What two guiding principles held by the Framers most affected the structure and functions of the US Constitution?

The first guiding principle shared by most of the framers was the need for a powerful central government. James Madison in particular had come to believe that the states, if left to their own devices on such matters as fiscal policy, would ruin the nation. So most (but not all) of the Framers agreed with Edmund Randolph's proposal early in the Constitutional Convention that the delegates adopt a new plan for government in which the...

The first guiding principle shared by most of the framers was the need for a powerful central government. James Madison in particular had come to believe that the states, if left to their own devices on such matters as fiscal policy, would ruin the nation. So most (but not all) of the Framers agreed with Edmund Randolph's proposal early in the Constitutional Convention that the delegates adopt a new plan for government in which the national government, not the states, would be supreme. Some delegates went even further, recommending such institutions as a federal veto on state legislation (Madison) and a unitary executive with a lifetime term (Hamilton). The powerful federal government that emerged from the Convention was a product of this more or less shared belief. Yet they also established a system known as federalism which maintained some of the state powers.

At the same time, most of the delegates shared a belief that the powers of government ought to be divided rather than unified in a single entity. Most were students of the British constitution, which divided power between a monarch, the Lords, and the Commons, and most had read Montesquieu's The Spirit of the Laws, which claimed that a divided form of government was the best suited to avoid tyranny. So the Framers established a government that vested legislative powers in Congress, executive powers in the presidency, and judicial powers in a judicial branch to be fleshed out later by legislation. They also granted each branch certain powers over the other--the veto power of the President, and the impeachment power of Congress, for example--to establish a system of checks and balances to provide a mechanism by which powers could be limited in practice. 

These two principles, centralized government and divided government, were very important to the Framers.