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Unformatted text preview: 05Ch05.qxd 9/24/08 390 4:59 AM Page 390 CHAPTER 5 Stresses in Beams (Basic Topics) Problem 5.4-3 A 4.5 in. outside diameter polyethylene pipe
designed to carry chemical wastes is placed in a trench and bent
around a quarter-circular 90° bend (see figure). The bent section of
the pipe is 46 ft long.
Determine the maximum compressive strain âmax in the pipe. Solution 5.4-3 90° Polyethylene pipe
Angle equals 90° or p/2 radians,
L length of 90° bend L 46 ft d r r r L
p/2 4.5 in.
4 L 552 in. pr
2 radius of curvature
4L âmax y
r âmax d/2
2L/p p 4.5 in.
4 552 in. 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 r, the curvature k, and the vertical
deflection d at the end of the beam. 6400 * 10 6 ; d A
B M0 L Solution 5.4-4
Deflection: constant curvature for pure bending so
gives a circular arc; assume flat deflection curve
(small defl.) so BC L NUMERICAL DATA
âmax L 2.0 m c 82.5 mm 0.0012 RADIUS OF CURVATURE
r 68.8 m
âmax sin(u) 1
r k 1.455 * 10 u L
asin a b
r 5 m 1 ; 0.029 radians 1 cos(u) d r (1 L
r 4.232 * 10
cos(u)) d 0.029
29.1 mm 6.875 * 104 mm
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11