Was Jesus crucified naked? Wikipedia's article on crucifixion says


  While a crucifixion was an execution, it was also a humiliation, by
  making the condemned as vulnerable as possible. Although artists have
  traditionally depicted the figure on a cross with a loin cloth or a
  covering of the genitals, the person being crucified was usually
  stripped naked.


Is there a scholarly consensus that Jesus was also crucified naked? 

How have Christian traditions and scholars explained this?
He most likely was crucified naked - this is consistent with the biblical narrative of the guards casting lots for his garment and with standard historical practice. 

In the paintings, the artists wanted to preserve some of the dignity and not turn the Lord's body into something that puerile youngsters might be titilated by. It is a condescension to the viewer, intentionally not in accord with the scriptures. 

He was naked on the cross - that was part of the shame of crucifixion. 

As J. Vernon McGee (Thru the Bible) says:


  He was crucified naked. It is difficult for us in this age of nudity and pornography to comprehend the great humiliation He suffered by hanging nude on the cross. They had taken His garments and gambled for ownership. My friend, He went through it all, crucified naked, that you might be clothed with the righteousness of Christ, and so be able to stand before God throughout the endless ages of eternity.