The magnitude of a moment about a line segmentconnecting points P and Q due to a force Fapplied at point R (with R not on the line through Pand Q) can be calculated using the scalar tripleproduct,MPQUPQ rx F,where r is a position vector from any point on theline through P and Q to R and upo is the unitvector in the direction of line segment PQ. The unitvector upq is then multiplied by this magnitude tofind the vector representation of the moment.Figure-As shown in the figure, the member is anchored atA and séction AB lies in the x-y plane. Thedimensions are x₁ = 1.5 m, y₁ = 1.7 m, and 2₁ =1.6 m. The force applied at point C isF = [-150 i+ 135j + 190 k] N.(Figure 1)Vi21B1 of 1> Part B-Calculating the moment about AB using the position vector ACUsing the position vector from A to C, calculate the moment about segment AB due to force F.Express the individual components to three significant figures, if necessary, separated by commas.View Available Hint(s)MAB =[Submit10 ΑΣΦ↑MAB =[vec4Part C- Calculating the moment about AB using the position vector BC?Using the position vector from B to C, calculate the moment about segment AB due to force F.Express the individual components to three significant figures, if necessary, separated by commas.► View Available Hint(s)VE ΑΣΦ $1 vec→i, j, k N.m?i, j, k N-m

Given data:- Member is anchored at A and section AB lies in the x-y plane. Dimensions, x1=1.5 m,…

Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ►View Available Hint(s) MAB =[ Submit VG ΑΣΦ ↑ MAB =[ vec B 4 Part C- Calculating the moment about AB using the position vector BC VE ΑΣΦ $1 vec ? Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. View Available Hint(s) wwwww. i, j, k N m ? i, j, k] N.m

Part B - Calculating the moment about AB using the position vector AC Using the position vector from A to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ►View Available Hint(s) MAB =[ Submit VG ΑΣΦ ↑ MAB =[ vec B 4 Part C- Calculating the moment about AB using the position vector BC VE ΑΣΦ $1 vec ? Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. View Available Hint(s) wwwww. i, j, k N m ? i, j, k] N.m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.

Question

The magnitude of a moment about a line segment
connecting points P and Q due to a force F
applied at point R (with R not on the line through P
and Q) can be calculated using the scalar triple
product,
MPQ
UPQ rx F,
where r is a position vector from any point on the
line through P and Q to R and upo is the unit
vector in the direction of line segment PQ. The unit
vector upq is then multiplied by this magnitude to
find the vector representation of the moment.
Figure
-
As shown in the figure, the member is anchored at
A and séction AB lies in the x-y plane. The
dimensions are x₁ = 1.5 m, y₁ = 1.7 m, and 2₁ =
1.6 m. The force applied at point C is
F = [-150 i+ 135j + 190 k] N.
(Figure 1)
Vi
21
B
1 of 1
>

Part B-Calculating the moment about AB using the position vector AC
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
MAB =[
Submit
10 ΑΣΦ
↑
MAB =[
vec
4
Part C- Calculating the moment about AB using the position vector BC
?
Using the position vector from B to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
► View Available Hint(s)
VE ΑΣΦ $1 vec
→
i, j, k N.m
?
i, j, k N-m

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