Taggart, driving a 2002 Dodge Stratus, was in the fast lane when a car in the middle lane started to drift toward her, apparently trying to pass the car in front of it, Folk said.
Taggart swerved left and hit the cable barrier, which separates northbound and southbound traffic, he said.
A post holding the cable was knocked down, loosening the cable, Folk said. The cable then slid over Taggart's car, which came to rest in a northbound lane, he said.
Taggart's car was damaged on the front, hood and side rear, Folk said. Its air bag did not deploy, but Taggart was wearing her seat belt, he said.
She was shaken up, but otherwise not injured, Folk said.
"Had it been a guardrail, I don't feel she would have gone all the way through," Folk said. "The only thing it (a cable barrier) does is keep us from crossing the interstate in an emergency situation."
Strauss has asked the governor, highway officials and local legislators to find a way to put up concrete barriers instead of the cable barrier.
The cable installation began when the interstate section along Martinsburg was expanded from four to six lanes.
Initial plans called for no barrier at all after the widening, but after local officials and residents voiced concern, highways officials announced plans to install the cable system, Strauss said.
Sgt. Deke Walker, of the West Virginia State Police, said he did not want to be "the one who second guesses the Department of Highways."
He said, however, a traditional guardrail, or ideally, concrete barriers, would have been a better option than the cable barrier.
"Obviously it is not the best system that could be put up," Walker said.
Although he could not recall any serious accidents involving the cable barrier, Walker said he has driven by it and seen cables down more than once.
If the cable did not stop a passenger car like the Stratus, a sport utility vehicle or pickup truck probably would go right through the wire, Walker said.
Clevenger said cable was selected because it is less expensive to install than concrete barriers and makes handling drainage cheaper.
In addition, cable barriers tend to do less damage to cars than concrete barriers, he said.
Crash tests indicate the cable has a "deflection" range of somewhere between 11 to 14 feet, space in which one's vehicle is supposed to hit the cable and then rebound backward, Clevenger said.
The median is wide enough that a car would not be deflected back into traffic, Clevenger said.
"We wouldn't have put it up if it didn't meet safety requirements," Clevenger said.
Cable barriers are in place in one other spot in the state - an eight-mile stretch of Interstate 64 in Cabell County, Clevenger said.
Along Interstate 81 Tuesday afternoon, motorists could see that some cable posts and cable had been knocked down. Taut in some spots, in other areas the cable was loose, drooping from post to post.
Where construction continues, concrete barriers, orange barrels or no barriers are in place.