A majority of the councilmembers shall constitute a quorum for the transaction of business. A less number may compel the attendance of absent members and may adjourn from time to time. The council shall determine its rules of proceedings. The council may punish their members for disorderly conduct and upon written charges entered upon the journal therefor, may, after trial, expel a member by two-thirds vote of all the members elected. All orders of the city council shall be entered upon the journal of its proceedings, which journal shall be signed by the officer who presided at the meeting. The journal shall be kept by the clerk under the council's direction.