Q.What mandatory plans are required to be carried on board ? Are the plan like Shell expansion plan, tank arrangement and dry docking plan mandatory plans ?

There are certificates and plans that are required as per various IMO conventions. A list of these certificates and plans can be found on the IMO website by clicking here. Apart from these certificates, manuals and plans, there are few drawing and plans that are required as per the ship's classification society. International association of classification societies (IACS) sets the rules for its member classification societies to follow. 

Most of the major classification societies are the member of IACS and thus adopts the classification rules of IACS. As per the rules of IACS there are minimum list of drawings and plans that are required onboard for a vessel to enter into a classification society and for the issuance of certificate of class. These drawing are as per follow

1. For All Vessels 

Main Plans

• General Arrangement plan
• Capacity Plan
• Hydrostatic curves
• Loading Manual, where required
• Damage stability calculation, where required

Steel Plans

• Midship Section
• Scantling Plan
• Decks
• Shell expansion plan
• Transverse bulkheads plan
• Rudder and Rudder stock
• Hatch Covers (if applicable)

Machinery Plans

• Machinery arrangement plan
• Intermediate, Thrust & Screw Shafts
• Propeller
• Main Engines, Propulsion gears and clutch systems
• Main Boilers, superheaters and economisers
• Bilge and Ballast Piping diagrams
• Wiring Diagram
• Steering gear system Piping & Arrangement and Steering gear manufacturer make and model information

Torsional Vibration Calculations

• For new vessels, Torsional vibration calculations are required

2. For Vessels with Ice class Notation

• Plans for flexible coupling and/or torque limiting shafting devices in the propulsion line shafting

3. For Oil Tankers

• Pumping arrangement and plan for drainage of cofferdams and pump rooms

4. For ships with Unattended Machinery space

• Instrument and alarm list
• Fire alarm safety plan
• List of Automatic safety Functions
• Function testing plan 

You may refer to SOLAS Annex I, which makes it madatory to carry all the as built drawings onboard.

You may also refer IACS URZ23, Section 3.1.1 and also Table 1, which mentiones mandatory documents and plans to be carried oboard.

Addressing particular plan you mentioned i would say; Shell expansion is a mandatory drawing, Tank arrangement is not mandatory drawing as it is only kept by class for reference.

docking plan is a must have plan during the dry docking of the vessel as the repair facility will ask for this document to prepare for the vessel's docking. Refer section 3.1.1 of URZ23.