The tube supports the four parallel forces. Determine the magnitudes of forces FC and FD acting at C and D so that the equivalent resultant force of the force system acts through the midpoint O of the tube.

Question

The tube supports the four parallel forces. Determine the magnitudes of forces { F }_{ C } and { F }_{ D } acting at C and D so that the equivalent resultant force of the force system acts through the midpoint O of the tube.

Accepted Answer

Since the resultant force passes through point O, the resultant moment components
about x and y axes are both zero.

[latex]\sum { M}_{ x }[/latex] = 0 ; [latex]{ F }_{ D }[/latex](0.4) + 600(0.4) - [latex]{ F }_{ C }[/latex](0.4) - 500(0.4) = 0

[latex]{ F }_{ C }[/latex] - [latex]{ F }_{ D }[/latex] = 100

[latex]\sum { M}_{ y }[/latex] = 0 ; 500(0.2) + 600(0.2) - [latex]{ F }_{ C }[/latex](0.2) - [latex]{ F }_{ D }[/latex](0.2) = 0

[latex] { F }_{ C }[/latex] + [latex]{ F }_{ D }[/latex] = 1100

Solving Eqs. (1) and (2) yields:

[latex]{ F }_{ C }[/latex] = 600 N [latex]{ F }_{ D }[/latex] = 500 N

Question : The tube supports the four parallel forces. Determine the ma...

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