<PAGE>   1
                                                                     Exhibit 3.8

                            SPIEKER PROPERTIES, INC.
                             ARTICLES SUPPLEMENTARY


        SPIEKER PROPERTIES, INC., a Maryland corporation, having its principal
office in the City of Baltimore, Maryland (the "Corporation"), hereby certifies
to the Maryland State Department of Assessments and Taxation that:

        FIRST: Pursuant to authority expressly vested in the Board of Directors
of the Corporation by the Charter of the Corporation, the Board of Directors has
duly reclassified 1,500,000 shares of the Common Stock (par value $.0001 per
share) of the Corporation into 1,500,000 shares of a class designated as Series
D Cumulative Redeemable Preferred Stock (par value $.0001 per share) of the
Corporation ("Series D Preferred Stock") and has provided for the issuance of
such shares.

        SECOND: The reclassification increases the number of shares classified
as Series D Preferred Stock from no shares immediately prior to the
reclassification to 1,500,000 shares immediately after the reclassification. The
reclassification decreases the number of shares classified as Common Stock (par
value $.0001 per share) from 654,500,000 shares immediately prior to the
reclassification to 653,000,000 shares immediately after the reclassification.

        THIRD: Subject in all cases to the provisions of Article NINTH of the
Charter of the Corporation with respect to Excess Stock, the following is a
description of the preferences, conversion and other rights, voting powers,
restrictions, limitations as to dividends, qualifications and terms and
conditions of redemption of Series D Preferred Stock of the Corporation:

               1. DESIGNATION AND AMOUNT.

                      The designation of Series D Preferred Stock described in
        Article FIRST hereof shall be "Series D Cumulative Redeemable Preferred
        Stock (par value $.0001 per share)." The number of shares of Series D
        Preferred Stock to be authorized shall be 1,500,000. The Series A
        Preferred Stock, par value $.0001 per share ("Series A Preferred
        Stock"), the Series B Cumulative Redeemable Preferred Stock, par value
        $.0001 per share ("Series B Preferred Stock") and the Series C
        Cumulative Redeemable Preferred Stock, par value $.0001 per share
        ("Series C Preferred Stock"), and the Series D Preferred Stock of the
        Corporation rank on a parity as to dividends and amounts upon
        liquidation, dissolution or winding up of the affairs of the
        Corporation.

                      Series D Preferred Stock will, with respect to dividends
        and amounts upon liquidation, dissolution or winding up of the affairs
        of the Corporation, rank senior to all classes or series of Common Stock
        (as defined in the Charter, including but not limited to Class A Common
        Stock, Class B Common Stock and Class C Common Stock) and to all classes
        or series of equity securities issued or outstanding, other than any
        class or series of equity securities expressly designated as ranking on
        a parity with or senior to the Series D Preferred Stock as to dividends
        and amounts upon liquidation, dissolution or winding up of the affairs
        of the Corporation.


<PAGE>   2
               2. DIVIDENDS AND DIVIDEND PROVISIONS.

                      (a) Subject to the rights of series of Preferred Stock
        ranking on a parity with or senior to the Series D Preferred Stock as to
        dividends which may from time to time come into existence, holders of
        Series D Preferred Stock shall be entitled to receive, when and as
        declared by the Board of Directors, out of funds legally available for
        the payment of dividends, cumulative preferential cash dividends of
        $3.84375 per annum per share. Such dividends shall be cumulative from
        the date of original issue and shall be payable quarterly in arrears on
        the last day of March, June, September and December, or, if not a
        business day, the next succeeding business day (each, a "Dividend
        Payment Date"). Any dividend payable on Series D Preferred Stock for any
        partial dividend period will be computed on the basis of a 360-day year
        consisting of twelve 30-day months. Dividends will be payable to holders
        of record as they appear in the records of the Corporation at the close
        of business on the applicable record date, which shall be on such date
        designated by the Board of Directors of the Corporation for the payment
        of dividends that is not more than 50 nor less than 10 days prior to
        such Dividend Payment Date (each, a "Dividend Record Date").
        Notwithstanding anything to the contrary set forth herein, each share of
        Series D Preferred Stock shall also accumulate all accrued and unpaid
        distributions, whether or not declared, up to the exchange date on any
        Series D Preference Unit (as defined in the Second Amended and Restated
        Limited Partnership Agreement of Spieker Properties, L.P., as amended
        (the "Partnership Agreement")) validly exchanged into such share of
        Series D Preferred Stock in accordance with the provisions of such
        Partnership Agreement and for purposes of these Articles Supplementary
        such accrued and unpaid distributions on such Series D Preference Units
        shall deem to constitute accrued and unpaid dividends with respect to
        past dividends periods on Series D Preferred Stock.

