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Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2023	May 31, 2022	May 31, 2023	May 31, 2022	Aug. 31, 2022
Segment Reporting Information [Line Items]
Revenue	$ 1,038.1	$ 793.5	$ 2,926.6	$ 2,027.0
Earnings (loss) from operations	50.7	19.6	113.3	56.6
Assets	3,921.7		3,921.7		$ 3,851.5
Manufacturing
Segment Reporting Information [Line Items]
Revenue	870.2	650.9	2,485.3	1,659.1
Maintenance Services
Segment Reporting Information [Line Items]
Revenue	122.9	101.5	306.4	260.5
Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	45.0	41.1	134.9	107.4
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(30.3)	(28.7)	(79.5)	(72.4)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(84.6)	(47.5)	(241.3)	(98.2)
Earnings (loss) from operations	(7.9)	(1.9)	(20.8)	(2.2)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	73.3	38.3	214.6	79.5
Earnings (loss) from operations	7.9	1.8	20.7	2.1
Intersegment Eliminations | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	11.0	8.6	25.7	17.4
Intersegment Eliminations | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	0.3	0.6	1.0	1.3
Earnings (loss) from operations		0.1	0.1	0.1
Operating Segments
Segment Reporting Information [Line Items]
Earnings (loss) from operations				56.6
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	943.5	689.2	2,699.9	1,738.6
Earnings (loss) from operations	52.0	22.3	108.0	36.7
Assets	1,891.1		1,891.1		1,853.9
Operating Segments | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	133.9	110.1	332.1	277.9
Earnings (loss) from operations	11.0	8.6	23.3	10.4
Assets	295.1		295.1		284.8
Operating Segments | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	45.3	41.7	135.9	108.7
Earnings (loss) from operations	25.9	19.3	82.3	84.1
Assets	1,325.6		1,325.6		1,152.2
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	409.9		409.9		$ 560.6
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	44.1	20.5	87.3	34.6
Reconciling Items | Maintenance Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	11.0	8.6	23.3	10.4
Reconciling Items | Leasing & Management Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 25.9	$ 19.2	$ 82.2	$ 84.0

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