Deflections method of virtual work deflection of a truss. Newtons laws can be linked to the energy methods i. Method of virtual work truss example part 12 structural. Principle of virtual work for a prismatic, elastic truss member. Virtual work allows us to solve determinate and indeterminate structures and to calculate their. Virtual work is the work done by the actual forces acting on the body moving through a virtual displacement. In this lesson, the unit load method is employed to calculate displacements. Using the method of section the virtual moment expressions are.
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. Virtual work is a fundamental theory in the mechanics of bodies. 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. To find a specific displacement, apply a virtual force p at that point. 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. Deflections using energy methods purdue university. The virtual work method can be used to determine the deflection of trusses.
Deflections since the virtual load is a unit load the previous expression reduces to. Types of internal real displacements of individual members external loading. Wprea wl ork done by p up real strain energy stored in ab due to p wp up truss virtual work now consider the forces and displacements produced by the virtual load, as shown below. Conversely, a particle is only in equilibrium if the virtual work done during a virtual displacement is zero. This means we solve an equilibrium problem through geometry.
Unlike the moment area method and the conjugate beam method, it can be used to. Truss virtual work virtual work is a procedure for computing a single component of deflection at any point on a structure. 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 calculated. The method of virtual work can be used to determine the displacement of a joint on a truss which is subjected to an external loading, temperature change, or fabrication errors. Computation of deflection using principle of virtual work pvw. The work in virtual work clearly implies energy, since work is a form of energy. Consider the method of virtual work applied to onebar truss, as shown below. Structural analysis for truss deflections using virtual work method example 1 find the vertical displacement at joint c of the steel truss. Virtual work there are two ways to define virtual work, as follows. Due to the conversation of energy an equivalent quantity of. Virtual work provides a basis upon which vectorial mechanics i. Truss analysis using method of joints is greatly simplified if. To compute a component of deflection by the method of virtual work the designer applies a force to of virtual work, the designer applies a force to.
Civl 3121 virtual work for trusses 14 medeek design. Example problem showing how to use the method of virtual work to calculate deflections in a statically determinate truss structure. Deflection of truss using virtual work method, structural. In a, the roller at a allows free rotation with no deflection while the. Virtual work is perhaps the most useful and widely applicable of the methods described in this chapter. W drea wl ork done by q u real strain energy stored in ab due to q wd ud truss virtual work now consider the forces and. As the structure deforms under the actual loads, external virtual work wqis done by the virtual loads as they move through real displacements.