He is charged with murdering Ms Rushworth, 43, Ms Armitage, 31, and Ms Blamires, 36.
Conservative Fiona Ferguson will hold the corporate resources brief and Conservative Stephen Rushworth takes over economy.
Stephen Griffiths, 40, has been charged with their murder, along with that of 42-year-old Susan Rushworth, also from Bradford.
Although the remains of Ms Blamires, 36, have been found, there has been no sign of Ms Armitage, 31, or Ms Rushworth, 43.
Stephen Griffiths, 40, who is accused of murdering Suzanne Blamires, Shelley Armitage and Susan Rushworth, was found in his cell on Wednesday evening.
Ms Armitage, from the Allerton area of Bradford, was last seen on 26 April and Ms Rushworth, of Manningham, disappeared on 22 June last year.
Ms Blamires was last seen on 21 May, Ms Armitage has been missing since 26 April, and Ms Rushworth disappeared on 22 June last year.
Ms Armitage, who was from the Allerton area of Bradford, was last seen on 26 April and Ms Rushworth, of Manningham, disappeared on 22 June last year.
Mr Griffiths, who was studying criminology at Bradford University, appeared at the city's crown court on 28 May accused of murdering Ms Blamires, 36, Ms Rushworth, 43, and Ms Armitage, 31.
While police have so far found no trace of Ms Rushworth, who disappeared in June 2009, body parts belonging to the other two women have been found in the River Aire in Bradford.
Craig Kieswetter could only contribute 10 before he swiped across the line to Chris Rushworth, but Peter Trego (33 not out) and James Hildreth (31 not out) combined for an unbroken stand of 46 that took Somerset to the close.
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