Searches for pair production of gauginos and squarks in e+e- collisions at a centre-of-mass energy of 189 GeV have been performed on data corresponding to an integrated luminosity of 158 pb^{-1} collected by the DELPHI detector at LEP. The data were analyzed under the assumption of non-conservation of R-parity through a single dominant Ubar Dbar Dbar coupling between squarks and quarks. Typical final states contain between 4 and 10 jets with or without additional leptons. No excess of data above Standard Model expectations was observed. The results were used to constrain domains of the MSSM parameter space and derive limits on the masses of supersymmetric particles. The following mass limits at 95% CL were obtained from these searches: neutralino mass: m_{\tilde{\chi^0_{1}}} \geq 32 GeV chargino mass: m_{\tilde{\chi^+_{1}}} \geq 94 GeV stop and sbottom mass (indirect decay) with \Delta M > 5 GeV: m_{\tilde{t_1}} \geq 74 GeV, for \Phi_{mix}=0 rad m_{\tilde{t_1}} \geq 59 GeV, for \Phi_{mix}=0.98 rad m_{\tilde{b_1}} \geq 72 GeV, for \Phi_{mix}=0 rad. The angle \phi_{mix} is the mixing angle between left and right handed quarks.