Property, Plant and Equipment, net - Property, Plant and Equipment (Details) - USD ($) $ in Thousands	Aug. 31, 2023	Aug. 31, 2022
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	$ 1,609,036	$ 1,519,152
Less accumulated depreciation	(902,231)	(855,032)
Property, plant and equipment, net	706,805	664,120
Machinery and equipment
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	952,480	875,904
Land and improvements
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	345,584	324,453
Buildings and leasehold improvements
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	169,940	148,634
Enterprise resource planning (ERP) systems
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	18,898	18,945
Office equipment and other software licenses
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	31,195	30,797
Construction in progress
Property, Plant and Equipment [Line Items]
Property, plant and equipment, gross	$ 90,939	$ 120,419