Deflection method previously we have discussed forceflexibility methods of analysis of statically indeterminate structures. Apter thirteen v a virtual worl method using virtual work method it wt lel m be equal to the virtual intemal bending moment acting on the nlml length dx, it will produce a virtual intemal work as it undergoes the real in lg. According to unit load method the deflection of a joint of truss is given by the following formula. Structural analysis for truss deflections using virtual work method example 2 calculate the vertical displacement at joint c if a 5 kn force is applied to joint c of the truss.
Method of consistent deformations force method 6 classes general procedure. Determine the values heights h i on the virtual moment diagram m at the centroids of the moments due to the real loads. The deformations or movements of a structure and its components, such as beam ends, truss joints etc. Method of virtual work for beams to find a deflection apply virtual force p at that point and in that direction. Method of virtual force unit load method external work must equal the internal strain energy. Newtons laws can be linked to the energy methods i. The unit load method when the principle of virtual work is used to calculate the displacement d. Deflections using energy methods purdue university. Thus the principle has more general application than most other methods of analysis. Deflection of beam theory at a glance for ies, gate, psu.
Deflections method of virtual work deflection of a truss. Nov 06, 2016 note so far virtual work has been produced by actual forces in equilibrium moving through imposed virtual displacements base on pvw, we can alternatively assume a set of virtual forces in equilibrium moving through actual displacements application of this principle, gives a very powerful method to analyze indeterminate structures 20. Deflections method of virtual work vertical deflection. Book on structural analysis chapter on virtual work method. Optimising structures using the principle of virtual work. Here is a typical example of how we can apply the principle of virtual work to. Therefore, the deflection of a truss due to any condition that causes a change in length of the members can be. Calculate the slope and deflection at various locations in a beam using the conjugatebeam method. The external virtual work done by the unit load is 1.
To find a sloperotation apply virtual moment m at that point and in that direction. Conjugate beam method the conjugatebeam method was developed by h. Method of virtual work structural analysis youtube. The virtual work method can be used to determine the deflection of trusses. By setting up an expression for the bending moment in a member because of the applied loads m, in terms of the applied loads on a beam and x, and integrating this expression twice, an equation can be obtained for the deflection of the beam.
In force method,theunknown redundant forces are determined first by solving the structures compatibility equations. Analysis of indeterminate structures by the slopedeflection method will be developed using the principles previously developed for deflection calculations. Unlike the moment area method and the conjugate beam method, it can be used to find the deflections of trusses, beams or frames or, in fact any mechanical system. Deflections using energy methods conservation of energy.
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. If you have never used the method of virtual work or need a refresher this is a good place to start. Member fixed end actions for uniform and concentrated load. Work done by external forces on a material point or a structure is. Nov 25, 2012 brief explanation of the principle of virtual work and a description of the process to calculate deflections in structures using the method of virtual work aka, the unit load or unit force method. Virtual work provides a basis upon which vectorial mechanics i.
Virtual work allows us to solve determinate and indeterminate structures and to calculate their deflections. Therefore, apply a unit load at point d in the horizontal direction. The member selection method is based on the principle of virtual work, and is called the virtual work optimisation v wo method. Part 2 sa29 fixedend moments sa30 slope deflection. Compute the work done when y and are increased a positive infinitesimal amount. Careful it is the virtual forcemoment time the actual displacement flae for trusses, and mei for beams. Structural deflections virtual workunit load method dr. Williot mohr diagram method virtual work method or unit load method the deflection.
Slope deflection method overview sa27 slope deflection equations. Beams and frames cv l cv dx ei m m 0 1 real load 1 r a r b x 1 x 2 r b r a x 1 x 2 b r b x 2 v 2 m 2 x 1 r a v 1 m 1. Virtual work methods since structural analysis based on finite element methods is usually based on a potential energy method, we will tend to use virtual work methods to compute beam deflections. Material stress strain relationships are needed only to calculate deflections. Pdf comments on the understanding of the virtual work method. In the design of steel structures, reinforced concrete and prestressed concrete, the study of structural analysis is a crucial stage in its design, since the axial forces, shear forces and moments are those that govern the design of rigid frames and for the case of beams. Y civil engineering department, jordan university of science and technology, irbid 22110. Sate principle of virtual displacement and principle of virtual forces. Energy methods are based on the principle of conservation of energy. These restrictions are lifted in the present paper. Approaches for modeling structures will be illustrated, including continuous beams and multistory sway and nonswayframes. We know from the principle of virtual work for trusses that the deflection can be calculated by the equation with n equal to the virtual force in the member and equal to the change in length of the member.
Virtual work is the work done by a real force acting through a virtual displacement or a virtual force acting through a real displacement. This method is quite limited in application since it is applicable only to deflection at a point of concentrated force. Comments on the understanding of the virtual work method numayr s. Slopedeflection method overview sa27 slopedeflection equations. Drive an expression of calculating deflections of structure using unit load method. Determine the slope and deflection by using unit load method expected outcomes.
State the difference between strain energy method and unit load method in the determination of deflection of structures. Structural deflectionsvirtual workunit load method dr. The following example utilizes the superposition method to determine the deflection of a frame. Virtual work allows us to solve determinate and indeterminate structures and to. Sidesway and nonsidesway frames will be presented and discussed. Determine the displacement and slope at point a on the beam i 1,000 in4, and e.
