problem-1
DESCRIPTION
PROBLEM-1. State of stress at a p oin t is represented by the element shown. Determine the state of stress at the p oin t on another element orientated 30 clockwise from the position shown. PROBLEM-1. PROBLEM-1. PROBLEM-2. - PowerPoint PPT PresentationTRANSCRIPT
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TUTORIAL-7: STRESS TRANSFORMATION
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PROBLEM-1
State of stress at a point is represented by
the element shown. Determine the state
of stress at the point on another element
orientated 30 clockwise from the position
shown.
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PROBLEM-1
2222 xy
yxyx'x sincos
MPa8.25
6)25(6025080
25080 o
o0-sincos
2222 xy
yxyx'y sincos
MPa15.4
6)25(6025080
25080 o
o0-sincos
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PROBLEM-1
222 xy
yx'y'x cossin
MPa8.68
6)25(6025080 o
o0-cossin
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PROBLEM-2State of plane stress at a point on a body is represented on the element shown. Represent this stress state in terms of1. the maximum in-plane shear stress and associated
average normal stress, and2. the in-plane principal stress and its orientation.
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PROBLEM-21. The maximum in-plane shear stress and associated average
normal stress.
2xy
2yxmax
planein 2
MPa4.81
6029020 2
2
xy
yxs
22tan
9167.0
6029020
s = 21.3o
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PROBLEM-2
MPa3529020
2yx
avg
2. The in-plane principal stress and its orientation.
2xy
2yxyx
2,1 22
MPa)4.8135(
6029020
29020 2
2
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PROBLEM-2
MPa4.46MPa)4.8135(MPa4.116MPa)4.8135(
2
1
2yx
xyp
2tan
Principal stress orientation.
091.129020
60
p = – 23.7o
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PROBLEM-3Steel pipe has inner diameter of 60 mm and outer diameter of 80 mm. It is subjected to a torsional moment of 8 kN·m and a bending moment of 3.5 kN·m. Determine:1. The maximum in-plane shear stress and associated average normal
stress.2. The in-plane principal stress and its orientation.
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Investigate a point on pipe that is subjected to a state of maximum critical stress.
• Torsional and bending moments are uniform throughout the pipe’s length.
• At arbitrary section a-a, loadings produce the stress distributions shown.
• Point A undergoes maximum compressive stress and point B undegoes maximum tensile stress.
• Thus, the critical point is at B.
PROBLEM-3
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PROBLEM-3
Maximum tensile stress at point B:
MPa86.101)0.03(0.04
4)(3500)(0.044
4π
zIcM
Maximum shear stress at point B:
MPa4.116)0.03(0.04
04)(-8000)(0.44
2π
J
cTτ
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PROBLEM-31. The maximum in-plane shear stress and associated average
normal stress.
2xy
2yxmax
planein 2
MPa127
)4.116(2
086.101 22
MPa9.502
086.101
2yx
avg
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PROBLEM-32. The in-plane principal stress and its orientation.
2xy
2yxyx
2,1 22
MPa)1279.50(
)4.116(2
086.1012
086.101 22
MPa1.76MPa)1279.50(MPa9.177MPa)1279.50(
2
1
2yx
xyp
2tan 285.2
2086.1014.116
p = – 33.1o
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PROBLEM-4
Stress in Shafts Due to Axial Load, Bending Load and Torsion
A shaft has a diameter of 4 cm. The cutting section shows in the figure is subjected to a compressive force of 2500 N, a bending moment of 800 Nm and a torque of 1500 Nm.
Determine: 1. The stress state of point A. 2. The principal stresses and its orientation
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PROBLEM-41. The stress state at point A has been
solved in Tutorial-6 Problem-3. The results are as follows
Shear stress: xy = A = 119.37 MPa
Normal stress: x = A’ + A”
= (– 1.99 – 127.32) MPa
= – 129.31 MPa
xy
x
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PROBLEM-42. The principal stress at point A and its orientation
2xy
2yxyx
2,1 22
MPa)75.13565.64(
37.1192
031.1292
031.129 22
MPa40.200MPa)75.13565.64(MPa10.71MPa)75.13565.64(
2
1
2yx
xyp
2tan 846.1
2031.12937.119
p = – 30.78o