Determine the resisting moment MRA at the base of the utility pole assuming forces T1 = 200# and T2 = 300# are as shown. What are the horizontal reactions Ax and Ay at the base? (Show FBD.)

Question

Determine the resisting moment [latex]M_{RA}[/latex] at the base of the utility pole assuming forces [latex] T_{1}[/latex] = 200# and [latex] T_{2}[/latex] = 300# are as shown. What are the horizontal reactions [latex] A_{x} [/latex] and [latex] A_{y} [/latex] at the base? (Show [latex]FBD[/latex].)

Accepted Answer

[latex] T_{1x}=T_{1} \cos 15 ^{\circ } =200\# (0.966)=193\# [/latex]

[latex] T_{1y}=T_{1} \sin 15 ^{\circ } =200\# (0.259)=51.8\# [/latex]

[latex] T_{2x}=T_{2} \cos 10 ^{\circ } =300\# (0.985)=295.4\# [/latex]

[latex]T_{2y}=T_{2} \sin 10 ^{\circ } =300\# (0.174)=52\# [/latex]

[latex]\left[\sum{} M_{A}=0 ight]-M_{RA}+295.4\# (30^{\prime } ) -193\# (35^{\prime } )+52\# (6^{\prime } )-51.8\# (4^{\prime } )=0[/latex] (1)

solving for [latex]M_{RA}[/latex] : [latex]M_{RA}=+2,212 \space \# -ft.[/latex]

[latex]\left[\sum{F_{x}} =0 ight] -295.4\# +193\# +A_{x}=0[/latex] (2)

[latex] herefore A_{x} =+102.4\# [/latex]

[latex]\left[\sum{F_{y}} =0 ight] -52 \#-51.8\# +A_{y}=0[/latex] (3)

[latex] herefore A_{y} =+103.8\#[/latex]

Question 2.30: Determine the resisting moment MRA at the base of the utilit...

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