The Answer: He couldn't. Without a reinforced skeletal structure, his body should crumple or his limbs should be torn from their far less durable organic host. The televised series, The Six Million Dollar Man does not address this egregious error in both physical capabilities of a human body, nor in the capabilities of physical science considered possible in that era.
The television series The Six Million Dollar Man was based on a book called Cyborg back in 1972. The novel does not talk in great detail about the surgery and the television show also does a significant amount of hand-waving regarding the cybernetic enhancements to Steve Austin and the amount of physical trauma such a series of modifications would require.
Let's assume that it was physically possible (baring the issues of nerve replacement, nerve connectivity, organic to inorganic interface, inorganic rejection and other like medical issues).
- His left and right legs (which probably meant his hip bones as well)
- One of his arms (in the book, his left, the TV series, his right)
- His eye (book, camera prosthetic, still blind, TV series, vision enhanced)
- At least some parts of his nervous system had to be augmented to allow the integration of all of his limbs to his mental control.
Cyborg version of Steve Austin - In the book, Steve Austin's bionic limbs were more powerful than his original limbs but did not have the range of capabilities the television series offered. His legs gave him greater running speed and even greater running endurance. The book made his arm an armored battering ram used to knock down doors, deflect bullets and crush human skulls with ease. He did not use it to lift extraordinary weights with any regularity. Cyborg, offered a superspy with superhuman strength with limited applications, tireless fighting machine who was ruthlessly efficient and capable of doing things normal spies would be challenged to do.
Television Series: The Six Million Dollar Man - The TV version of Steve Austin was physically superior to even the book version of the character. It showed Austin regularly (with requisite sound effect) super-leaping twelve foot fences and (in slow motion) running speeds upwards of forty-five to fifty miles per hour. The TV series was far more generous and allowed him numerous feats of lifting that would seem incongruous with having ONLY a bionic arm. The TV series also did not have Steve use his bionic limb to damage people if he didn't have to. He would hit them but rarely kill them. In the TV series, we have the same spy, much less ruthless, with an emphasis on the science fiction aspects whose bionics were made more powerful without explaining how Steve Austin could perform those feats as easily as he did.
Media Creep: This is a sign of how books are translated into other media without having a corresponding analysis to be sure of internal continuity. His powers were increased without understanding of the potential physical implications. (Science fiction in the 1970's required a strong suspension of belief, likely because science literacy was less common then.)
Possible Explanation: If I were to hazard a reasonable means of explaining, the television version of the Bionic Man would have had to had additional reinforcement, both to deal with the shock of running at 40-50 miles per hour and as a back support whenever he used his arm to lift weights that should tear the arm from his body.
The simplest option would be to augment his skeletal structure, particularly his spinal column, and rib cage with both synthetic muscle tissues designed particularly to reduce stress, wear on his body, support for his organs and to reinforce his bones with carbon reinforced polymers. Both of these technologies would be reasonable, considering the strength of his limbs, their incredibly tiny power supplies and their overall durability.
The nanotube treatment could require reapplication, which might explain why he would need to stay under government care for as long as he wanted to maintain his bionic limbs. Rejection must have already been handled because his limbs were seamlessly integrated into his nervous system and in the case of the TV series, into his brain stem's visual cortex. While nanotechnology was not part of the story origin, it would make sense since any other technology would require the removal or replacement of his spinal column, leaving very little of the main other than his internal organs, his brain and his left organic arm.
The television cyborg was far more sophisticated than the original story's version and the technology required was certainly more advanced as well.