Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023	Aug. 31, 2023
Segment Reporting Information [Line Items]
Revenue	$ 862.7	$ 1,122.0	$ 1,671.5	$ 1,888.5
Earnings (loss) from operations	63.5	67.4	128.4	62.6
Assets	4,043.6		4,043.6		$ 3,978.4
Manufacturing
Segment Reporting Information [Line Items]
Revenue	735.8	968.6	1,411.7	1,615.1
Maintenance Services
Segment Reporting Information [Line Items]
Revenue	75.2	98.0	159.0	183.5
Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	51.7	55.4	100.8	89.9
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(33.1)	(26.7)	(59.4)	(49.2)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(70.9)	(103.5)	(138.8)	(156.7)
Earnings (loss) from operations	(3.8)	(8.9)	(8.5)	(12.9)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	61.5	96.8	120.0	141.3
Earnings (loss) from operations	3.7	8.8	8.4	12.8
Intersegment Eliminations | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	9.1	6.2	18.3	14.7
Intersegment Eliminations | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	0.3	0.5	0.5	0.7
Earnings (loss) from operations	0.1	0.1	0.1	0.1
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	797.3	1,065.4	1,531.7	1,756.4
Earnings (loss) from operations	62.5	55.4	121.5	56.0
Assets	1,814.5		1,814.5		1,847.0
Operating Segments | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	84.3	104.2	177.3	198.2
Earnings (loss) from operations	4.6	6.8	15.2	12.3
Assets	309.5		309.5		294.4
Operating Segments | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	52.0	55.9	101.3	90.6
Earnings (loss) from operations	33.3	40.8	59.6	56.4
Assets	1,592.2		1,592.2		1,458.1
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	327.4		327.4		$ 378.9
Reconciling Items
Segment Reporting Information [Line Items]
Earnings (loss) from operations			128.4	62.6
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	58.8	46.6	113.1	43.2
Reconciling Items | Maintenance Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	4.6	6.8	15.2	12.3
Reconciling Items | Leasing & Management Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 33.2	$ 40.7	$ 59.5	$ 56.3