Node b cannot move horizontally since it is restrained by members ab. Fixed end moments for a member ab with a length l and any given load the fixed end moments are given by. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. To compute a component of deflection by the method of virtual work, the designer applies a force to structure at the point and in the direction of the desired displacement. A simply supported prismatic beam ab carries a uniformly distributed load of intensity w. The force system created by the virtual loads is called. Apply a horizontal fictitious load p1 0 at b and replace the 84kn load by p2 so that differentiation of the total strain energy can be carried out with respect to p1 and. Determine the slope and deflection by using moment area method expected outcomes.
This method can be used to solve moments, deflections and slopes. Background theory beam deflections virtual work consider the following. General procedure of slopedeflection method of analysis. Determine the vertical and horizontal deflections at. Scan the beam and identify the number of a segments and b kinematic unknowns. For information on beam deflection, see our reference on. This method considers the deflection as the primary unknowns, while the redundant forces were used in.
The force is called the dummy loador the virtual load. The slopedeflection method for beams will be illustrated using the example structure shown in figure 9. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Nodes a and c are fixed and so do not have any degreesoffreedom dofs. Equilibrium equations end moments are expressed in terms of unknown rotation. Mechanics of materials chapter 6 deflection of beams. Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. Analysis of statically indeterminate structures by the. Serviceability deflection calculation deflection example. The important formulas that should be memorized in this method are.
Approximating realworld beam deflection newports maximum relative motion formula provides an excellent approximation of maximum worstcase table top deflection. This structure is 4 indeterminate, and so would be difficult to solve using the force method. This is a detailed example analyzing a statically indeterminate beam using slope deflection equations. Frames with sidesway civil engineering ce notes edurev is made by best teachers of civil engineering ce. 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. Application of slope deflection equations to statically indeterminate beamsindeterminate beams. If i 240 in4 and e 30,000 kipsin2, determine the horizontal displacement of joint b. This method is based on the following simplified assumptions.
This technical note explains and quantifies the relationship between maximum relative motion and actual beam deflection in realworld applications. P was defined as p i p i10 where i percentage of maximum load. Geometry of the structure, including shape and flexural rigidity of member. Deflection of blame is a common way in which we excuse ourselves. Dec 05, 20 assumptions in the slope deflection method. Shear and moment diagrams for a continuous beam the slopedeflection method is used to determine the shear and moment diagram for the beam shown below. This gives the deflection at all values of x and produces a maximum value at the tip of the cantilever when x 0, i. Degrees of freedom are treated as unknowns in slope deflection method.
There are many methods to find out the slope and deflection at a section in a loaded beam. In the slopedeflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. When autoplay is enabled, a suggested video will automatically play next. Example 92 determine the equation of deflection curve for a cantilever beam ab subjected to a uniform load of intensity q also determine b and b at the free end. Excessive deflection of a beam not only is visually disturbing but also may cause. The position of the maximum deflection is found out by equating the slope equation zero. The tables below give equations for the deflection, slope, shear, and moment along straight beams for different end conditions and loadings. While deflection is the translational movement of the beam from its original position. When a structural is loaded may it be beam or slab, due the effect of loads acting upon it bends from its initial position that is before the load was applied. Slope is the angle formed by the tangent of the curve to the horizontal axis. Determine the vertical and horizontal deflections at the point b of the truss shown. Part ii check the aci code crack width provisions at midspan of the beam.
Note that in the solution, for spans ab and cd the shorthand slopedeflection formula along with pinnedfixed fems are used. The basic assumption used in the slopedeflection method is that a typical member can. 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 nd deflection ppt free download as powerpoint presentation. This video sets up the slope deflection equations for an indeterminate frame. Displacement method of analysis slope deflection method. The same definition was applied to delta deflection or. Since none of the supports of the continuous beam translates, the chord rotations of the three members are zero. Calculating deflection by integration uniform load. Shear and moment diagrams for a continuous beam the slope deflection method is used to determine the shear and moment diagram for the beam shown below. A laser beam reflected in the mirror will be affected by two types of table top vibrational modes.
Example 1 determine the moments at b and d, then draw the moment diagram. The ultimate goal is to find the end moments for each member in the structure as a function of all of the dofs associated with both ends of the member. In unit load method, an unit load instead of p is applied at the point where the deflection is desired. The procedure is the same whether it is applied to beams or frames.
For example, building codes specify limits on deflections as well as stresses. Slope deflection examples slope deflection examples fixed. An important characteristic of the slope deflection method is that it does not become increasingly complicated to apply as the number of unknowns in the problem increases. 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. 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. The deflection will depend on the following factors. What is the difference between slope and deflection. Beam deflection formulae beam type slope at free end deflection at any section in terms of x maximum deflection 1. A simple setup illustrates the examples that follow. A segment is the portion of the beam between two nodes. In strain energy method, an imaginary load p is applied at the point where the deflection is desired to be determined.
Similarly dy 1 wx2 wl2 dx ei and produces a maximum value again when x 0. A comparison between results obtained from the hand solution and spslabspbeam software is provided to illustrate the features and capabilities of the spbeam and spslab software programs. Introduction slopedeflection method is the second of the two classical methods presented in this course. The basic assumption used in the slope deflection method is that a typical member can flex but the shear and axial deformation are negligible. This document is highly rated by civil engineering ce students and has been viewed 1480 times. Example 1 determine the moment at each joint of the battercolumn frame. So that the total deflection after 14 days will be. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. The ultimate goal is to find the end moments for each member in the structure as a function of all of the dofs associated with both ends.
Work examples on slopedeflection method of analysis. You can find comprehensive tables in references such as gere, lindeburg, and shigley. P is equated to zero in the final step and the deflection is obtained. Wood page 19 of 26 additional slope deflection insights. Now, the required equation to solve for the rotation. The slope deflection method sdm is usually used for determinate and indeterminate frame analysis. All the joints of the frame are rigid, distortion, due to axial and shear stresses, being very small, are neglected. Able to analyze determinate beam deflection and slope by moment area method. Identify all kinematic degrees of freedom for the given problem.
Cantilever beam concentrated load p at any point 2 2 pa ei. It means the beam is deflected from its original position it is called as deflection, a. Slope deflection method example structural analysis. Application of slopedeflection equations to statically indeterminate beamsindeterminate beams. Note that in the first example, the pinned support conditions for the columns were taken advantage of and the shorthand slopedeflection formula is used in calculating the mba and mcd. In the book, the theory and practice of modern framed structures, written by j. Substitute moment values into the deflection expression and integrate to solve for the deflection at the point of interest. Assume a and c are pinned and b and d are fixed connected. Degrees of freedom are treated as unknowns in slopedeflection method. Wood page 19 of 26 additional slopedeflection insights. Structural design and inspection deflection and slope of beams by dr. Deflection of beams study notes for mechanical engineering. Slope deflection examples slope deflection examples. Determine the reactions, draw the moment curves for the members, and sketch the deflected shape.
Determine the moments at the ends of each member of the frame. In the slope deflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. Analysis of beams slopedeflection method general procedure. Degrees of freedom joints c, d and e are free to rotate. However, the tables below cover most of the common cases. Deflection is defined as the vertical displacement of a point on a loaded beam. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4.
The maximum deflection occurs where the slope is zero. Dec 04, 2012 this is a detailed example analyzing a statically indeterminate beam using slope deflection equations. Structural deflectionsvirtual workunit load method dr. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. Cantilever beam concentrated load p at the free end 2 2 pl ei.
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