재료역학7판05-01_chap

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Solution 5.4-3 Polyethylene pipe
286 CHAPTER 5 Stresses in Beams
90°
Angle equals 90º or /2 radians, r

radius of
curvature
emax

d
4L



4
¢
4.5 in.
552 in.
≤
6400106
r

L

2


2L

emax

y
r


d
2
2L

r
radius
r
d
L
Problem 5.4-4 A cantilever beam AB is loaded by a couple M0 at
its free end (see figure). The length of the beam is L
1.5 m and the
longitudinal normal strain at the top surface is 0.001. The distance
from the top surface of the beam to the neutral surface is 75 mm.
Calculate the radius of curvature , the curvature , and the vertical
deflection  at the end of the beam.
Solution 5.4-4 Cantilever beam
A
B
M0

L
L
length of beam
L
1.5 m max
0.001
k

1
r

0.01333 m1
∴ r

y
emax


75 mm
0.001

75 m
y
75 mm
emax

y
r
A
C B
M0

L


u
0
L
length of 90º bend
L
46 ft
552 in.
d
4.5 in.
L

2r
4


r
2
Assume that the deflection curve is nearly flat.
Then the distance BC is the same as the length L
of the beam.

arcsin 0.02
0.02 rad

 (1  cos )
(75 m)(1  cos (0.02 rad))

15.0 mm
NOTE: which confirms that the deflection
curve is nearly flat.
L


100,
∴ sin u

L
r


1.5 m
75 m

0.02

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