*25. A hitch-mounted bicycle rack is designed to carry up to four 135 N bikes mounted on and strapped to two arms GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W, = 45 N, centered 9 in. from A [see the figure part (b)] and the rest of the rack weighs W, 180 N, centered 480 mm from A. Segment ABCDG is a steel tube 50 X 50 mm, of thickness t 3 mm Segment BCDGH pivots about a bolt at B of diameter dg 6 mm to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C (diameter of pin d, = 8 mm) [see photo and figure part (c)]. The overturning effect of the bikes on the rack is resisted by a force couple F.hat BC. (a) Find the support reactions at A for the fully loaded rack; (b) Find forces in the bolt at B and the pin at C. assumed to be like a cantilever (c) Find average shear stresses Taver in both the bolt at B and the pin at C. (d) Find average bearing stresses o, in the bolt at B and the pin at C. Bike loads y 4 bike loads 480 mm G 685 mm 3 @ 100 mm Release pins at C & G .(dp = 8 mm) W2 150 mm 50 mm X 50 mm X 3 mm MA Ay D. F 54 mm h = 175 mm A Fixed W1 a support at A F Bolt at B h=D175 mm (dp = 6 mm) 230 mm 200 mm (а) (b)
*25. A hitch-mounted bicycle rack is designed to carry up to four 135 N bikes mounted on and strapped to two arms GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W, = 45 N, centered 9 in. from A [see the figure part (b)] and the rest of the rack weighs W, 180 N, centered 480 mm from A. Segment ABCDG is a steel tube 50 X 50 mm, of thickness t 3 mm Segment BCDGH pivots about a bolt at B of diameter dg 6 mm to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C (diameter of pin d, = 8 mm) [see photo and figure part (c)]. The overturning effect of the bikes on the rack is resisted by a force couple F.hat BC. (a) Find the support reactions at A for the fully loaded rack; (b) Find forces in the bolt at B and the pin at C. assumed to be like a cantilever (c) Find average shear stresses Taver in both the bolt at B and the pin at C. (d) Find average bearing stresses o, in the bolt at B and the pin at C. Bike loads y 4 bike loads 480 mm G 685 mm 3 @ 100 mm Release pins at C & G .(dp = 8 mm) W2 150 mm 50 mm X 50 mm X 3 mm MA Ay D. F 54 mm h = 175 mm A Fixed W1 a support at A F Bolt at B h=D175 mm (dp = 6 mm) 230 mm 200 mm (а) (b)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![*25. A hitch-mounted bicycle rack is designed to carry up to four 135 N bikes mounted on and strapped to two arms
GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and is assumed to be like a cantilever
beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W1 = 45 N, centered 9 in. from A [see the figure
part (b)] and the rest of the rack weighs W2
50 mm, of thickness t = 3 mm Segment BCDGH pivots about a bolt at B of diameter dg =6 mm to allow access to the
rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C
(diameter of pin d, = 8 mm) [see photo and figure part (c)]. The overturning effect of the bikes on the rack is resisted by
a force couple F hat BC.
(a) Find the support reactions at A for the fully loaded rack;
(b) Find forces in the bolt at B and the pin at C.
180 N, centered 480 mm from A. Segment ABCDG is a steel tube 50 X
(c) Find average shear stresses Taver in both the bolt at B and the pin at C.
(d) Find average bearing stresses o, in the bolt at B and the pin at C.
Bike loads
y
4 bike loads
480 mm
685 mm
3 @ 100 mm
Release pins
at C & G
.(dp = 8 mm)
W2
150 mm
50 mm X 50 mm X 3 mm
MA
Ay
D
F
54 mm
h = 175 mm
A
Fixed
W1
a
support
at A
B
B
F
Bolt at B
h = 175 mm
(dg = 6 mm)
230 mm 200 mm
(a)
(b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9eea264-28d6-47f8-8c05-ae39f302e92c%2F4b3b2883-b28e-458b-b9b2-c45daef88a29%2Fy1opcip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:*25. A hitch-mounted bicycle rack is designed to carry up to four 135 N bikes mounted on and strapped to two arms
GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and is assumed to be like a cantilever
beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W1 = 45 N, centered 9 in. from A [see the figure
part (b)] and the rest of the rack weighs W2
50 mm, of thickness t = 3 mm Segment BCDGH pivots about a bolt at B of diameter dg =6 mm to allow access to the
rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C
(diameter of pin d, = 8 mm) [see photo and figure part (c)]. The overturning effect of the bikes on the rack is resisted by
a force couple F hat BC.
(a) Find the support reactions at A for the fully loaded rack;
(b) Find forces in the bolt at B and the pin at C.
180 N, centered 480 mm from A. Segment ABCDG is a steel tube 50 X
(c) Find average shear stresses Taver in both the bolt at B and the pin at C.
(d) Find average bearing stresses o, in the bolt at B and the pin at C.
Bike loads
y
4 bike loads
480 mm
685 mm
3 @ 100 mm
Release pins
at C & G
.(dp = 8 mm)
W2
150 mm
50 mm X 50 mm X 3 mm
MA
Ay
D
F
54 mm
h = 175 mm
A
Fixed
W1
a
support
at A
B
B
F
Bolt at B
h = 175 mm
(dg = 6 mm)
230 mm 200 mm
(a)
(b)
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