                      (b) Dividends on Series D Preferred Stock will accrue
        whether or not the Corporation has earnings, whether or not there are
        funds legally available for the payment of such dividends and whether or
        not such dividends are declared. No interest, or sum of money in lieu of
        interest, shall be payable in respect of any dividend payment or
        payments on Series D Preferred Stock which may be in arrears. Holders of
        the Series D Preferred Stock will not be entitled to dividends in excess
        of the full cumulative dividends as described above.

                      (c) If, for any taxable year, the Corporation elects to
        designate as "capital gain dividends" (as defined in Section 857 of the
        Internal Revenue Code of 1986, as amended, or any successor revenue code
        or section (the "Code")) any portion (the "Capital Gains Amount") of the
        total distributions (as determined for federal income tax purposes) paid
        or made available for the year to holders of all classes of capital
        stock (the "Total Distributions"), then the portion of the Capital Gains
        Amount that shall be allocable to holders of Series D Preferred Stock
        shall be in the same portion that the Total Distributions paid or made
        available to the holders of Series D Preferred Stock for the year bears
        to the Total Distributions.

                      (d) If any shares of Series D Preferred Stock are
        outstanding, no dividends shall be declared or paid or set apart for
        payment on any shares of series of capital stock of the Corporation
        ranking, as to dividends, on a parity with or junior to Series D
        Preferred Stock for any period unless full cumulative dividends have
        been or contemporaneously are declared and paid or declared and a sum
        sufficient for the full payment thereof deposited irrevocably in trust
        for the benefit of holders of Series D Preferred Stock on shares of
        Series D Preferred Stock for all past dividend periods and the then
        current dividend period. When dividends are not paid in full (or a sum
        sufficient for such full payment 


<PAGE>   3
        is not deposited irrevocably in trust for the benefit of holders of
        Series D Preferred Stock) upon the shares of Series D Preferred Stock
        and the shares of any other series of capital stock ranking on parity as
        to dividends with shares of Series D Preferred Stock, all dividends
        declared upon shares of Series D Preferred Stock and any other series of
        capital stock ranking on a parity as to dividends with Series D
        Preferred Stock shall be declared pro rata so that the amount of
        dividends declared per share on Series D Preferred Stock and such other
        series of capital stock shall in all cases bear to each other the same
        ratio that accrued dividends per share on Series D Preferred Stock and
        such other series of capital stock bear to each other.

