Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Definition

Net number of non-option equity instruments granted to participants.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(1)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Fair value of options vested. Excludes equity instruments other than options, for example, but not limited to, share units, stock appreciation rights, restricted stock.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Percent of Shares Authorized under Plan, Aggregate Shares Issued and Outstanding

+ References

No definition available.

+ Details

Name:	wsr_PercentofSharesAuthorizedunderPlanAggregateSharesIssuedandOutstanding
Namespace Prefix:	wsr_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_PlanNameAxis=wsr_A2016PlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=wsr_RestrictedCommonSharesandRestrictedShareUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VestingAxis=wsr_TimeBasedVestingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VestingAxis=wsr_TimeandPerformanceBasedVestingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VestingAxis=wsr_PerformanceVestingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_TitleOfIndividualAxis=wsr_BoardOfTrusteesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Incentive Equity Plan - Narrative (Details) - USD ($) $ in Thousands			3 Months Ended		9 Months Ended
	Aug. 07, 2020	Jul. 01, 2019	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shared-based compensation			$ 16		$ 52
2016 Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of total shares authorized					12.50%
Available for grant (in shares)			2,130,293		2,130,293
Restricted Common Shares and Restricted Share Units [Member] \| Time-Based Vesting [Member] \| 2016 Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Restricted stock granted (in shares)	122,665	45,031
Award vesting period		3 years
Restricted Common Shares and Restricted Share Units [Member] \| Time and Performance-Based Vesting [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shared-based compensation				$ 28	$ 196
Restricted Common Shares and Restricted Share Units [Member] \| Performance Vesting [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award vesting period					3 years
Board of Trustees [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shared-based compensation			$ 165
Board of Trustees [Member] \| Restricted Common Shares and Restricted Share Units [Member] \| Time and Performance-Based Vesting [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shared-based compensation					$ 165