This paper gives a new formulation to synthesize load-responsive structures through shape morphing. The design method is based on the minimization of the whole-life energy, which comprises an embodied share in the material and an operational share for adaptation. Target shapes that counteract the effect of the design loads are obtained through geometry and sizing optimization. Adaptation through shape morphing enables effective stress redistribution so that the design is not dominated by peak loads with long return periods. Material utilization is maximized, and therefore embodied energy is significantly reduced. The geometry is controlled through length changes of optimally-placed linear actuators. The actuator commands are computed through minimization of the operational energy to satisfy safety and serviceability criteria. Minimum energy solutions are obtained through a univariate optimization process in which embodied and operational energy minimization are nested. Numerical benchmarks between adaptive and mass-optimized passive solutions are provided on a truss bridge and multistory frame configurations. Parametric studies show that mass and energy savings are significant for slender structures and when the live load is dominant over the permanent load. Generally, larger shape bounds result in a greater reduction of mass and embodied energy at the cost of a larger operational energy.