                      (e) Except as provided in Section 2(d), unless full
        cumulative dividends on shares of Series D Preferred Stock have been or
        contemporaneously are declared and paid or declared and a sum sufficient
        for the full payment thereof has been deposited irrevocably in trust for
        the benefit of holders of Series D Preferred Stock for all past dividend
        periods and the then current dividend period, no dividends (other than
        in shares of Common Stock or other capital stock ranking junior to
        Series D Preferred Stock as to dividends and amounts upon liquidation,
        dissolution or winding up of the affairs of the Corporation) shall be
        declared or paid or set aside for payment or other dividend shall be
        declared or made upon the shares of Common Stock, Class B Common Stock,
        Class C Common Stock, Series A Preferred Stock, Series B Preferred
        Stock, Series C Preferred Stock or any other capital stock of the
        Corporation ranking junior to or on a parity with Series D Preferred
        Stock as to dividends or amounts upon liquidation, nor shall any shares
        of Common Stock, Class B Common Stock, Class C Common Stock, Series A
        Preferred Stock, Series B Preferred Stock, Series C Preferred Stock or
        any other capital stock of the Corporation ranking junior to or on a
        parity with Series D Preferred Stock as to dividends or amounts upon
        liquidation, dissolution or winding up of the affairs of the Corporation
        be redeemed, purchased or otherwise acquired for any consideration (or
        any moneys be paid to or made available for a sinking fund for the
        redemption of any such capital stock) by the Corporation (except by
        conversion into or exchange for other capital stock of the Corporation
        ranking junior to Series D Preferred Stock as to dividends and amounts
        upon liquidation, dissolution or winding up of the affairs of the
        Corporation).

                      (f) Any dividend payment made on shares of Series D
        Preferred Stock shall first be credited against the earliest accrued but
        unpaid dividend due with respect to shares of Series D Preferred Stock
        which remains payable.

               3. LIQUIDATION RIGHTS.

                      (a) Subject to the rights of series of Preferred Stock
        ranking on a parity with or senior to the Series D Preferred Stock as to
        amounts upon liquidation, dissolution or winding up of the affairs of
        the Corporation which may from time to time come into existence, upon
        any voluntary or 


<PAGE>   4
        involuntary liquidation, dissolution or winding up of the affairs of the
        Corporation, then, before any distribution or payment shall be made to
        the holders of any shares of Common Stock or any other class or series
        of capital stock of the Corporation ranking junior to Series D Preferred
        Stock in the distribution of assets upon any liquidation, dissolution or
        winding up of the affairs of the Corporation, the holders of shares of
        Series D Preferred Stock shall be entitled to receive out of assets of
        the Corporation legally available for distribution to stockholders,
        liquidation distributions in the amount of the liquidation preference of
        $50.00 per share, plus an amount equal to all dividends accrued and
        unpaid thereon. After payment of the full amount of the liquidating
        distributions to which they are entitled, the holders of shares of
        Series D Preferred Stock will have no right or claim to any of the
        remaining assets of the Corporation. In the event that, upon any such
        voluntary or involuntary liquidation, dissolution or winding up of the
        affairs of the Corporation, the available assets of the Corporation are
        insufficient to pay the amount of the liquidation distributions on all
        outstanding shares of Series D Preferred Stock and the corresponding
        amounts payable on all shares of other classes or series of capital
        stock of the Corporation ranking on a parity with Series D Preferred
        Stock as to dividends and amounts upon liquidation, dissolution or
        winding up of the affairs of the Corporation, including the Series A
        Preferred Stock, the Series B Preferred Stock and the Series C Preferred
        Stock ("Parity Stock"), then the holders of shares of Series D Preferred
        Stock and Parity Stock shall share ratably in any such distribution of
        assets in proportion to the full liquidating distributions to which they
        would otherwise be respectively entitled.

                      (b) A consolidation or merger of the Corporation with or
        into any other entity or entities, or a sale, lease, conveyance or
        disposition of all or substantially all of the assets of the Corporation
        or the effectuation by the Corporation of a transaction or series of
        related transactions in which more than 50% of the voting power of the
        Corporation is disposed of, shall not be deemed to be a liquidation,
        dissolution or winding up of the affairs of the Corporation within the
        meaning of this Section 3.

