The equivalent resultant couple moment about the point O is 15.375KNm
The load carried by section (1)
F1 = 1/2 × 1.5 × (w1 - w2)
F1 = 1/2 × 1.5 × 4 = 3KN
the load carried by section (2).
F2 = w2 × (1.5 + 0.75)
F2 = 4 × 2.25 = 9KN
F3 = 1/2 × 0.75 × 4 = 1.5 KN
Determine the equivalent resultant force.
∑Fr = F1 + F2 + F3 = 13.5 KN
the moment about the point O due to distributed loading,
∑ Mr = F1 x1 + F2x2 + F3x3
x1 = 0.5m
x2 = 1.125m
x3 = 2.5m
the equivalent resultant couple moment about the point O is
Mr = ∑Mr = 15.375KNm
The equivalent resultant couple moment about any point on the given beam is equal to the sum of couple moment developed by each of the distributed loading about that point. Calculate the moment caused by each force about point O, using the distance of the centroid from end O.
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