A bar of a uniform cross-section is rigidly fixed at one end and loaded by an off-centre tensile point load F = 1.5 kN at the other end, see Fig. Q1a. The Figure Q1b presents the view of the beam from the free end where the point of application of the load F is indicated as A. The allowable stress [0]=234 MPa The geometrical parameters are given as follow h=18 mm, b=37 mm

Structural Analysis
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Chapter2: Loads On Structures
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A bar of a uniform cross-section is rigidly fixed at one end and loaded by an off-centre tensile point
load F = 1.5 kN at the other end, see Fig. Q1a. The Figure Q1b presents the view of the beam from the
free end where the point of application of the load F is indicated as A. The allowable stress [0]=234
MPa
The geometrical parameters are given as follow
h 18 mm, b=37 mm
N
y
b
Figure Q1a
Figure Q1b
h
F
X
Transcribed Image Text:A bar of a uniform cross-section is rigidly fixed at one end and loaded by an off-centre tensile point load F = 1.5 kN at the other end, see Fig. Q1a. The Figure Q1b presents the view of the beam from the free end where the point of application of the load F is indicated as A. The allowable stress [0]=234 MPa The geometrical parameters are given as follow h 18 mm, b=37 mm N y b Figure Q1a Figure Q1b h F X
a)
Find:
Q1 - the magnitude of the maximum normal stress in the beam and where within the beam it is
achieved.
The bending moment relative to z-axis Mz on the cross section can be calcualted as
The bending moment relative to y-axis My on the cross section can be calcualted as
The second moment of area relatve to z-axis can be calculated as
mm4
mm4
The second moment of area relative to y-axis can be calculated as
Let B denote the point that achieves maximum normal stress on the cross section of the beam
The y-coordinate of B is
The z-coordinate of B is
mm
mm
The magnitude of the maximum normal stress in the beam can be calculated as
N.mm
N.mm
MPa
Transcribed Image Text:a) Find: Q1 - the magnitude of the maximum normal stress in the beam and where within the beam it is achieved. The bending moment relative to z-axis Mz on the cross section can be calcualted as The bending moment relative to y-axis My on the cross section can be calcualted as The second moment of area relatve to z-axis can be calculated as mm4 mm4 The second moment of area relative to y-axis can be calculated as Let B denote the point that achieves maximum normal stress on the cross section of the beam The y-coordinate of B is The z-coordinate of B is mm mm The magnitude of the maximum normal stress in the beam can be calculated as N.mm N.mm MPa
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