King Saud University
College of Engineering, Department of Civil Engineering
Student name
GE201 Statics
Final Exam, 1st Semester 1430 - 31 H
page 3/6
Marks obtained for Q 2
Student number
Question # 2 (10 points)
The turnbuckle, shown in Figure 4, is tightened until
the tension in the cable AB equals 2.4 kN.
Determine:
(a)
(b)
(c)
The vector expression for the tension T as a
force acting in cable AB.
Magnitude of the moment about point O of the
force acting on point A.
Value of the moment of the force acting on
point A about the line OB.
Figure 4
Note: O (0, 0, 0); A (0, 2, 5); B (2, 3, 0)
(a)
r
⎡ 2ir + rj − 5k
r
r
r
T AB = T n AB ⇒ T AB = 2.4 ⎢
⎢⎣ 2 2 +12 + (−5) 2
r
r
r
r
⇒ T AB = 0.876i + 0.438 j − 2.19k
(b)
r
r
r
M O = rOB × T AB =
r
i
2
r
j
3
⎤
⎥
⎥⎦
Course
Learning Obj.
#
1
Percentage
%
100
r
k
0
0.876 0.438 − 2.19
r
r
r
r
⇒ M O = −6.57i + 4.38 j − 1.75k
r
∴ M O = (−6.57) 2 + 4.38 2 + (−1.75) 2 = 8.08 kN.m
(c)
r
r
r ⎡ 2i + 3 j ⎤
r r
r
r
M OB = M O .nOB = (−6.57i + 4.38 j − 1.75k ).⎢
⎥
2
2
⎣ 2 +3 ⎦
⇒ M OB = −3.64 + 3.64 = 0
Note: Since line OB is intersecting the line of action of the force TAB, moment of the force TAB about the line
OB is very well expected to be zero.