You can do it, but it’s stupid. At least for the rest of the road users.
The topic of “safety” is often brought up here. Safety in the sense that people driving their trucks down the middle of a construction site believe they are doing the public a favor.
But let’s take a closer look at this.
Sure, if you drive down the middle, you don’t risk having someone next to you whom you might accidentally hit with a sudden swerve.
However, from my perspective, driving in the middle actually endangers following traffic more. You force others to have to drive side-by-side within a construction site. Specifically, those behind you.
Typically, lanes in a construction site are wide enough that trucks can stay well within their lane. Sure, a swerve might happen occasionally, but it’s something that can usually be corrected quickly with a steering adjustment.
Therefore, stop driving down the middle; it’s not safe for everyone and is also illegal anyway.