               4. REDEMPTION.

                      (a) Shares of Series D Preferred Stock are not redeemable
        prior to April 20, 2003. On and after April 20, 2003, the Corporation at
        its option upon not less than 30 nor more than 60 days' written notice
        may redeem outstanding shares of Series D Preferred Stock, in whole or
        in part, at any time or from time to time, for cash at a redemption
        price of $50.00 per share, plus an amount equal to all dividends accrued
        and unpaid thereon, whether or not declared, to the date fixed for
        redemption, without interest. The redemption price of shares of Series D
        Preferred Stock (other than the portion thereof consisting of accrued
        and unpaid dividends) is payable solely out of proceeds (with giving
        effect to any temporary use of such proceeds) from the sale of other
        capital stock of the Corporation, which may include Common Stock,
        Preferred Stock, depository shares, interests, participations or other
        ownership interests in the Corporation however designated (other than
        debt securities converted into or exchangeable for capital stock), and
        any rights, warrants or options to purchase any thereof. Holders of
        shares of Series D Preferred Stock to be redeemed shall surrender such
        shares of Series D Preferred Stock at the place designated in such
        notice and shall be entitled to the redemption price and any accrued and
        unpaid dividends payable upon such redemption following such surrender.
        If fewer than all of the outstanding shares of Series D Preferred Stock
        are to be redeemed, the number of shares to be redeemed will be
        determined by the Corporation and such shares may be redeemed pro rata
        from the holders of record of such shares in proportion to the number of
        such shares held by such holders (with adjustments to avoid redemption
        of fractional shares) or by lot in a manner determined by the
        Corporation.

                      (b) Unless full cumulative dividends on all shares of
        Series D Preferred Stock and Parity Stock shall have been or
        contemporaneously are declared and paid or declared and a sum sufficient
        for the full payment thereof deposited irrevocably in trust for the
        benefit of holders of Series D Preferred Stock for all past dividend
        periods and the then current dividend period, no shares of Series D
        Preferred Stock or Parity Stock shall be redeemed unless all outstanding
        shares of Series D Preferred Stock and Parity Stock are simultaneously
        redeemed; provided, however, that the foregoing shall not prevent the
        purchase or acquisition of shares of Series D Preferred Stock or Parity
        Stock pursuant to a purchase or exchange offer made on the same terms to
        holders of all outstanding shares of Series D Preferred Stock or Parity
        Stock, as the case may be. Furthermore, unless full 


<PAGE>   5
        cumulative dividends on all outstanding shares of Series D Preferred
        Stock and Parity Stock have been or contemporaneously are declared and
        paid or declared and a sum sufficient for the payment thereof deposited
        irrevocably in trust for the benefit of holders of Series D Preferred
        Stock for all past dividend periods and the then current dividend
        period, the Corporation shall not purchase or otherwise acquire directly
        or indirectly any shares of Series D Preferred Stock or Parity Stock
        (except by conversion into or exchange for shares of capital stock of
        the Corporation ranking junior to Series D Preferred Stock and Parity
        Stock as to dividends and amounts upon liquidation, dissolution or
        winding up of the affairs of the Corporation).

                      (c) Notice of redemption will be mailed and telecopied (if
        possible) at least 30 days but not more than 60 days before the
        redemption date to each holder of record of shares of Series D Preferred
        Stock at the address or telecopier number shown on the stock transfer
        books of the Corporation. Each notice shall state: (i) the redemption
        date; (ii) the number of shares of Series D Preferred Stock to be
        redeemed; (iii) the redemption price per share; (iv) the place or places
        where certificates for shares of Series D Preferred Stock are to be
        surrendered for payment of the redemption price; and (v) that dividends
        on shares of Series D Preferred Stock will cease to accrue on such
        redemption date. If fewer than all shares of Series D Preferred Stock
        are to be redeemed, the notice mailed and telecopied (if possible) to
        each such holder thereof shall also specify the number of shares of
        Series D Preferred Stock to be redeemed from each such holder. If notice
        of redemption of any shares of Series D Preferred Stock has been given
        and if the funds necessary for such redemption have been set aside by
        the Corporation in trust for the benefit of the holders of shares of
        Series D Preferred Stock so called redemption, then from and after the
        redemption date, dividends will cease to accrue on such shares of Series
        D Preferred Stock, such shares of Series D Preferred Stock shall no
        longer be deemed outstanding and all rights of the holders of such
        shares will terminate, except the right to receive the redemption price.

