Revenue - Narrative (Details) - USD ($) $ in Thousands	3 Months Ended
Mar. 31, 2023	Dec. 31, 2022
Revenue from Contract with Customer [Abstract]
Contract assets	$ 31,207	$ 33,613
Balance as of December 31, 2022	3,243	$ 6,781
Contract assets transferred to receivables	3,696
Increase in billings in excess of cost, excluding revenue recognized	1,983
Revenue recognized from contract liability	$ 3,443

Contract with Customer, Liability, Increase from Cash Receipts

No definition available.

Name:	fstr_ContractWithCustomerLiabilityIncreaseFromCashReceipts
Namespace Prefix:	fstr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount, after allowance for credit loss, of right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130531-203044

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 3
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130533-203044

+ Details

Name:	us-gaap_ContractWithCustomerAssetNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of decrease in right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time from transfer to receivable due to right to consideration becoming unconditional.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (d)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130551-203045

+ Details

Name:	us-gaap_ContractWithCustomerAssetReclassifiedToReceivable
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130531-203044

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130532-203044

+ Details

Name:	us-gaap_ContractWithCustomerLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

+ Details

Name:	us-gaap_ContractWithCustomerLiabilityRevenueRecognized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_RevenueFromContractWithCustomerAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration