Cluttered construction sites will make hash out of cushion tires. especially if the forklift is trying to run-over dimensional lumber scraps and being driven off-slab. The steer axle can only articulate a small amount on cushion trucks so it is much easier to lift a drive tire and get stuck than you might think. Nissan had a model called the "nomad" that was kindof a crossover between cushion and pneumatic for customers that spent equal time on and off-slab but i don't think this is the direction you want to go. I would go with a 5000lb truck with solid softys or foam-fill tires for the large diameter puncture resistance and softer tires will conform more to rough surfaces giving more traction and the increased steer axle articulation of pneumatic trucks. you might find something in reasonable condition for 10-15K. but a 5000lb truck is not a cheap machine to own or operate no matter how you slice it... Good Luck
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