ABSTRACT
The principle of virtual work, proposed in Section 8.4 in the context of 3D solids, may be extrapolated, following a similar line of demonstration, to 1D and 2D solids. As regards rectilinear beams, it is sufficient to substitute Equation 8.23 with
= − ∂∫([ ]*{ }) { }T dη 0
(12.1)
whereby, instead of Equation 8.24, we obtain
L Q z QF a b l
= ∂ −∫{ } [ ]{ } [{ } { }]T Tdη η 0
0 (12.2)
0 and l being the coordinates of the beam ends. We then obtain the equation of the principle of virtual work for a rectilinear beam, sub-
jected to loads distributed over the span and to loads concentrated at the ends,
{ } { } { } { } [{ } { }]Q q z z Qa b l
0 ∫ ∫= + η η (12.3)
where, adopting the same nomenclature used in Section 10.3, {Qa} is the vector of the static characteristics, {qb} is the vector of deformation characteristics, {ℱa} is the vector of the distributed forces and {ηb} is the displacement vector.
