Use slope deflection equations to find the resultant end moments for the continuous beam shown in figure 74a. Identify all kinematic degrees of freedom for the given problem. Example 3 determine the moments at the ends of each member of the frame. Determine the member end moments and reactions for the frame shown by the slope. Able to analyze determinate beam deflection and slope by unit load method references mechanics of materials, r. Learning outcome upon completion of this topic, students should be able to. The main advantages for using the slope deflection method are the ease of programing and the wide range applicability for the indeterminate structures. Analysis of sway frame by slope deflection method 1 youtube.
The idea that the choice of the analytical tool is guided partly by the method of design to be used and partly by the user as a function of software availability is introduced. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method. The colors of the loads and moments are used to help indicate the contribution of each force to the deflection or rotation being calculated. The moment diagrams show the moments induced by a load using the same color as the load. Bending moment and deflection are symmetrical quantities steps involved in moment distribution method. D c e i 1,600 in4 i 1,600 in4 20 ft 800 in 4 800 in 4 ab i i e 29 000 ki 24 30 ft 30 ft e 29,000 ksi. 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. Able to identify the frame with or without side sway. Structural design and inspection deflection and slope of beams by dr.
The slope deflection method is one of the classical displacement methods which is used to analyze the statically indeterminate beams and frames. Analysis of statically indeterminate structures by the. Skew roller support beam analysis using the stiffness method. Mention any three reasons due to which sway may occur in portal frames. Deflections method of virtual work horizontal deflection. Method of joints method of sections compound trusses 47.
Part 3 sa31 support settlement sa32 frame analysis sa33 analysis of a building frame using slope deflection method sa44 8. Able to analyze determinate beam deflection and slope by moment area method. Slope deflection method examples purdue engineering. Frames with sidesway version 2 ce iit, kharagpur instructional objectives after reading this chapter the student will be able to 1. Equilibrium equations end moments are expressed in terms of unknown rotation. Example 8 solve example 7 assuming the supports at a and e are fixed. Replacing them back into the slope deflection equations, member end moments are instantly found. The method of analysis and results of a test of a full size, single span gabled frame are presented in this report. In the slope deflection equations, the deformations are caused by a shear force b bending moment c axial force d none 3. Differential equation of the elastic curve as shown, the vertical deflection of a, denoted by v, is considered to be positive if directed in the positive direction of the yaxis that is, upward in fig.
Sway portal frame analysis using slope deflection equation. Virtual work method frames force method part 1 force method part 2 a. The slopedeflection method uses displacements as unknowns and is referred to as a displacement method. Rigid frames ii elastic critical load slope deflection method nonsway case 1. Degrees of freedom joints c, d and e are free to rotate. The basic idea of this method is to identify the redundant forces first. Pdf new modification for slope deflection equation in. Civil engineering moment distribution method portal frame with sway. Slope deflection method example 33 structural analysis.
An important characteristic of the slope deflection method is that it does not become increasingly. The given beam in figure 74a is statically indeterminate of degree 1. New modification for slope deflection equation in structural. Write the fixed end moments for a beam carrying a central clockwise moment. Able to analyse plane frames restrained against sidesway by slopedeflection equations. The frame was subjected to combined verical and wind loads. There is a uniformly distributed load on the top beam member cd and a single lateral horizontal load at node c. Then using the compatibility conditions, determine the redundant forces. 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. Distortion, due to axial and shear stresses, being very small, are neglected. Derive slopedeflection equations for the frames undergoing sidesway.
Slope deflection method for statically indeterminate portal frames by. In the slopedeflection method, the moments at the ends of the members are expressed in terms of displacements and end rotations of these ends. Computer codes for the analysis of lattice structures. Understand the basic concept of slope deflection method for solving the indeterminate beams. The slope deflection method belongs to a structural analysis method for beams and frames. Design procedure and fabrication of joints are first described. Determine the moments at the ends of each member of the frame. Analysis of indeterminate by the slopedeflection method. Sep 29, 2018 analysis of sway frame by slope deflection method 1 duration. Analyze sway frame by slope deflection method problem 6. Characteristic equation of the frame p p ei b ei c ei c l c l b. Slope deflection method frame structure structural. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. This is a simple portal frame structure with pinned column bases.
