Asaappp (a) of the figure. The frame has pin supports at A and C. A concentrated load P acts at joint B, thereby placing*20. The frame ABC consists of two members AB and BC that are rigidly connected at joint B, as shown in partmember AB in direct compression.e assist in determining the buckling load for member AB, we represent it as a pinned-end column, askoun in part (b) of the figure. At the top of the column, a rotational spring of stiffness BR represents theSraining action of the horizontal beam BC on the column (note that the horizontal beam provides resistancein rotation of joint B when the column buckles). Also, consider only bending effects in the analysis (i.e., disre-gard the effects of axial deformations).(a) By solving the differential equation of the deflection curve, derive the following buckling equation forthis column:BRL(kL cot kL – 1) – k²L² = 0EIin which L is the length of the column and El is its flexural rigidity.(b) For the particular case when member BC is identical to member AB, the rotational stiffness BR equals3EI/L (see Case 7, Table G-2, Appendix G). For this special case, determine the critical load Per-PiBRВL.LEIAyA(b)(a)

Answered: Image /qna-images/answer/8003ed0e-fb6b-46af-9951-944cb7820c49.jpg

20. 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 ember AB in direct compression. Te assist in determining the buckling load for member AB, we represent it as a pinned-end column, as Laun in part (b) of the figure. At the top of the column, a rotational spring of stiffness BR represents the estraining action of the horizontal beam BC on the column (note that the horizontal beam provides resistance e rotation of joint B when the column buckles). Also, consider only bending effects in the analysis (i.e., disre- gard the effects of axial deformations). (a) By solving the differential equation of the deflection curve, derive the following buckling equation for this column: BRL (kL cot kL - 1) - k²L² = 0 EI %3D in which L is the length of the column and EI is its flexural rigidity. (b) For the particular case when member BC is identical to member AB, the rotational stiffness BR equals

20. 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 ember AB in direct compression. Te assist in determining the buckling load for member AB, we represent it as a pinned-end column, as Laun in part (b) of the figure. At the top of the column, a rotational spring of stiffness BR represents the estraining action of the horizontal beam BC on the column (note that the horizontal beam provides resistance e rotation of joint B when the column buckles). Also, consider only bending effects in the analysis (i.e., disre- gard the effects of axial deformations). (a) By solving the differential equation of the deflection curve, derive the following buckling equation for this column: BRL (kL cot kL - 1) - k²L² = 0 EI %3D in which L is the length of the column and EI is its flexural rigidity. (b) For the particular case when member BC is identical to member AB, the rotational stiffness BR equals

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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