Despite the abundance of studies on the control of standing balance, insights about the roles of biomechanics and neural control have been limited. Previous work introduced an analysis combining the direction and orientation of foot-ground forces. The "intersection point" of the lines of actions of these forces exhibited a consistent pattern across healthy, young subjects when computed for different frequency components of the center of pressure signal. To investigate the control strategy of quiet stance, we applied this intersection point analysis to experimental data of 15 healthy, young subjects balancing in tandem stance on a narrow beam and on the ground. Data from the sagittal and frontal planes were analyzed separately. The task was modeled as a double-inverted pendulum controlled by an optimal controller with torque-actuated ankle and hip joints and additive white noise. To test our prediction that the controller that minimized overall joint effort would yield the best fit across the tested conditions and planes of analyses, experimental results were compared with simulation outcomes. The controller that minimized overall effort produced the best fit in both balance conditions and planes of analyses. For some conditions, the relative penalty on the hip and ankle joints varied in a way relevant to the balance condition or to the plane of analysis. These results suggest that unimpaired quiet balance in a challenging environment can be best described by a controller that maintains minimal effort through the adjustment of relative ankle and hip joint torques. NEW & NOTEWORTHY This study explored balance control in humans during a challenging task using the novel intersection point analysis, based on foot-ground force direction and point of application. Experimental data of subjects standing on a narrow beam in tandem stance were compared with modeling results of a double-inverted pendulum. The analysis showed that individuals minimized effort by adjusting ankle and hip torques, shedding light on the interplay of biomechanics and neural control in maintaining balance.