The paper presents some approximate solutions for the time-dependent a
nalysis of composite steel-concrete beams with flexible shear connecto
rs. These permit evaluating the migration of the stresses from the con
crete slab to the steel beam and the increment of the deflections, whi
ch occur gradually with time as a result of creep and shrinkage of the
concrete part. The mathematical formulation of this problem, which in
volves a coupled system of three equations, with two being integral-di
fferential-type equations, is reduced to a system of ordinary differen
tial equations by applying the algebraic methods (age-adjusted-effecti
ve-modulus, effective-modulus, and mean-stress methods). The simplific
ations introduced by these methods permit obtaining solutions in close
d form, which can be useful for practical applications. The accuracy o
f the numerical results is successively estimated by comparing these v
alues with those of the exact numerical solution, obtained by employin
g the numerical algorithm proposed elsewhere using the numerical step-
by-step procedures of the general method.