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Unformatted text preview: 11Ch11.qxd 9/27/08 3:39 PM Page 879 879 SECTION 11.5 Columns with Eccentric Axial Loads Problem 11.5-13 A frame ABCD is constructed of steel wide-flange
members (W 8 * 21; E 30 * 106 psi) and subjected to triangularly
distributed loads of maximum intensity q0 acting along the vertical
members (see figure). The distance between supports is L 20 ft and
the height of the frame is h 4 ft. The members are rigidly connected
at B and C. A D
h E B C
L (a) Calculate the intensity of load q0 required to produce a maximum
bending moment of 80 k-in. in the horizontal member of BC.
(b) If the load q0 is reduced to one-half of the value calculated in
part (a), what is the maximum bending moment in member BC?
What is the ratio of this moment to the moment of 80 k-in.
in part (a)? Section E-E Solution 11.5-13 Frame with triangular loads
(a) LOAD q0 TO PRODUCE M max 80 k-in. Substitute numerical values into Eq. (1).
Units: pounds and inches
M max 80,000 lb-in.
0.1170093 2P (radians) P resultant force
P A EI
P A 4EI P
q0 Pe sec PL I2 E 30 * 106 psi L h 4 ft 48 in.
3 e 9.77 in.4 (from Table E-1a)
20 ft 240 in. 2P
h 186 lb/in. 2230 lb/ft ; (1) NUMERICAL DATA
W 8 * 21 I (2) 0 4461.9 lb 2 ‹ M max P sec (0.0070093 1P) SOLVE EQ. (2) NUMERICALLY MAXIMUM BENDING MOMENT IN BEAM BC
From Eq. (11-56): M max Pe sec
k P(16 in.) [sec (0.0070093 1P)] 5,000 [cos (0.0070093 1P)] 80,000
e (b) LOAD q0 IS REDUCED TO ONE-HALF ITS VALUE
‹ P is reduced to one-half its value.
(4461.9 lb) 2231.0 lb
Substitute numerical values into Eq. (1) and solve
80 M max ; This result shows that the bending moment varies
nonlinearly with the load. ...
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- Fall '11