The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded cylindrically curved shell structure subjected to combined mechanical and thermal loading conditions. This approach yields the transverse shear and normal stresses in the adhesive, as well as the membrane stress resultants and bending moments in the adherends. The solution method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. This approach presents a rapid-solution alternative to the finite element method. The applicability of the present method is demonstrated by modeling a cylindrical component of a rigidizable/inflatable (RI) truss structure as a tubular bonded lap-joint subjected to uniaxial tension or torsion loading along with environmental temperature changes. The steep variation of both peeling and shearing stresses near the adhesive edges is successfully captured.