Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021	Aug. 31, 2021
Segment Reporting Information [Line Items]
Revenue	$ 793.5	$ 450.2	$ 2,027.0	$ 1,148.8
Earnings (loss) from operations	19.6	25.7	56.6	(2.1)
Assets	3,706.1		3,706.1		$ 3,390.7
Manufacturing
Segment Reporting Information [Line Items]
Revenue	650.9	339.7	1,659.1	845.7
Maintenance Services
Segment Reporting Information [Line Items]
Revenue	101.5	80.9	260.5	218.1
Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	41.1	29.6	107.4	85.0
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(28.7)	(22.1)	(72.4)	(56.9)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(47.5)	(9.8)	(98.2)	(35.7)
Earnings (loss) from operations	(1.9)	(0.6)	(2.2)	(3.3)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	38.3	7.5	79.5	30.5
Earnings (loss) from operations	1.8	0.5	2.1	3.1
Intersegment Eliminations | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	8.6	2.3	17.4	4.2
Earnings (loss) from operations		0.1		0.1
Intersegment Eliminations | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	0.6		1.3	1.0
Earnings (loss) from operations	0.1		0.1	0.1
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	689.2	347.2	1,738.6	876.2
Earnings (loss) from operations	22.3	29.6	36.7	19.8
Assets	1,814.1		1,814.1		1,493.5
Operating Segments | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	110.1	83.2	277.9	222.3
Earnings (loss) from operations	8.6	4.3	10.4	6.5
Assets	266.8		266.8		260.9
Operating Segments | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	41.7	29.6	108.7	86.0
Earnings (loss) from operations	19.3	14.5	84.1	31.8
Assets	1,158.3		1,158.3		949.4
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	466.9		466.9		$ 686.9
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	20.5	29.1	34.6	16.7
Reconciling Items | Maintenance Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	8.6	4.2	10.4	6.4
Reconciling Items | Leasing & Management Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 19.2	$ 14.5	$ 84.0	$ 31.7