                      (d) The holders of shares of Series D Preferred Stock at
        the close of business on a Dividend Record Date will be entitled to
        receive the dividend payable with respect to such shares of Series D
        Preferred Stock on the corresponding Dividend Payment Date
        notwithstanding the redemption thereof between such Dividend Record Date
        and the corresponding Dividend Payment Date or the Corporation's default
        in the payment of the dividend due.

                      (e) Series D Preferred Stock will not be subject to any
        sinking fund or mandatory redemption, except as provided in Article
        NINTH of the Charter of the Corporation.

                      (f) The redemption price shall be payable on to the
        holders of the Series D Preferred Stock upon surrender of the
        certificate evidencing the Series D Preferred Stock by such holders at
        the place designated in the notice of redemption. If fewer than all
        Series D Preferred Stock evidenced by any certificate is being redeemed,
        a new certificate shall be issued upon surrender of the certificate
        evidencing all Series D Preferred Stock, evidencing the unredeemed
        Series D Preferred Stock without cost to the holder thereof. If any
        redemption date is not a business day, then payment of the redemption
        price payable on such redemption date will be made on the next
        succeeding business day (and without any interest or other payment in
        respect of any such delay) except that, if such business day falls in
        the next calendar year, such payment will be made on the immediately
        preceding business day, in each case with the same force and effect as
        if made on such redemption date. If payment of the redemption price or
        any accumulated or unpaid distributions in respect of the Series D
        Preferred Stick is improperly withheld or refused and not paid by the
        Corporation, distributions on such Series D Preferred Stock will
        continue to accumulate from the original 


<PAGE>   6
        redemption date to the date of payment, in which case the actual payment
        date will be considered the date fixed for redemption for purposes of
        calculating the applicable redemption price and any accumulated and
        unpaid distributions.

               5. VOTING RIGHTS.

                      (a) Except as indicated in this Section 5, or except as
        otherwise from time to time required by applicable law, the holders of
        shares of Series D Preferred Stock will have no voting rights.

                      (b) (i) If six quarterly dividends (including quarterly
        distributions on the Series D Preferred Units prior to the exchange into
        Series D Preferred Stock) (whether or not consecutive) payable on shares
        of Series D Preferred Stock or any Parity Stock are in arrears, whether
        or not earned or declared, the number of directors then constituting the
        Board of Directors of the Corporation will be automatically increased by
        two, and the holders of shares of Series D Preferred Stock, voting
        together as a class with the holders of shares of any other series of
        Parity Stock entitled to such voting rights which are then exercisable
        (any such other series, the "Voting Preferred Stock"), will have the
        right to elect two additional directors (the "Preferred Stock
        Directors") to serve on the Corporation's Board of Directors at any
        annual meeting of stockholders or a properly called special meeting of
        the holders of Series D Preferred Stock and such other Voting Preferred
        Stock until all such dividends have been declared and paid in full or
        deposited irrevocably in trust for the benefit of holders of Series D
        Preferred Stock. At any such meeting, the Preferred Stock Directors
        shall be elected by plurality vote on the basis of one vote per $25.00
        of liquidation preference to which such Series D Preferred Stock and
        Voting Preferred Stock is entitled (excluding amounts in respect of
        accumulated and unpaid dividends). The term of office of all Preferred
        Stock Directors so elected will terminate with the termination of such
        voting rights. (ii) Any Preferred Stock Director may be removed at any
        time with or without cause by the vote of, and shall not be removed
        otherwise than by the vote of, the holders of record of a majority of
        the outstanding Series D Preferred Stock. Any vacancy in the office of a
        Preferred Stock Director may be filled by written consent of the
        Preferred Stock Director remaining in office, or if none remains in
        office, by a vote of the holders of record of shares of Series D
        Preferred Stock, voting together as a class with the holders of Voting
        Preferred Stock. The Preferred Stock Director shall each be entitled to
        one vote per director on any matter.

