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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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Elementary beam theory predicts that the axial bending stress ox in a
prismatic beam is given by:
ox =
(M.I,M,L)y+(M,I.-M.I.)
(1,1₂-13/2)
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 =
2.87x106 mm4. Show that lyz = 1.35x106 mm² (use the parallel
axis theorem).
100
60
10
y
-10
10
60
Figure QB2
N
(iv) Bending moments Mz = 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?

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