Deflection interpolation interpolate the deflection vs in terms of four nodal dofs use cubic function. In this method it is assumed that all deformations are. Sep 16, 2019 assumptions in the slope deflection method. Displacement method of analysis two main methods of analyzing indeterminate structure. Sep 11, 2015 in bc m cb m b a cb bc m m version 2 ce iit, kharagpur page 4 module 3 analysis of statically indeterminate structures by the displacement method version 2 ce iit, kharagpur lesson 17 the slopedeflection method. Why slope deflection method is called a displacement method state the limitations of slope deflection method. Classical structural analysis, on the other hand, has been around for a long time and is meant to be performed by hand.
Ppt slope deflection method kalyso isemin academia. The equation to nd these moments can be found in most textbooks or in the aisc steel construction manual. Part 2 sa29 fixedend moments sa30 slope deflection equations. Introduction slopedeflection method is the second of the two classical methods presented in this course. Example 1 determine the moments at b and d, then draw the moment diagram. Analysis of sway frame by slope deflection method 1 duration. Determine the member end moments and reactions for the frame due to settlement of. In other words, the classical methods of structural analysis, herein, are analytical methods rather than computational methods. The support at a and c and joint b are fixed connected.
Force method truss analysis slope deflection method overview slope deflection equations part 1 slope deflection equations part 2 slope deflection method fixedend moments slope deflection equations part 3 slope. Slope deflection method overview sa27 slope deflection equations. Plastic strength and deflection of a gabled frame, july 1958. Slope deflection method in the slope deflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. For member ab both m ab and m ba are the same xed end moment. Maney in 1915 as a method of analysis for rigidjointed beam and frame structure.
Which of the following methods of structural analysis is a force method. Now, the required equation to solve for the rotation. Assume a and c are pinned and b and d are fixed connected. Part 2 unit load method aims determine the slope and deflection by using unit load method expected outcomes. Deflection equations when a continuous beam or a frame is subjected to external loads, internal moments generally develop at the ends of its individual members.
The procedure is the same whether it is applied to beams or frames. The slope deflection method can be used to analyze statically determinate and indeterminate beams and frames. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Note that in the solution, for spans ab and cd the shorthand slope deflection formula along with pinnedfixed fems are used. Slope deflection method study notes for civil engineering. 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. To find a slope rotation apply virtual moment m at that point and in that direction. This method is based on the following simplified assumptions. Also compute the reactions at support d, and draw the shear and moment curves for members ab and bd. Calculate fixed end moments due to applied loads following the same sign convention and procedure, which was adopted in the slope deflection method. Several classical methods have been developed to solve for the forces and displacements of statically indeterminate systems.
Problem 6 sway frame slope deflection method analysis of rigid jointed portal frame analysis of indeterminate structures by displacement method hindi structural analysis 2. By forming slope deflection equations and applying joint and shear equilibrium conditions, the rotation angles or the slope angles are calculated. The slope deflection method uses displacements as unknowns and is referred to as a displacement method. Deflections using energy methods purdue university. 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. In this case two spans ac and cd of the beam are to be considered. Determine the moment at each joint of the gable frame. Using the slopedeflection method, determine the member end moments in the braced frame shown in figure 12. Degrees of freedom are treated as unknowns in slope deflection method. The slope deflection method is a structural system analysis method developed by heinrich manderla and otto mohr which was later presented by professor g. The following example utilizes the superposition method to determine the deflection of a frame.
Analyze two span continuous beam abc by slope deflection method. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4. Application of slope deflection equations to statically indeterminate beamsindeterminate beams. Rigid frame analysis structural analysis methods such as the portal method approximate, the method of virtual work, castiglianos theorem, the force method, the slope displacement method, the stiffness method, and matrix analysis, can be used to solve for internal. The slope deflection method is still used in quick analysis, preliminary design, checking the analysis, and for. Method of virtual work for beams to find a deflection apply virtual force p at that point and in that direction. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. Solving continuous beam by slopedeflection equations.
The class is an introduction to the basic tools of structural analysis and design. Draw bending moment and shear force diagrams for the plane frame. Step two is to nd all of the xed end moments in both of our members independently. This way the structure is essentially reduced to a statically determinate structure. In this course, we will introduce two important classical approaches. In addition, when evaluating the deformation of a frame structure, you may have to consider both bending and axial internal force components. 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. Determine the member end moments and reactions for the frame structure shown. Virtual work for frames compute the deflection at point c on the frame shown below. An important characteristic of the slopedeflection method is that it does not become increasingly. The slope deflection method for sway frames will be illustrated using the example structure shown in figure 9. Elastic deflection castiglianos method 1 obtain expression for all components of energy table 5. Displacement method of analysis slope deflection method. Determine the end moment for frame using slope deflection method.
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