Looking at the map below, and from north to south: highways 4 (through the Delta region), 84 (between 280 and the coast), 35 (especially the southern end), 9 (all but the southernmost end), and 130 (all of it) are unsuitable for trucks.
Highways 116, 121, 12, 1, 92, 238 (from Fremont to Sunol/680), and 17 are often narrow and winding, but trucks do use them.
