If your vehicle is showing burning smell from under the hood after steering heavily, here are the most likely causes and the parts you'll need to fix each one.
Heavy steering puts maximum load on the power steering pump pulley. If the belt driving the pump is worn, loose, or contaminated with fluid, it will slip under this load and create a burning rubber smell.
High pressure generated during heavy steering maneuvers can force fluid out of degraded hoses or loose fittings. This fluid drips onto the hot engine block or exhaust, creating an acrid, burning chemical smell.
If the power steering fluid was recently topped off and spilled, or overfilled causing it to vent out of the reservoir cap under heavy load, the excess fluid will burn off on hot engine components.
Internal friction from a failing pump bearing or running the system with low fluid causes the pump to overheat severely under heavy steering loads, burning the residual fluid or scorching the belt.
On modern vehicles with electric power steering, excessive lock-to-lock turning (like tight parking maneuvers) can overwork and overheat the electric assist motor, producing an electrical burning smell.
Seals inside the steering rack can blow out under extreme pressure spikes from heavy steering, spraying fluid onto the hot exhaust or lower engine components.