principle of virtual work structural analysis examples

These forces and virtual displacements must satisfy the principle of conservation of energy i.e. While the body is displaced, the real forces acting on the body move through these displacements.

Let the body undergoes to a set of compatible virtual displacement δD.These displacements are imaginary and fictitious as shown by dotted line. Further, consider a small element within the structural system and stresses on the surfaces caused by the P forces are shown in Figure 4.11(b) and referred as σ p.

Simplified PVW for beams and frames using multiplication of bending moment diagram.Ĭonsider a structural system subjected to a set of forces (P 1,P 2,P 3.referred as P force) under stable equilibrium condition as shown in Figure 4.11(a).

Application of PVW to beams and frames.

Computation of deflection using principle of virtual work ( PVW ).

Obtain the vertical deflection at point C due to the externally applied load (AE = constant). N = axial load in member i due to externally applied loadĪ truss is loaded as shown below. N = axial force in member i due to virtual unit load The summation of the deflection of the individual members using the formula below gives the deflection of the roof truss at the point of interest. The truss is re-analysed for the axial forces in the members due to the virtual unit load. The direction of the unit load should be in the same direction with where the deflection is sought. Subsequently, the external forces are removed and replaced with a unit virtual load at the node where the deflection is to be obtained. In the virtual work method, the truss is analysed for the axial forces due to the externally applied load. In this article, we are going to explore how to determine the deflection of trusses using the virtual work method (unit load method). The principle of virtual work can be used to compute the maximum deflection of the truss, which is then compared to the allowable deflection. For bridges, AASHTO design code states that the maximum deflection of a truss bridge due to live load should not exceed span/800. On the other hand, a span to depth ratio of 15 is often found adequate for all practical purposes. The deflection of roof trusses is often limited to span/240.

Principle of virtual work structural analysis examples