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873_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

873_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.4 Columns with Other Support Conditions 867 Solution Column BD Column CE P cr CE 1859 lb L 45 in. P cr CE p 2 EI L 2 P cr BD 768.4 lb P cr BD p 2 EI 4 L 2 L 35 in. I 0.01272 in. 4 I b 4 12 b 0.625 in. E 30 # 10 6 psi (a) F IND The system collapses when both columns buckle. (b) IS MAXIMUM WHEN Q cr 10065 lb ; Q cr P cr BD (10 in.) + P cr CE (50 in.) a + 10 in. a 0 in. Q cr Q cr 4575 lb ; Q cr P cr BD (10 in.) + P cr CE (50 in.) a 10 in. Q cr ( a + 10in.) 0 P cr BD (10 in.) + P cr CE (50 in.) © M A 0 Q cr if a 12 in. Problem 11.4-7 The horizontal beam ABC shown in the figure is supported by column BD and CE . The beam is prevented from moving horizontally by the pin support at end A . Each column is pinned at its upper end to the beam, but at the lower ends, support D is a guided support and support E is pinned. Both columns are solid steel bars ( ) of square cross section with width equal to 0.625 in. A load Q acts at distance a from column BD . (a) If the distance , what is the critical value Q cr of the load? (b) If the distance a can be varied between 0 and 40 in., what is the maximum possible value of Q
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Unformatted text preview: Q cr ? What is the corresponding value of the distance a ? a 12 in. E 30 * 10 6 psi B A a C E D Q 0.625 in. 0.625 in. 40 in. 10 in. 35 in. 45 in. Problem 11.4-8 The roof beams of a warehouse are supported by pipe columns (see figure on the next page) having outer diameter and inner diameter . The columns have length , modulus , and fixed supports at the base. Calculate the critical load P cr of one of the columns using the following assumptions: (1) the upper end is pinned and the beam prevents horizontal displacement; (2) the upper end is fixed against rotation and the beam prevents horizontal displacement; (3) the upper end is pinned but the beam is free to move horizontally; and (4) the upper end is fixed against rotation but the beam is free to move horizontally. E 210 GPa L 4.0 m d 1 90 mm d 2 100 mm d 2 Pipe column Roof beam L 11Ch11.qxd 9/27/08 3:39 PM Page 867...
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