Restructuring and Other Expense (Income), Net - Additional Information (Detail)		1 Months Ended		3 Months Ended	9 Months Ended	12 Months Ended
	Nov. 01, 2019 USD ($)	Feb. 29, 2020 USD ($)	Nov. 30, 2019 USD ($)	May 31, 2020 USD ($)	May 31, 2020 USD ($)	May 31, 2020 USD ($)	May 31, 2019 USD ($) Facility	May 31, 2018 USD ($)
Restructuring Cost and Reserve [Line Items]
Net gain (loss) on disposal of assets						$ (123,000)	$ 13,420,000
Gain on sale of assets						5,057,000	7,059,000	$ 10,522,000
Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense				$ 2,175,000
Oil & gas equipment
Restructuring Cost and Reserve [Line Items]
Facility exit costs					$ 522,000
Severance expense					$ 2,313,000
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
Severance expense						203,000
Cabs Joint Venture
Restructuring Cost and Reserve [Line Items]
Net gain on deconsolidation	$ 258,000		$ 50,000
Net gain on adjustment						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
Cryogenics
Restructuring Cost and Reserve [Line Items]
Net proceeds from sale of business						8,295,000
Net gain (loss) on disposal of assets						(481,000)
Engineered Cabs
Restructuring Cost and Reserve [Line Items]
Gain on sale of assets						100,000
Steel Processing | Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense				2,296,000
Steel Processing | Other Restructuring
Restructuring Cost and Reserve [Line Items]
Facility exit costs						53,000	10,000
Other | Covid19
Restructuring Cost and Reserve [Line Items]
Severance expense				873,000
Worthington Steel
Restructuring Cost and Reserve [Line Items]
Severance expense				$ 166,000
Pressure Cylinders
Restructuring Cost and Reserve [Line Items]
Net proceeds from sale of business							27,577,000
Net gain (loss) on disposal of assets							11,458,000
Severance expense							89,000
Pressure Cylinders | AMTROL
Restructuring Cost and Reserve [Line Items]
Facility exit costs							513,000
Severance expense							1,086,000
Pressure Cylinders | Oil & gas equipment
Restructuring Cost and Reserve [Line Items]
Net proceeds from sale of business							20,256,000
Net gain (loss) on disposal of assets							$ 1,962,000
Number of facilities sold | Facility							2
Pressure Cylinders | Other Restructuring
Restructuring Cost and Reserve [Line Items]
Facility exit costs						$ 151,000
Severance expense							$ 205,000
CNG Fuel Systems | North America
Restructuring Cost and Reserve [Line Items]
Severance expense							$ 519,000