The 150-lb man sits in the center of the boat, which has a uniform width and a weight per linear foot of 3 lb>ft. Determine t
he maximum internal bending moment. Assume that the water exerts a uniform distributed load upward on the bottom of the boat
1 answer:
Answer:
M = 281.25 lb*ft
Explanation:
Given
W<em>man</em> = 150 lb
Weight per linear foot of the boat: q = 3 lb/ft
L = 15.00 m
M<em>max</em> = ?
Initially, we have to calculate the Buoyant Force per linear foot (due to the water exerts a uniform distributed load upward on the bottom of the boat):
∑ Fy = 0 (+↑) ⇒ q'*L - W - q*L = 0
⇒ q' = (W + q*L) / L
⇒ q' = (150 lb + 3 lb/ft*15 ft) / 15 ft
⇒ q' = 13 lb/ft (+↑)
The free body diagram of the boat is shown in the pic.
Then, we apply the following equation
q(x) = (13 - 3) = 10 (+↑)
V(x) = ∫q(x) dx = ∫10 dx = 10x (0 ≤ x ≤ 7.5)
M(x) = ∫10x dx = 5x² (0 ≤ x ≤ 7.5)
The maximum internal bending moment occurs when x = 7.5 ft
then
M(7.5) = 5(7.5)² = 281.25 lb*ft
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(a) 0.1509 mm
(b) 0.00525 mm
Explanation:
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hence
where d is the diameter. Substituting 9970 N for F and 10mm=0.01 m for d hence
From the attached stress-strain diagram, the stress of 127 Mpa corresponds to strain of 0.0015 and since strain is given by
where
is the strain,
is elongation and l is original length and making elongation the subject
and substituting strain with 0.0015 and length l with 100.6 mm then
(b)
Lateral strain is given by
and substituting
for
where v is poisson ratio then
and making
the subject then
and substituting 0.35 for v, 0.0015 for strain and 10 mm for d
and the negative sign indicates decrease in diameter
