Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: (M.I, -M,I)y+(M,I.-M.I.) (1,1. – 13) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross--section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y 10 10 60 Figure QB2 Z (iv) Bending moments M₂ = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?

Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: (M.I, -M,I)y+(M,I.-M.I.) (1,1. – 13) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross--section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y 10 10 60 Figure QB2 Z (iv) Bending moments M₂ = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?

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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