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Goodwill and Other Long-Lived Assets - Additional Information (Detail) - USD ($)
2 Months Ended 3 Months Ended 12 Months Ended
Feb. 29, 2020
Feb. 29, 2020
Aug. 31, 2020
Aug. 31, 2019
May 31, 2022
May 31, 2021
May 31, 2020
Goodwill And Other Intangible Assets [Line Items]              
Goodwill         $ 401,469,000 $ 351,056,000 $ 321,434,000
Amortization expense         14,937,000 12,257,000 12,870,000
Impairment of long lived assets to be disposed of   $ 4,679,000          
Impairment of goodwill and long-lived assets         3,076,000 13,739,000 82,690,000
Fixed asset net book value             14,274,000
Intangible assets with net book value             6,577,000
Operating lease assets         98,769,000 35,101,000  
Oil and Gas Equipment              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of goodwill             22,097,000
Other              
Goodwill And Other Intangible Assets [Line Items]              
Goodwill         0 0 13,556,000
Impairment of long lived assets to be disposed of         11,810,000 77,051,000
Impairment of goodwill         198,290,000 198,290,000  
Cryogenics              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of long lived assets to be disposed of           3,662,000  
Impairment of goodwill and long-lived assets           4,333,000  
Jefferson              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of goodwill and long-lived assets           1,423,000  
Superior Tools              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of goodwill and long-lived assets           506,000  
Building Products              
Goodwill And Other Intangible Assets [Line Items]              
Goodwill [1]         65,408,000 72,273,000 67,120,000
Impairment of long lived assets to be disposed of         1,423,000 3,800,000
Impairment of goodwill and long-lived assets             3,800,000
Twinsburg              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of goodwill         3,076,000    
TWB Hermosillo              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of ROU assets             565,000
Packing Solutions Business              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of goodwill and long-lived assets             2,544,000
Engineered Cabs              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of long lived assets to be disposed of       $ 35,194,000      
Fixed asset net book value     $ 1,469,000        
Engineered Cabs | Stow, Ohio              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of ROU assets     905,000        
Engineered Cabs | Greensburg, Indiana              
Goodwill And Other Intangible Assets [Line Items]              
Operating lease assets     3,938,000        
Fair Value, Inputs, Level 2 | Canton              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets $ 700,000 $ 700,000          
Fair Value, Nonrecurring              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets         700,000 400,000  
Fair Value, Nonrecurring | Fair Value, Inputs, Level 2              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets         $ 700,000 400,000  
Long Lived Assets Held And Used              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets             2,800,000
Long Lived Assets Held And Used | Jefferson              
Goodwill And Other Intangible Assets [Line Items]              
Carrying value long-lived assets           1,823,000  
Long Lived Assets Held And Used | Building Products              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets             6,600,000
Long Lived Assets Held And Used | Packing Solutions Business              
Goodwill And Other Intangible Assets [Line Items]              
Carrying value long-lived assets             2,810,000
Long Lived Assets Held And Used | Fair Value, Inputs, Level 2 | Cryogenics              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets           9,193,000  
Carrying value long-lived assets           13,526,000  
Long Lived Assets Held And Used | Fair Value, Inputs, Level 2 | Canton              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of long lived assets to be disposed of $ 1,274,000            
Long Lived Assets Held And Used | Fair Value, Nonrecurring              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of long lived assets to be disposed of           1,441,000  
Fixed asset net book value           7,375,000  
Intangible assets with net book value           2,374,000  
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Jefferson              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets           400,000  
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Packing Solutions Business              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets             $ 266,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Engineered Cabs              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets     12,860,000        
Impairment of long lived assets to be disposed of     $ 35,194,000        
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 2              
Goodwill And Other Intangible Assets [Line Items]              
Fair market value of assets           5,934,000  
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 3              
Goodwill And Other Intangible Assets [Line Items]              
Impairment of long lived assets to be disposed of           $ 2,374,000  
Minimum              
Goodwill And Other Intangible Assets [Line Items]              
Definite-lived intangible assets, estimated useful lives         10 years    
Maximum              
Goodwill And Other Intangible Assets [Line Items]              
Definite-lived intangible assets, estimated useful lives         20 years    
[1] In connection with the realignment of the our legacy Pressure Cylinders business, as discussed further in Note P - Segment Data, the goodwill of our legacy Pressure Cylinders business unit was allocated to the new reporting units on a relative fair value basis.