in the figure below. Lo- pplied at the midpoint B or at the end of the beam C A, will depend on the magnitudes of the loads at Ba a) Determine the sample space of MA- b) Determine the following events: E = (MA> %3D
in the figure below. Lo- pplied at the midpoint B or at the end of the beam C A, will depend on the magnitudes of the loads at Ba a) Determine the sample space of MA- b) Determine the following events: E = (MA> %3D
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![Paragraph
Styles
A 20-ft cantilever beam is shown in the figure below. Load W, = 200 lb, or W,= 500 lb, or both may
be applied at the midpoint B or at the end of the beam C. The bending moment induces at the fixed support
A, MA, will depend on the magnitudes of the loads at B and C.
(a) Determine the sample space of MA-
(b) Determine the following events:
E, = (MA> 5,000 ft – lb)
E2
(1000 < MA < 12,000 ft – lb)
E3 = (2,000, 7,000 ft – lb)
Are the events E1 and E2 mutually exclusive? Explain why.
%3D
(c) Assume the following respective probabilities for the positions of the two loads:
P(W1 at B)
0.25
P(W1 at C) = 0.60
P(W2 at B) = 0.30
P(W2 at C)
0.50
Assuming that the positions of W1 and W2 are statistically independent; what are the
respective probabilities associated with each of the possible values of MA ?
(d) Determine the probabilities of the following events:
E1, E2, E3 E1 0 E2 E1 U E2, and E2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F997510da-997a-4e27-a580-b3c79cbe21d6%2F1e33bf04-69d1-4f81-8f5b-16decb4902b6%2F2zzoxqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Paragraph
Styles
A 20-ft cantilever beam is shown in the figure below. Load W, = 200 lb, or W,= 500 lb, or both may
be applied at the midpoint B or at the end of the beam C. The bending moment induces at the fixed support
A, MA, will depend on the magnitudes of the loads at B and C.
(a) Determine the sample space of MA-
(b) Determine the following events:
E, = (MA> 5,000 ft – lb)
E2
(1000 < MA < 12,000 ft – lb)
E3 = (2,000, 7,000 ft – lb)
Are the events E1 and E2 mutually exclusive? Explain why.
%3D
(c) Assume the following respective probabilities for the positions of the two loads:
P(W1 at B)
0.25
P(W1 at C) = 0.60
P(W2 at B) = 0.30
P(W2 at C)
0.50
Assuming that the positions of W1 and W2 are statistically independent; what are the
respective probabilities associated with each of the possible values of MA ?
(d) Determine the probabilities of the following events:
E1, E2, E3 E1 0 E2 E1 U E2, and E2
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