We have obtained deep near-infrared K(s)-band William Herschel Telescope observations of a sample of 15 nearby spiral galaxies having a range of Hubble types and apparent bar strengths. The near-infrared light distributions are converted into gravitational potentials, and the maximum relative gravitational torques due to the bars and the spirals are estimated. We find that spiral strength, Q(s), and bar strength, Q(b), correlate well with other measures of spiral arm and bar amplitudes and that spiral and bar strengths also correlate well with each other. We also find a correlation between the position angle of the end of the bar and the position angle of the inner spiral. These correlations suggest that the bars and spirals grow together with the same rates and pattern speeds. We also show that the strongest bars tend to have the most open spiral patterns. Because open spirals imply high disk-to-halo mass ratios, bars and spirals most likely grow together as a combined disk instability. They stop growing for different reasons, however, giving the observed variation in bar-spiral morphologies. Bar growth stops because of saturation when most of the inner disk is in the bar, and spiral growth stops because of increased stability as the gas leaves and the outer disk heats up.