Lecture 4 Q4 Reference: Two Ways to Find Zero Shear and Max Moment
Same beam, same answer. Left = diagram/area method. Right = equation/calculus form of the same area idea.
Common setup for both methods
METHOD 1 - Lecture Diagram / Area Method
METHOD 2 - Equation / Calculus Method
Idea: use geometry areas. No integration needed.
Idea: write the same area rule as equations.
At x=3 m, shear is +200 N. The downward load must
accumulate 200 N of area before V reaches zero.
The load starts at x=3 m, so define u=x-3.
This makes u=0 at the start and u=3 at B.
Shear equation from the load area:
Set V=0, then integrate V to get moment:
Partial load area from start of load to zero-shear point:
Then use area under the shear diagram to get moment:
Result: same x and same Mmax as the area method.
Result: x = 3.873 m, Mmax = 690.99 N*m
Key: the calculus method is not a different concept - it is the area method written with integrals. For your lecture style, use geometry areas unless equations are requested.