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Unformatted text preview: 06Ch06.qxd 9/24/08 540 5:54 AM Page 540 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.5-12 A C 200 17.1 channel section has an angle
with equal legs attached as shown; the angle serves as a lintel
beam. The combined steel section is subjected to a bending
moment M having its vector directed along the z axis, as shown
in the figure. The centroid C of the combined section is located
at distances xc and yc from the centroid (C1) of the channel alone.
Principal axes x1 and y1 are also shown in the figure and properties Ix1, Iy1 and up are given below.
Find the orientation of the neutral axis and calculate the
maximum tensile stress st and maximum compressive stress sc if
the angle is an L 76 76 6.4 section and M 3.5 kN # m. Use
the following properties for principal axes for the combined
section: Ix1 18.49 106 mm4 Iy1 1.602 106 mm4,
up 7.448° (CW), xc 10.70 mm, yc 24.07 mm. y1 y C C1 M z yc
up xc L 76 76
lintel x1 C 200 6.4 Solution 6.5-12
M 3.5 kN # m ANGLE: ca CHANNEL: up zpA 7.448° 21.2 mm
cc 14.5 mm bc La zpA 76 mm
dc ypA 203 mm 57.4 mm ypA
st BUILT-UP SECTION:
ybar 24.07 mm Izp Ix1 Izp 18.49 Iyp xbar 10.70 mm st (yA) sin ( up) up) + (yA) cos ( (zA) cos ( up) up) 63.18 mm
(zA) sin ( 69.83 mm
Myp(zpA) Mzp(ypA) Iyp Izp
; 31.0 MPa Iy1
106 mm4 Iyp 1.602 106 mm4 MAXIMUM COMPRESSIVE STRESS (AT POINT B)
zB BENDING MOMENTS xbar cc Myp Msin( up) Myp 454 N # m zpB (zB) cos ( Mzp Mcos( up) Mzp 3470 N # m zpB 20.05 mm ypB (zB) sin ( ypB dc
2 yB 124.0 mm NEUTRAL AXIS nn
b a tan a Izp
Iyp tan( up)
b b 56.5° sc MAXIMUM TENSILE STRESS (AT POINT A)
zA xbar cc bc ; yA dc
2 sc up) (yB) sin ( up) up) + (yB) cos ( up) Myp(zpB) Mzp(ypB) Iyp Izp 29.0 MPa ; 17.1 ...
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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