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Determine the equivalent resultant force of the distributed loading and its location, measured from point A. Evaluate the integrals using Simpson’s rule.

Units Used:

kN = { 10 }^{ 3 } N

Given:

{ c }_{ 1 } = 5

{ c }_{ 2 } = 16

a = 3

b = 1

Step-by-step

{ F }_{ R } = \int _{ 0 }^{ a+b }{ \sqrt { { c }_{ 1 }x\sqrt { { c }_{ 2 }+{ x }^{ 2 } } } dx } \quad \quad \quad \quad { F }_{ R } = 14.9

d = \frac { \int _{ 0 }^{ a+b }{ x\sqrt { { c }_{ 1 }x\sqrt { { c }_{ 2 }+{ x }^{ 2 } } } dx } }{ { F }_{ R } } \quad \quad\quad\quad\quad\quad \quad d = 2.27

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