3/8" glass isn't thick, for a tank that size it definitely requires bracing. A center brace however isn't the only option, most tanks utilize a euro style brace as shown below. If your tank has this then you should be fine, if not, some form of bracing should be added.
![](http://i1188.photobucket.com/albums/z414/mcaqua390g/Glass%20Build/DSC_5475.jpg)