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. In the slope deflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements. Using the slopedeflection method determine the end moments of the members and draw the shear force and bending moment diagrams of the frame. A segment is the portion of the beam between two nodes. It means the beam is deflected from its original position it is called as deflection, a. Deflection of beams study notes for mechanical engineering. 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.
The important formulas that should be memorized in this method are. P is equated to zero in the final step and the deflection is obtained. Structural deflectionsvirtual workunit load method dr. The same definition was applied to delta deflection or. Example 1 determine the moment at each joint of the battercolumn frame. Determine the moments at the ends of each member of the frame.
The slope deflection method sdm is usually used for determinate and indeterminate frame analysis. Dec 04, 2012 this is a detailed example analyzing a statically indeterminate beam using slope deflection equations. Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4. 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. You can find comprehensive tables in references such as gere, lindeburg, and shigley. Determine the reactions, draw the moment curves for the members, and sketch the deflected shape.
This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Introduction slopedeflection method is the second of the two classical methods presented in this course. Cantilever beam concentrated load p at the free end 2 2 pl ei. 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 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. Slope deflection examples slope deflection examples. The force system created by the virtual loads is called. Beam deflection formulae beam type slope at free end deflection at any section in terms of x maximum deflection 1.
Identify all kinematic degrees of freedom for the given problem. Degrees of freedom joints c, d and e are free to rotate. Analysis of beams slopedeflection method general procedure. This gives the deflection at all values of x and produces a maximum value at the tip of the cantilever when x 0, i. Displacement method of analysis slope deflection method. Cantilever beam concentrated load p at any point 2 2 pa ei. Serviceability deflection calculation deflection example. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. Determine the slope and deflection by using moment area method expected outcomes. Mechanics of materials chapter 6 deflection of beams. 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.
General procedure of slopedeflection method of analysis. 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. A cantilever beam is subjected to a concentrated load w at the free end, it is required to determine the deflection of the beam. If i 240 in4 and e 30,000 kipsin2, determine the horizontal displacement of joint b. Dec 05, 20 assumptions in the slope deflection method.
The deflection will depend on the following factors. The tables below give equations for the deflection, slope, shear, and moment along straight beams for different end conditions and loadings. Substitute moment values into the deflection expression and integrate to solve for the deflection at the point of interest. 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 deflection examples slope deflection examples fixed. Similarly dy 1 wx2 wl2 dx ei and produces a maximum value again when x 0. This structure is 4 indeterminate, and so would be difficult to solve using the force method. Able to analyze determinate beam deflection and slope by moment area method. Analysis of statically indeterminate structures by the. In the slopedeflection method, the relationship is established between moments at the ends of the members and the corresponding rotations and displacements.
This video sets up the slope deflection equations for an indeterminate frame. In unit load method, an unit load instead of p is applied at the point where the deflection is desired. Wood page 19 of 26 additional slopedeflection insights. In the book, the theory and practice of modern framed structures, written by j. Equilibrium equations end moments are expressed in terms of unknown rotation. For example, building codes specify limits on deflections as well as stresses. The slopedeflection method for beams will be illustrated using the example structure shown in figure 9. Part ii check the aci code crack width provisions at midspan of the beam. Degrees of freedom are treated as unknowns in slope deflection method.
A simple setup illustrates the examples that follow. Degrees of freedom are treated as unknowns in slopedeflection method. However, the tables below cover most of the common cases. This method considers the deflection as the primary unknowns, while the redundant forces were used in. 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. Example 1 determine the moments at b and d, then draw the moment diagram. Background theory beam deflections virtual work consider the following.
Structural design and inspection deflection and slope of beams by dr. Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. All the joints of the frame are rigid, distortion, due to axial and shear stresses, being very small, are neglected. When autoplay is enabled, a suggested video will automatically play next. A simply supported prismatic beam ab carries a uniformly distributed load of intensity w. Note that in the solution, for spans ab and cd the shorthand slopedeflection formula along with pinnedfixed fems are used. Wood page 19 of 26 additional slope deflection insights. Since none of the supports of the continuous beam translates, the chord rotations of the three members are zero. Application of slopedeflection equations to statically indeterminate beamsindeterminate beams. P was defined as p i p i10 where i percentage of maximum load. The position of the maximum deflection is found out by equating the slope equation zero. 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. Slope is the angle formed by the tangent of the curve to the horizontal axis.
Calculating deflection by integration uniform load. Now, the required equation to solve for the rotation. Deflection is defined as the vertical displacement of a point on a loaded beam. This is a detailed example analyzing a statically indeterminate beam using slope deflection equations.
Application of slope deflection equations to statically indeterminate beamsindeterminate beams. Geometry of the structure, including shape and flexural rigidity of member. Slope deflection method example structural analysis. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. A laser beam reflected in the mirror will be affected by two types of table top vibrational modes. This technical note explains and quantifies the relationship between maximum relative motion and actual beam deflection in realworld applications. 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.
For information on beam deflection, see our reference on. This document is highly rated by civil engineering ce students and has been viewed 1480 times. So that the total deflection after 14 days will be. Excessive deflection of a beam not only is visually disturbing but also may cause. Determine the vertical and horizontal deflections at the point b of the truss shown. Approximating realworld beam deflection newports maximum relative motion formula provides an excellent approximation of maximum worstcase table top deflection. Nodes a and c are fixed and so do not have any degreesoffreedom dofs. Work examples on slopedeflection method of analysis. While deflection is the translational movement of the beam from its original position. The procedure is the same whether it is applied to beams or frames. The maximum deflection occurs where the slope is zero. Fixed end moments for a member ab with a length l and any given load the fixed end moments are given by.
In strain energy method, an imaginary load p is applied at the point where the deflection is desired to be determined. 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. What is the difference between slope and deflection. Scan the beam and identify the number of a segments and b kinematic unknowns. Slope nd deflection ppt free download as powerpoint presentation. This method can be used to solve moments, deflections and slopes. 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. There are many methods to find out the slope and deflection at a section in a loaded beam. Assume a and c are pinned and b and d are fixed connected.
The basic assumption used in the slope deflection method is that a typical member can flex but the shear and axial deformation are negligible. 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. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. 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. Determine the vertical and horizontal deflections at. Node b cannot move horizontally since it is restrained by members ab. Frames with sidesway civil engineering ce notes edurev is made by best teachers of civil engineering ce. The force is called the dummy loador the virtual load. This method is based on the following simplified assumptions.
691 646 1276 620 817 562 708 645 1525 883 627 43 711 536 887 244 607 342 995 1268 1284 1419 513 198 154 1162 976 975 1131 1025 1035 961 491 561 224 632 611 1033 1402 863 1445