Why is that in proving the theorem

[xter]

Why is that in proving the theorem of minimum potential energy the potential "V" taken negative.Let us say i am applying a load to a spring and as a result spring is deflecting downwards?

 

[sven]

xter,

It's just a sign convention. You can use any mathematically consistant system. Many structural engineers prefer to call downwards deflection "+ve" and the corresponding bending moment positive also. Mathematically however, a downwards load causing a downwards deflection is usually referred to as "-ve" in the conventional x-y coordinate system.

Text books use either convention, depending usually on the author's preference.