The Web Between the Worlds — Charles Sheffield

Rob Merlyn was the best engineer who had ever lived. That was why Darius Regulo, "The King of Space," had to have Rob for the most spectacular construction project in the history of the human race--even though Rob was a potentially fatal threat to Darius's power...

Thus begins a breakthrough novel, written by the President of the American Astronautical Society, about an idea whose time has come: a shimmering bridge between earth and space, a veritable beanstalk that mankind will climb to the stars!