(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?
(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?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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please do the question (iv)
i will be extremly appreciate!!
Transcribed Image Text:100
60
10
y
10
10
60
Figure QB2
Z
All dimensions
in mm.
(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?
Transcribed Image Text:Elementary beam theory predicts that the axial bending stress ox in a
prismatic beam is given by:
(M.I, -M,1)+(M,I.- M.I, )
(1,1-12)
where My and M₂ are bending moments applied to a cross-section, and
where ly, Iz 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).
(i) What assumptions have been made in the derivation of the
above expression?
(ii) Indicate by means of a sketch the directions in which positive
values of the bending moments My and M₂ act on a cut plane
facing in the positive x direction.
(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= 1.12x10 mm4 and /z =
2.87x10 mm4. Show that lyz = 1.35x106 mmª (use the parallel
axis theorem).
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