In this paper, an algorithm is presented for the optimum design of thr
ee-dimensional rigidly jointed frames which takes into account the non
linear response due to the effect of axial forces in members. The stab
ility functions for three-dimensional beam-columns are used to obtain
the nonlinear response of the frame. These functions are derived by co
nsidering the effect of axial force on flexural stiffness and effect o
f flexure on axial stiffness. The optimum design algorithm considers d
isplacement limitations and restricts combined stresses not to be more
than yield stress. It employs the optimality criteria approach togeth
er with nonlinear overall stiffness matrix to develop a recursive rela
tionship for design variables in the case of dominant displacement con
straints. The combined stress constraints are reduced into nonlinear e
quations of design variables. The algorithm initiates the optimum desi
gn at the selected load factor and carries out elastic instability ana
lysis until the ultimate load factor is reached. During these iteratio
ns checks of the overall stability of frame is conducted. If the nonli
near response is obtained without loss of stability, the algorithm the
n proceeds to the next design cycle. The method developed is applied t
o the optimum design of a number of rigid space frames to demonstrate
its versatility. (C) 1998 Elsevier Science Limited and Civil-Comp Limi
ted. All rights reserved.