deflection equation the member end moments are. Unlike the previous examples, in which we wrote explicit equations for the shear force and bending moment variation. Solving continuous beam by slopedeflection equations. Analysis of statically indeterminate beams and frames slope deflection method 1. After deriving the slopedeflection equation in section 15.
Equilibrium equations end moments are expressed in terms of unknown rotation. Degrees of freedom the continuous beam is kinematically indeterminate to second degree. From this equation, any deflection of interest can be found. A beam abc, 10m long, fixed at ends a and b is continuous over joint b and is loaded as shown in fig. Analyze the propped cantilever shown by using slope defection method. Method aims determine the slope and deflection by using moment area method expected outcomes. Analyze two span continuous beam abc by slope deflection method. In order to develop general form of slope deflection. Used by engineers for analysis of small structures. Force flexibility method for determinate structures, the force method allows us to find internal forces using equilibrium i. This document is highly rated by civil engineering ce students and has been viewed 366 times. A free powerpoint ppt presentation displayed as a flash slide show on. Thus, the material covered in existing textbooks on structural analysis contains more than what is necessary to learn indeterminate structural analysis.
Mechanics of materials civl 3322 mech 3322 deflection of beams the elastic curve. The 2222nnddnd possibilitypossibility of ooffof solution solutionsolution. Analysis of statically indeterminate structures slope. Solve example 8 assuming the supports at a and e are fixed.
Using the slopedeflection method, determine the member end. Unknowns to be solved for are usually redundant forces coefficients of the unknowns in equations to be solved are flexibility coefficients. Frequently only the magnitude of the deflection, called the displacement, is required. Calculate the slope and deflection at the free end. In this case two spans ac and cd of the beam are to be considered. Sudarshan sri siddhartha institute of tech, tumkur. The author shall not be liable to any viewer of this site or any third party for any damages arising from the use of this site, whether direct or indirect. Force method for analysis of indeterminate structures. Use the method of sections to determine the bending moment. The basic idea of the slope deflection method is to write the equilibrium equations for each node in terms of the deflections and rotations.
In the book, the theory and practice of modern framed structures, written by j. Now, the required equation to solve for the rotation. An introduction part 1 civil engineering ce notes edurev is made by best teachers of civil engineering ce. The slopedeflection equations for the end moments are as follows. Ppt 6 slope deflection method powerpoint presentation. This tutorial goes through a slope deflection method example problem that is 4 degrees statically indeterminate and 1 degree kinematically. Stiffness method, which forms the basis of most computer software currentlyused for stt ltructural analilysis.
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