"tall and sturdy, robust," originally applied to women, 1650s, from present participle of strap (v.), apparently in the sense of "to beat with a strap." Compare similar senses of whopping, spanking, bouncing and other present-participle adjectives of violent action expressing something large in size.
a strapping boy of eighteen
strangulation
strap
strap-hanger
strapless
strapline
strapping
strappy
strata
stratagem
strategic
strategist