11-02 Chap Gere

# 11-02 Chap Gere - 682 CHAPTER 11 Columns Columns with Other...

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682 CHAPTER 11 Columns Columns with Other Support Conditions The problems for Section 11.4 are to be solved using the assumptions of ideal, slender, prismatic, linearly elastic columns (Euler buckling). Buckling occurs in the plane of the figure unless stated otherwise. Problem 11.4-1 An aluminum pipe column ( E 5 10,400 ksi) with length L 5 10.0 ft has inside and outside diameters d 1 5 5.0 in. and d 2 5 6.0 in., respectively (see figure). The column is supported only at the ends and may buckle in any direction. Calculate the critical load P cr for the following end conditions: (1) pinned-pinned, (2) fixed-free, (3) fixed-pinned, and (4) fixed-fixed. Solution 11.4-1 Aluminum pipe column d 1 d 2 d 2 5 6.0 in. d 1 5 5.0 in. E 5 10,400 ksi L 5 10.0 ft 5 120 in. (1) P INNED - PINNED 5 235 k P cr 5 p 2 EI L 2 5 p 2 (10,400 ksi)(32.94 in. 4 ) (120 in.) 2 I 5 p 64 ( d 4 2 2 d 4 1 ) 5 32.94 in. 4 (2) F IXED - FREE (3) F IXED - PINNED (4) F IXED - FIXED P cr 5 4 p 2 EI L 2 5 939 k P cr 5 2.046 p 2 EI L 2 5 480 k P cr 5 p 2 EI 4 L 2 5 58.7 k Problem 11.4-2 Solve the preceding problem for a steel pipe column ( E 5 210 GPa) with length L 5 1.2 m, inner diameter d 1 5 36 mm, and outer diameter d 2 5 40 mm. Solution 11.4-2 Steel pipe column d 2 5 40 mm d 1 5 36 mm E 5 210 GPa (1) P INNED - PINNED P cr 5 p 2 EI L 2 5 62.2 kN I 5 p 64 ( d 4 2 2 d 4 1 ) 5 43.22 3 10 3 mm 4 Ê L 5 1.2 m (2) F IXED - FREE (3) F IXED - PINNED (4) F IXED - FIXED P cr 5 4 p 2 EI L 2 5 249 kN P cr 5 2.046 p 2 EI L 2 5 127 kN P cr 5 p 2 EI 4 L 2 5 15.6 kN Probs. 11.4-1 and 11.4-2

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SECTION 11.4 Columns with Other Support Conditions 683 Problem 11.4-3 A wide-flange steel column ( E 5 30 3 10 6 psi) of W 12 3 87 shape (see figure) has length L 5 28 ft. It is supported only at the ends and may buckle in any direction. Calculate the allowable load P allow based upon the critical load with a factor of safety n 5 2.5. Consider the following end conditions: (1) pinned-pinned, (2) fixed-free, (3) fixed-pinned, and (4) fixed-fixed. Solution 11.4-3 Wide-flange column 11 2 2 W 12 3 87 E 5 30 3 10 6 psi L 5 28 ft 5 336 in. n 5 2.5 I 2 5 241 in. 4 (1) P INNED - PINNED 5 253 k (2) F IXED - FREE P allow 5 p 2 EI 2 4 n L 2 5 63.2 k P allow 5 P cr n 5 p 2 EI 2 nL 2 (3) F IXED - PINNED (4) F IXED - FIXED P allow 5 4 p 2 EI 2 n L 2 5 1011 k P allow 5 2.046 p 2 EI 2 n L 2 5 517 k Problem 11.4-4 Solve the preceding problem for a W 10 3 60 shape with length L 5 24 ft. Solution 11.4-4 Wide-flange column W 10 3 60 E 5 30 3 10 6 psi L 5 24 ft 5 288 in. n 5 2.5 I 2 5 116 in. 4 (1) P INNED - PINNED (2) F IXED - FREE P allow 5 p 2 EI 2 4 nL 2 5 41.4 k P allow 5 P cr n 5 p 2 EI 2 nL 2 5 166 k (3) F IXED - PINNED (4) F IXED - FIXED P allow 5 4 p 2 EI 2 nL 2 5 663 k P allow 5 2.046 p 2 EI 2 nL 2 5 339 k Probs. 11.4-3 and 11.4-4
B 2.9 m 2.1 m 2.0 m A 684 CHAPTER 11 Columns Problem 11.4-5 The upper end of a W 8 3 21 wide-flange steel column ( E 5 30 3 10 3 ksi) is supported laterally between two pipes (see figure). The pipes are not attached to the column, and friction between the pipes and the column is unreliable. The base of the column provides a fixed support, and the column is 13 ft long.

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## This note was uploaded on 03/19/2008 for the course E M 316 taught by Professor Korkolis during the Spring '08 term at University of Texas.

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11-02 Chap Gere - 682 CHAPTER 11 Columns Columns with Other...

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