876_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

876_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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870 CHAPTER 11 Columns Solution 11.4-10 F REE - BODY DIAGRAM OF THE BEAM Q 200 kN d 200 mm L 2.0 m n 3.0 E 72 GPa a 1.0 m C RITICAL LOAD M OMENT OF INERTIA t min 10.0 mm ; t min d 4 A d 4 I 64 p 2 I p 64 c d 4 ( d 2 t ) 4 d I 4 P cr L 2 p 2 E I 27.019 * 10 6 mm 4 P cr p 2 EI 4 L 2 P cr P # n P cr 1200 kN P 400 kN © M c 0 P 2 Q Problem 11.4-11 The frame ABC consists of two members AB and BC that are rigidly connected at joint B , as shown in part (a) of the figure. The frame has pin supports at A and C . A concentrated load P acts at joint B , thereby placing member AB in direct compression. To assist in determining the buckling load for member , we represents it as a pinned-end column, as shown in part (b) of the figure. At the top of the column, a rotational spring of stiffness represents the restraining action of the horizontal beam BC on the column (note that the horizontal beam provides resistance to rotation of joint

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