The Answer
Dump trucks may get stuck in mud or snow. Pushing on the bed of the truck with another construction vehicle would likely damage the hinges or the hydraulic hoist that connect the bed of the truck to the chassis.
If you’ve ever driven behind a dump truck you’ve probably seen the words “DO NOT PUSH” emblazoned on the back. This raises the question of who would want to push a dump truck and why, and the related question, why not?
It is pretty common for dump trucks and other construction equipment to operate in muddy conditions. In the winter they also operate in snowy and icy conditions. This means that construction vehicles will occasionally get stuck.
Unlike cars, large construction vehicles aren’t going to get unstuck by people pushing on the bumper. This means that they’ll need a bit of a stronger push and another vehicle is the likely candidate for giving such a push.
A dump truck is made from two main parts – the chassis (the truck part) and the bed (the dumping part). These connections between these two parts are designed to be strong in supporting the weight of the load and lifting that load. They are not designed to withstand a horizontal shear force and these connections could break or bend under such loads.
Reddit user Nick explains thusly.
The bed of a dump truck is only secured by two hinges and a Hydraulic hoist. It is not designed to be pushed by a wheel loader bulldozer or other piece of equipment in the event it becomes stuck.
An aluminum bed could easily be crushed just from the extra force imposed upon the tailgate, And in the least case scenario would be severely misaligned thus enabling it to close securely and preventing a load from Leaking, and depositing into the roadway, etc. Also, a misaligned push could actually bend the frame of the truck ruining its capacity to be operated safely again.