For determinate structures, the force method allows us to find internal forces using equilibrium i. Virtual work is the work done by a virtual force acting on the body moving through the actual displacements. The following paragraphs briefly describe this concept. This process is experimental and the keywords may be updated as the learning algorithm improves. Deflections method of virtual work rotations by the. Force method for analysis of indeterminate structures. Beams frames department of civil 3 virtual unit load c a b w c a b method of virtual work. Feb 01, 2016 structural analysis virtual work method 1.
Q4 use the unit load method to calculate the deflection at the free end of the cantilever beam abc. The work in virtual work clearly implies energy, since work is a form of energy. First we will calculate member forces n due to the real loading and then n due to unit virtual load applied at the point of required deflection in this case joint e. A derivation of the virtualwork expressions for linear structures is given in the following section. Virtual work 3rd year structural engineering 200910 colin caprani. Deflection is caused by many sources, such as, loads, temperature. The displacement at point c due to bending moment work and axial force. Virtual work done by a system of forces p b while undergoing. The information on this website is provided without warantee or guarantee of the accuracy of the contents. In strain energy method, an imaginary load p is applied at the point where the deflection is. The present paper demonstrates an alternative method for calculating the linear elastic deflection of statically indeterminate structures using the virtual work approach. Indeterminate beam analysis by virtual work method. Beams and frames theory of structure i department of civil 2 contents method of virtual work.
This means we solve a geometry problem through equilibrium as shown below. The virtual work or unitload method can be used to obtain the displacement of a single point in a beam. However, in contrast to conventional applications, the internal action state under applied loading is not required to be known. The virtual work method, also referred to as the method of virtual force or unitload method, uses the law of conservation of energy to obtain the deflection and. Lagrangian methods which are the basis for finite element analysis and advanced mechanics of materials. The method of virtual work, or sometimes referred to as the unitload method, is one of the several techniques available that can be used to solve for displacements and rotations at any point on a structure. Deflections method of virtual work horizontal deflection of a frame superposition. Virtual work is perhaps the most useful and widely applicable of the methods described in this chapter. A virtual displacement is any displacement consistent with the constraints of the structure, i. Application of principle of virtual work to find displacement in statically indeterminate structures. M are generally employed for a body whose equilibrium position is known or specified for problems in which bodies are composed of interconnected members that can move relative to each other, various equilibrium configurations are possible and must be examined. In this case, we want to know the horizontal deflection at point d. Some of the methods used in this chapter include the method of double integration, the method of singularity function, the momentarea method, the unitload method, the virtual work method, and the energy methods. Deflection of truss using virtual work method, structural.
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. The choice of a particular method is dependent on the nature of the loading and the type of problem being solved. Principle of virtual work truss virtual work virtual work is a procedure for computing a single component of deflection at any point on a structure. Deflection of beam theory at a glance for ies, gate, psu 5. Principle of virtual work in structural analysis 1.
Pdf students studying elementary structural analysis usually experience some. Virtual work is the work done by the actual forces acting on the body moving through a virtual displacement. Virtual work method of virtual work previous methods fbd. This means we solve an equilibrium problem through geometry. In addition, when evaluating the deformation of a frame structure, you may have to consider both bending and axial internal force components. The indeterminate beam will be analyzed by virtual work method c a b d p let.
Virtual work energy method external work unit load vertical deflection these keywords were added by machine and not by the authors. Draw the shearforce and bendingmoment diagrams for the real beam. The colors of the loads and moments are used to help indicate the contribution of each force to the deflection or rotation being calculated. Structures and structural members deform under load, which means that if we.
Applying the virtual work equations to a frame structure is as simple as separating the frame into a series of beams and summing the virtual work for each section. Jun, 2016 structural analysis for truss deflections using virtual work method example 2 calculate the vertical displacement at joint c if a 5 kn force is applied to joint c of the truss. Use the portal method to calculate the corresponding i applied loads p 1 and p 2, ii column bending moments, iii beam axial forces. Book on structural analysis chapter on virtual work. Apply the virtual load at the point of interest in the desired direction. The theory that supports calculating deflections using virtual work. Structural design and inspection principle of virtual work by dr. Ei 0 1 extlitlitldti thb ithttdditi fternal virtual unit load acting on the beam in the stated direction of. Brief explanation of the principle of virtual work and a description of the process to calculate deflections in structures using the method of virtual work aka, the unit load or unit force method. This is needed to carry out the integration by using the equation given in the introduction, heights h i and locations by the cantilever method.
The following example illustrates the steps to be followed to calculate deflections of statically determinate structures using superposition and the method of virtual work. Method of virtual work for beams example 1 part 12 structural. The figure below shows the shear forces kips in the interior columns of a twostoried frame. Virtual work there are two ways to define virtual work, as follows. Effects of support settlement movement, temperature change, and fabrication errors. Deflections method of virtual work horizontal deflection. Equilibrium statics compatibility geometry principle of virtual forces external virtual work internal virtual work virtual force e. Also, if more than one force is applied to the system, a solution becomes impossible since there will be many deformations. To find a specific displacement, apply a virtual force p at that point. Application of principle of virtual work to find displacement in.