2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of...
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Transcript of 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of...
![Page 1: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/1.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
1
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.
![Page 2: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/2.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
2
PROBLEM-1
2222 xy
yxyx'x sincos
MPa8.25
6)25(602
5080
2
5080 o
o0-sincos
2222 xy
yxyx'y sincos
MPa15.4
6)25(602
5080
2
5080 o
o0-sincos
![Page 3: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/3.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
3
PROBLEM-1
222 xy
yx'y'x cossin
MPa8.68
6)25(602
5080 o
o0-cossin
![Page 4: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/4.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
4
PROBLEM-2
State of plane stress at a point on a body is represented on the element shown. Represent this stress state in terms of
1. the maximum in-plane shear stress and associated average normal stress, and
2. the in-plane principal stress and its orientation.
![Page 5: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/5.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
5
PROBLEM-2
1. The maximum in-plane shear stress and associated average normal stress.
2xy
2yxmax
planein 2
MPa4.81
602
9020 22
xy
yxs
22tan
9167.060
29020
qs = 21.3o
![Page 6: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/6.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
6
PROBLEM-2
MPa352
9020
2yx
avg
2. The in-plane principal stress and its orientation.
2xy
2yxyx
2,1 22
MPa)4.8135(
602
9020
2
9020 22
![Page 7: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/7.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
7
PROBLEM-2
MPa4.46MPa)4.8135(
MPa4.116MPa)4.8135(
2
1
2yx
xyp
2tan
Principal stress orientation.
091.129020
60
qp = – 23.7o
![Page 8: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/8.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
8
PROBLEM-3
Steel 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.
![Page 9: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/9.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
9
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
![Page 10: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/10.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
10
PROBLEM-3
Maximum tensile stress at point B:
MPa86.101)0.03(0.04
4)(3500)(0.044
4π
zI
cM
Maximum shear stress at point B:
MPa4.116)0.03(0.04
04)(-8000)(0.44
2π
J
cTτ
![Page 11: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/11.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
11
PROBLEM-3
1. 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
![Page 12: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/12.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
12
PROBLEM-3
2. The in-plane principal stress and its orientation.
2xy
2yxyx
2,1 22
MPa)1279.50(
)4.116(2
086.101
2
086.101 22
MPa1.76MPa)1279.50(
MPa9.177MPa)1279.50(
2
1
2yx
xyp
2tan 285.2
2086.101
4.116
qp = – 33.1o
![Page 13: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/13.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
13
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
![Page 14: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/14.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
14
PROBLEM-4
1. The stress state at point A has been solved in Tutorial-6 Problem-3. The results are as follows
Shear stress: txy = tA = 119.37 MPa
Normal stress: sx = sA’ + sA”
= (– 1.99 – 127.32) MPa
= – 129.31 MPa
txy
sx
![Page 15: 2005 Pearson Education South Asia Pte Ltd TUTORIAL-7: STRESS TRANSFORMATION 1 PROBLEM-1 State of stress at a point is represented by the element shown.](https://reader033.fdocuments.in/reader033/viewer/2022052913/56649d895503460f94a6f670/html5/thumbnails/15.jpg)
2005 Pearson Education South Asia Pte Ltd
TUTORIAL-7: STRESS TRANSFORMATION
15
PROBLEM-4
2. The principal stress at point A and its orientation
2xy
2yxyx
2,1 22
MPa)75.13565.64(
37.1192
031.129
2
031.129 22
MPa40.200MPa)75.13565.64(
MPa10.71MPa)75.13565.64(
2
1
2yx
xyp
2tan 846.1
2031.129
37.119
qp = – 30.78o