                      (c) The approval of two-thirds of the outstanding Series D
        Preferred Stock is required in order to (i) enter into a share exchange
        that affects shares of Series D Preferred Stock, or consolidate with or
        merge the Corporation with or into any other corporation or convey,
        lease or transfer all of its assets as an entirety, unless in each such
        case each share of Series D Preferred Stock remains outstanding without
        a material adverse change to its terms, preferences, privileges, voting
        powers and rights or is converted into or exchanged for preferred stock
        of the surviving entity having preferences, conversion and other rights,
        voting powers, restrictions, limitations as to dividends, qualifications
        and terms or conditions of redemption thereof identical to that of a
        share of Series D Preferred Stock, or (ii) authorize, reclassify,
        create, or increase the authorized amount of any class of stock having
        rights senior to Series D Preferred Stock with respect to the payment of
        dividends or amounts upon liquidation, dissolution or winding up of the
        affairs of the Corporation. However, the Corporation may create
        additional classes of Parity Stock and capital stock ranking junior to
        Series D Preferred Stock as to dividends or amounts upon liquidation,
        dissolution or winding up of the affairs of the Corporation ("Junior
        Stock"), increase the authorized number of shares of Parity Stock and
        Junior Stock and issue additional series of Parity Stock and Junior
        Stock without the consent of any holder of Series D Preferred Stock,


<PAGE>   7
        unless, in the case of Parity Stock, such Parity Stock is created or
        increased solely for the purpose of issuance to an affiliate (as defined
        in Rule 144 under the Securities Act of 1933) of the Company, which
        requires the approval of two-thirds of the outstanding Series D
        Preferred Stock.

                      (d) The approval of two-thirds of the outstanding Series D
        Preferred Stock, voting as a single class, is required in order to amend
        the Corporation's Articles Supplementary or Charter to affect materially
        and adversely the rights, preferences or voting power of the holders of
        shares of Series D Preferred Stock.

                      (e) Except as provided above and as required by law, the
        holders of Series D Preferred Stock are not entitled to vote on any
        merger or consolidation involving the Corporation, on any share exchange
        or on a sale of all or substantially all of the assets of the
        Corporation.

               6. CONVERSION.

                      The shares of Series D Preferred Stock are not convertible
        into or exchangeable for any other property or securities of the
        Corporation, except that each share of Series D Preferred Stock is
        exchangeable into Excess Stock as provided in Article NINTH of the
        Charter of the Corporation.

               7. STATUS OF REDEEMED OF REACQUIRED STOCK.

                      In the event any shares of Series D Preferred Stock shall
        be redeemed pursuant to Section 4 hereof or reacquired, the shares so
        redeemed or reacquired shall revert to the status of authorized but
        unissued shares of Series D Preferred Stock available for future
        issuance and reclassification by the Corporation.


<PAGE>   8
               IN WITNESS WHEREOF, SPIEKER PROPERTIES, INC. has caused these
presents to be signed in its name and on its behalf by its Chief Financial
Officer and Executive Vice President and witnessed by its Secretary on April 20,
1998.

WITNESS:                                    SPIEKER PROPERTIES, INC.




  /s/ Sara H. Reynolds                       By:   /s/ Craig G. Vought
-------------------------------                -------------------------------
Vought                       
Sara H. Reynolds                               Craig G. Vought
Secretary                                      Chief Financial Officer and
                                               Executive Vice President


        THE UNDERSIGNED, Chief Financial Officer and Executive Vice President of
SPIEKER PROPERTIES, INC., who executed on behalf of the Corporation the Articles
Supplementary of which this certificate is made a part, hereby acknowledges in
the name and on behalf of said Corporation the foregoing Articles Supplementary
to be the corporate act of said Corporation and hereby certifies that the
matters and facts set forth herein with respect to the authorization and
approval thereof are true in all material respects under the penalties of
perjury.




                                            /s/ Craig G. Vought
                                            ----------------------------
                                            Craig G. Vought