Question 2 - Stress Transformation The state of stress at a point A on the surface of a beam is shown below, assuming the x - y coordinate system shown. A L The stresses point in the directions as indicated above, and have magnitudes given by: • %a = 25 MPa • Ob = 220 MPa T = 190 MPa y b) Find the in-plane principal stresses (assume 'maximum' refers to the most positive value): Omax = MPa Omin = MPa X Part One: Principal Stresses a) Find the in-plane principal angle at the point A on the surface of the pressure vessel, measured relative to the positive x-axis: Op degrees % Part Two: Mohr's Circle An example sketch of Mohr's circle for the state of stress is shown below. It is not drawn to scale, and it is recommended you draw your own Mohr's circle to perform the following calculations.
Question 2 - Stress Transformation The state of stress at a point A on the surface of a beam is shown below, assuming the x - y coordinate system shown. A L The stresses point in the directions as indicated above, and have magnitudes given by: • %a = 25 MPa • Ob = 220 MPa T = 190 MPa y b) Find the in-plane principal stresses (assume 'maximum' refers to the most positive value): Omax = MPa Omin = MPa X Part One: Principal Stresses a) Find the in-plane principal angle at the point A on the surface of the pressure vessel, measured relative to the positive x-axis: Op degrees % Part Two: Mohr's Circle An example sketch of Mohr's circle for the state of stress is shown below. It is not drawn to scale, and it is recommended you draw your own Mohr's circle to perform the following calculations.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 2 - Stress Transformation
The state of stress at a point A on the surface of a beam is shown below, assuming the x - y coordinate system shown.
A
L
The stresses point in the directions as indicated above, and have magnitudes given by:
• %a = 25 MPa
• Ob = 220 MPa
T = 190 MPa
y
b) Find the in-plane principal stresses (assume 'maximum' refers to the most positive value):
Omax =
MPa
Omin =
MPa
X
Part One: Principal Stresses
a) Find the in-plane principal angle at the point A on the surface of the pressure vessel, measured relative to the positive x-axis:
Op
degrees
%
Part Two: Mohr's Circle
An example sketch of Mohr's circle for the state of stress is shown below. It is not drawn to scale, and it is recommended you draw your own Mohr's
circle to perform the following calculations.

Transcribed Image Text:σ
min
P₁
α
((OST)
b) Find the radius of the circle:
R=
MPa
(C₂,0)
ayy=
Txy =
α
a) Find the horizontal coordinate of the centre of the circle:
Cx =
MPa
(0₁-T)
MPa
MPa
P
2
max
Consider the points Pi (0x'x' x'y) and P₂(yy-Txy) shown on Mohr's circle, which differ by an angle of a = 33 degrees rotated clockwise from
the values representing measurements in the x-y plane as shown.
₂0₁
c) What are the stresses for this x'-y coordinate system represented by the red line on Mohr's circle?
Ox'x'=
MPa
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