Determine the magnitudes of FA and FB so that the resultant force passes through point O of the column.

Question

Determine the magnitudes of { F }_{ A } and { F }_{ B } so that the resultant force passes through point O of the column.

Accepted Answer

Equivalent Resultant Force: By equating the sum of the forces in Fig. a along the z
axis to the resultant force [latex]{ F }_{ R }[/latex] , Fig. b,

[latex]+\uparrow[/latex] [latex]{ F }_{ R }[/latex] = [latex] \sum { F}_{ z }[/latex] ; [latex]-{ F }_{ R }[/latex] = [latex]-{ F }_{ A }[/latex] [latex]-{ F }_{ B }[/latex] - 8 - 6

[latex]{ F }_{ R }[/latex]= [latex]{ F }_{ A }[/latex] + [latex]{ F }_{ B }[/latex] + 14

Point of Application: Since [latex]{ F }_{ R }[/latex] is required to pass through point O, the moment of [latex]{ F }_{ R }[/latex]
about the x and y axes are equal to zero.Thus,

[latex]{ ({ M }_{ R }) }_{ x }[/latex] = [latex]\sum { M}_{ x }[/latex] ; 0= [latex]-{ F }_{ B }[/latex](750) + 6(650) - [latex]-{ F }_{ A }[/latex](600) - 8(700)

750[latex]{ F }_{ B }[/latex] - 600[latex]{ F }_{ A }[/latex] - 1700 = 0

[latex]{ ({ M }_{ R }) }_{ x }[/latex] = [latex]\sum { M}_{ y }[/latex] ; 0= [latex]{ F }_{ A }[/latex](150) + 6(100) - [latex]{ F }_{ B }[/latex](150) - 8(100)

159[latex]{ F }_{ A }[/latex] - 150 [latex]{ F }_{ B }[/latex] + 200 = 0

Solving Eqs. (1) through (3) yields

[latex]{ F }_{ A }[/latex] = 18.0 kN [latex]{ F }_{ B }[/latex] = 16.7 kN [latex]{ F }_{ R }[/latex] = 48.7 kN

Question : Determine the magnitudes of FA and FB so that the resultant ...

This Question has been Answered.

Already have an account?

Login