Slopedeflection method overview sa27 slopedeflection equations. Assume a and c are pinned and b and d are fixed connected. The basic idea of the slope deflection method is to write the equilibrium equations for each node in terms of the deflections and rotations. The slope deflection method belongs to a structural analysis method for beams and frames.
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. This document is highly rated by civil engineering ce students and has been viewed 1480 times. 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 basic idea of this method is to identify the redundant forces first. An important characteristic of the slopedeflection method is that it does not become increasingly. Elastic deflection castiglianos method 1 obtain expression for all components of energy table 5. Lo, shihching, analysis of continuous space frames by threedimensional momentdistribution and slopedeflection methods 1941. Ppt slope deflection method kalyso isemin academia. Frames with sidesway civil engineering ce notes edurev is made by best teachers of civil engineering ce. Replacing them back into the slope deflection equations, member end moments are instantly found. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. The slopedeflection method for sway frames will be illustrated using the example structure shown in figure 9. The slope deflection equations for final moment at each end are. That is, node displacements are treated as the unknowns, after solving the stiffness equation for displacements, member forces and reactions are obtained.
Degrees of freedom joints c, d and e are free to rotate. Slope deflection method study notes for civil engineering. Example 1 determine the moments at b and d, then draw the moment diagram. Sudarshan sri siddhartha institute of tech, tumkur. The slopedeflection method uses displacements as unknowns and is referred to as a displacement method.
The frames will sidesway the frames will be displaced to the right or left or will be displaced up or down. We will eliminate the rotation of the simple support at end e by using the modified slope. Detailed example problem showing how to determine the internal end moments of a statically indeterminate unbraced frame with lateral. Part 2 slope deflection aims determine the end moment for frame using slope deflection method.
Hence, the slope deflection method is an easy process following the procedures which is the same whether it is applied to beams or frames and may be summarized as follows. 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 structure is thus reduced to a determinate structure. The beam, which behaves elastically, carries a concentrated load at midspan. This is a simple portal frame structure with pinned column bases.
The slopedeflection method can be used to analyze statically determinate and indeterminate beams and frames. Determine the member end moments and reactions for the frame shown by the slope. Introduction slopedeflection method is the second of the two classical methods presented in this course. If i 240 in 4 and e 30,000 kipsin 2, compute the magnitude of the slope at. Pdf the slopedeflection method is one of the classical displacement. Then using the compatibility conditions, determine the. The frame was subjected to combined verical and wind loads. In this case two spans ac and cd of the beam are to be considered. Equilibrium equations end moments are expressed in terms of unknown rotation. Displacement method of analysis slope deflection method. Determine the member end moments and reactions for the frame structure shown. In this question we solve a basic frames reactions and sfdbmd using the slope deflection method. Pdf new modification for slope deflection equation in structural. In slope deflection method we directly know unknown joints.
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. There is a uniformly distributed load on the top beam member cd. All the joints of the frame are rigid, distortion, due to axial and shear stresses, being very small, are neglected. Slope deflection method frame with support settlement example duration. Able to identify the frame with or without side sway. The roof load is transmitted to each of the purlins over simply supported sections of the roof decking. The given beam in figure 74a is statically indeterminate of degree 1.
Analyze the propped cantilever shown by using slope defection method. Method aims determine the slope and deflection by using moment area method expected outcomes. Slope deflection method university of nebraskalincoln. Slope deflection method frame with support settlement example. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. 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. Since b is simply supported, the bm at b is zero ie. Force method for analysis of indeterminate structures. Derive slopedeflection equations for the frames undergoing sidesway.
Why do we use the slope deflection method in frames. This method considers the deflection as the primary unknowns, while the redundant forces were used in. Analysis of sway frame by slope deflection method 1 youtube. Slope deflection method examples purdue engineering. Slope deflection method and moment distribution method are both stiffness methods. Using the slopedeflection method, determine the member end moments in the braced frame shown in figure 12. After the end moments are determined, draw the shear and moment curves. Solving continuous beam by slopedeflection equations. Most structures in the real world are statically indeterminate. Using moment displacement relations, moments are then known. Able to analyse plane frames restrained against sidesway by slopedeflection equations.
Able to analyze determinate beam deflection and slope by moment area method. Smaller deflections for similar members redundancy in load carrying capacity redistribution increased stability advantages. Primarily to determine the frame end moments by solving the slope deflection equations simultaneously. This method is based on the following simplified assumptions. 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 slope deflection equations for final moment at each end are 2 l 4ei 12 wl 2 l 2ei m f 1 l 2ei 12 wl 2 l 2ei m f b 2 ba ba b a b 2 ab ab a b in the above equations there is only one unknown b. A basic overview of the slopede ection method 7 4 conclusion hopefully, this helped in understanding the slopede ection method for nding internal moments in indeterminate structures. Distortion, due to axial and shear stresses, being very small, are neglected.
Pdf new modification for slope deflection equation in. Use slope deflection equations to find the resultant end moments for the continuous beam shown in figure 74a. A modified equation for the slopedeflection method is used in some special cases of end spans to reduce the computations. In the slopedeflection method the individual equations are relatively easy to construct regardless of the number of unknowns. What is the difference between slope deflection method and. Part 3 sa31 support settlement sa32 frame analysis sa33 analysis of a building frame using slopedeflection method sa44 8. The slope deflection method is more preferable than flexibility method because as its calculations are easy. Scribd is the worlds largest social reading and publishing site. Determine the moment at each joint of the gable frame. 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. Plastic strength and deflection of a gabled frame, july 1958. In the book, the theory and practice of modern framed structures, written by j.
Slope deflection method frame structure structural. By forming slope deflection equations and applying joint and shear equilibrium conditions, the rotation angles or the slope angles are calculated. The information on this website is provided without warantee or guarantee of the accuracy of the contents. Slope deflection method sidesway frame analysis 33 structural analysis. Force method for analysis of indeterminate structures number of unknown reactions or internal forces number of equilibrium equations note. Analysis of continuous space frames by threedimensional. Now, the required equation to solve for the rotation. Draw bending moment and shear force diagrams for the plane frame. With this tool, it becomes easy to calculate moments without calculus or repetitive iterative calculations. Computer codes for the analysis of lattice structures. The center column, connected to the ridge point c, is incompressible. Structural design and inspection deflection and slope of beams by dr.