3.2 The task is to analyze the structure supporting five
highway signs (Figure P3.2). Draw physical model and freebody diagram of the structure, assuming that wind is blowing in
direction 300 relative to the highway signs.
Figure P3.2 Highway signs.
4.2 A force vector F forms a 30 degrees angle with the y-axis. Determine its components in the
coordinate system x’-y’.
y
y’
x
x’
Figure P4.2
M6.3(212) Load Q = 100 N is supported by the rod AO and by two horizontal cables OB and OC.
Determine the axial force in AO and tension in the cables.
45° C
O
B
45°
A
Q
B136. Box (weight P) is lifted along the incline by block M. What should be weight of the block M
so the box will flip over when is in the position shown?
2c
A
C
2b
a
B
M
α
M4.11 The horizontal rod is suspended by three ropes. Its weight is 42 kN and is it applied at the
point D. Determine tension in each rope.
A
D 60° B F
2m 1m
4m
C
45°
E
288. A 5-m boom AL (weight P = 2 kN) is held by the ball-and-socket joint at A and two cables
DF and DC. Each cable makes angle β = 30o.with the horizontal plane. For the loading
shown determine the reaction forces at A and the tensions in each cable. M = 2.4 kN, LK = 1
m, AD = 2 m, α1 = 45o, α 2 = 60o,
F
β
K
B
α2
z
A
E
C
D α1 β
L
x
M
Make DE and DF ropes; AL – blue;
y
M9.14(296). Locate the centroid of the plane area shown (all dimensions are in mm).
y
C
D
E
A
B
a
320.
x
Locate the centroid of the homogeneous body assembled from a cube with a base a
and a prism of height b. Centroid is located at the plane ABCD. Determine b.
z
D
C
B
A
x
y
8.32 Determine the forces acting in each member of the truss
4kN
A
a
1
a
2
6 a 7 8
5
a
M5.12
a
3
9 a 4
1kN
B
8.71 Determine the force in each member of the truss. What are the reaction forces at A and B?
P1 = 2 kN, P2 = P3 = 4 kN, P4 = 6 kN, P5 = P6 = 2 kN, α = 30o.
P2
P4
P3
1.2a
P1
A
B
P5
a
a
a
8.? – 8.? Determine forces in each truss member , when P = 3 kN, Q = 2 kN, a = 20 cm, b =40cm
and c = 50 cm. Force P is always acting along the line AB and force Q along the line DE.
P
A
1
Q
6
D
4 5
2
c
E
3
a
B
b
9.7 Calculate the internal forces and bending moments in the
bridge if the heavy rain would wash away the earth from both
ends of the bridge. Assume that in such case bridge is
supported by two columns only.
b) The weight of the bridge is 106 lbs and of the truck is 105 lbs.
Assume that the distance between the supporting columns is 30
ft and left and right overhangs are 14 and 20 ft, respectively.
Figure P9.3 Truck on the bridge
Use an intuitive approach (do not write equations for each region)
167-176. Determine the reaction forces and moments at A, B and C.
y
C
A
B
a
168
α
l
x
Change M and 2M to NON italic, like F above
B148. The crank and slider mechanism is activated by moment M. Determine force P to keep the
mechanism from moving. OA = r.
A
M
α
C
β
B
D
P
Can you fill with blue color, not grey?
Ja4.14
P1
A
30°
P2
q
M1
B
E
C
2.0
2.5
2.5
2.0
D
2.0
30°
2.0
Ja2.2
P
o
60
60
q
o
B
A
M0
a a
a
F
3a
4.27 (M2.25) The slender rod ABN (weight 160 N, length 1.2 m) is held in the state of equilibrium
by two cables AC and BC. Determine the tension in each cable. AC = BC = 1 m.
C
Fig. P4.32
5.5 The box is loaded by forces FA =4i-2j+6z,acting at A(0,1,1), FB =-4i+2j-6z ,acting at
B(1,0,1)and FC =4i-2j+6z, ,acting at C(1,-1,1). Reduce these forces to a force-couple system. Is it
possible to reduce them to one force only?
4.25 (M2.18) Pipe O is supported by two frictionless planes which are normal one to another.
Knowing that the weight of the pipe is 60 N, determine the force exerted by the pipe on each plane.
C
A
O
E
D
60°
B
Fig. P4.25
M4.22 The bridge’s weight of 100 kN is applied at the middle of the span AB. The effect of the
wind is represented by a force F = 20 kN acting in the horizontal direction as shown. Determine the
reactions at A and B.
y
20m
B
30°
A
4m
F
x