Three forces act on the pole, as shown in the figure below. Find: (1) FRijk, the

Question

Three forces act on the pole, as shown in the figure below. Find: (1) FRijk, the resultant force vector passing through the origin of the axes (point O) in {i,j,k} format (2) FRmag, the magnitude of resultant force FR (3) MRijk, the resultant moment vector passing through the origin of the axes (point O) in {ij,k} format (4) MRmag, the absolute magnitude of resultant moment MR Example of {i,j,k} form: 22.4i-1 1 .3j-70.3k A (3,-4,0) B (4,3,0) C (-4,3,0) Answer all numeric solutions with five significant figures. Fi =72kN D (0,0,H) F2=67kN F3=75kN H = 10m

Explanation / Answer

F1 in vector form is

unit vector along F1

=(3i-4j-Hk)/sqrt(9+16+H2)

F1=F1(3i-4j-Hk)/sqrt(25+H2)

F2 in vector form is

unit vector along F2

=(4i+3j-Hk)/sqrt(16+9+H2)

F2=F2(4i+3j-Hk)/sqrt(25+H2)

F3 in vector form is

unit vector along F3

=(-4i+3j-Hk)/sqrt(16+9+H2)

F3=F3(-4i+3j-Hk)/sqrt(25+H2)

1) Resultant force vector

FRijk = F1+F2+F3

   =72(3i-4j-10k)/sqrt(25+100)+67(4i+3j-10k)/sqrt(25+100)+75(-4i+3j-10k)/sqrt(25+100)

FRijk =(184i+138j-2140k)/sqrt125

2) FRmag=sqrt(1842+1382+21402)/sqrt125=192.5kN

3) MRijk=FRijk *-10k

=(184i+138j-2140k)/sqrt125*-10k

MRijk=(1840j-1380k)/sqrt125

4) MRmag=sqrt(18402+13802)/sqrt125

=205.7kNm

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