Restructuring and Other Expense (Income), Net - Additional Information (Detail)					1 Months Ended			3 Months Ended			12 Months Ended
	May 31, 2021 USD ($)	Mar. 12, 2021 USD ($)	Jan. 29, 2021 USD ($) Property	Nov. 01, 2019 USD ($)	Oct. 31, 2020 USD ($)	Feb. 29, 2020 USD ($)	Nov. 30, 2019 USD ($)	Feb. 28, 2021 USD ($)	May 31, 2020 USD ($)	Feb. 29, 2020 USD ($)	May 31, 2021 USD ($)	May 31, 2020 USD ($)	May 31, 2019 USD ($)
Restructuring Cost and Reserve [Line Items]
Net (gain) loss on sale of assets											$ (53,345,000)	$ (123,000)
Restructuring and other expense (income), net											56,097,000	10,048,000	$ (11,018,000)
Net (gain) loss on sale of assets											(53,607,000)	5,057,000	7,059,000
Facility Exit And Other Costs
Restructuring Cost and Reserve [Line Items]
Facility exit costs												103,000
Other Restructuring
Restructuring Cost and Reserve [Line Items]
Facility exit costs											204,000
Cabs Joint Venture
Restructuring Cost and Reserve [Line Items]
Net gain on deconsolidation				$ 258,000			$ 50,000					208,000
TWB joint venture | MX
Restructuring Cost and Reserve [Line Items]
Severance expense						$ 620,000
WSP Joint Venture
Restructuring Cost and Reserve [Line Items]
Severance expense						$ 450,000
Oil & gas equipment
Restructuring Cost and Reserve [Line Items]
Facility exit costs										$ 522,000
Severance expense										$ 2,313,000
LPG Fuel Storage
Restructuring Cost and Reserve [Line Items]
Restructuring and other expense (income), net	$ 11,034,000
Business Combination Consideration Transferred1	$ 6,000,000
Cryogenics
Restructuring Cost and Reserve [Line Items]
Net proceeds from sale of business					$ 21,275,000						8,295,000
Net (gain) loss on sale of assets					$ (7,064,000)						(481,000)
Pressure Cylinders
Restructuring Cost and Reserve [Line Items]
Restructuring and other expense (income), net											54,155,000	5,282,000	(11,009,000)
Pressure Cylinders | Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense									$ 2,296,000
Pressure Cylinders | Other Restructuring
Restructuring Cost and Reserve [Line Items]
Facility exit costs											151,000
Pressure Cylinders | Oil & gas equipment
Restructuring Cost and Reserve [Line Items]
Number of real property | Property			3
Restructuring and other expense (income), net			$ 27,671,000
Pressure Cylinders | Oil & gas equipment | Maximum
Restructuring Cost and Reserve [Line Items]
Sales proceeds upon the exit of the business by the acquirer, Percent			15.00%
Engineered Cabs
Restructuring Cost and Reserve [Line Items]
Gain from auction of certain assets								$ 181,000
Net (gain) loss on sale of assets												100,000
Structural Composites Industries, LLC
Restructuring Cost and Reserve [Line Items]
Net proceeds from sale of business		$ 19,059,000
Restructuring and other expense (income), net		$ 7,219,000
Steel Processing
Restructuring Cost and Reserve [Line Items]
Restructuring and other expense (income), net											1,883,000	$ 3,501,000	$ (9,000)
Steel Processing | Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense									2,175,000
Steel Processing | Other Restructuring
Restructuring Cost and Reserve [Line Items]
Facility exit costs											53,000
Severance expense											$ 203,000
Other | Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense									873,000
Worthington Steel
Restructuring Cost and Reserve [Line Items]
Severance expense									$ 166,000