Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022	Aug. 31, 2022
Segment Reporting Information [Line Items]
Revenue	$ 1,122.0	$ 682.8	$ 1,888.5	$ 1,233.5
Earnings (loss) from operations	67.4	25.2	62.6	37.0
Assets	3,952.5		3,952.5		$ 3,851.5
Manufacturing
Segment Reporting Information [Line Items]
Revenue	968.6	555.7	1,615.1	1,008.2
Maintenance Services
Segment Reporting Information [Line Items]
Revenue	98.0	86.6	183.5	159.0
Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	55.4	40.5	89.9	66.3
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(26.7)	(27.1)	(49.2)	(43.7)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(103.5)	(8.3)	(156.7)	(50.7)
Earnings (loss) from operations	(8.9)		(12.9)	(0.3)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	96.8	1.8	141.3	41.2
Earnings (loss) from operations	8.8		12.8	0.3
Intersegment Eliminations | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	6.2	6.1	14.7	8.8
Intersegment Eliminations | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	0.5	0.4	0.7	0.7
Earnings (loss) from operations	0.1		0.1
Operating Segments
Segment Reporting Information [Line Items]
Earnings (loss) from operations				37.0
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	1,065.4	557.5	1,756.4	1,049.4
Earnings (loss) from operations	55.4	1.8	56.0	14.4
Assets	1,923.0		1,923.0		1,853.9
Operating Segments | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	104.2	92.7	198.2	167.8
Earnings (loss) from operations	6.8	2.9	12.3	1.8
Assets	313.9		313.9		284.8
Operating Segments | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	55.9	40.9	90.6	67.0
Earnings (loss) from operations	40.8	47.6	56.4	64.8
Assets	1,267.2		1,267.2		1,152.2
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	448.4		448.4		$ 560.6
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	46.6	1.8	43.2	14.1
Reconciling Items | Maintenance Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	6.8	2.9	12.3	1.8
Reconciling Items | Leasing & Management Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 40.7	$ 47.6	$ 56.3	$ 64.8