Mechanics of Materials CIVL 3322 / MECH 3322 Shear Stress in Beams What is the cross-section area of the tube shown in mm 2 ? 141.37 5 565.5 5 141.4 4 565.49 4 OTHER 9 Matched Acceptable Value: 2, Within Range: 12 Acceptable Value: 565, Acceptable Range: {563, 567}
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14 January 2011
1
Mechanics of Materials CIVL 3322 / MECH 3322
Shear Stress in Beams
What is the cross-section area of the tube shown in mm2 ?
Shear Stress in Beams I 2
141.37 5 565.5 5 141.4 4 565.49 4 OTHER 9
Matched Acceptable Value: 2, Within Range: 12 Acceptable Value: 565, Acceptable Range: {563, 567}
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What is the cross-section area of the tube shown in mm2 ?
Shear Stress in Beams I 3
What is the radius of a cylinder with an equivalent cross-section area in mm ?
Shear Stress in Beams I 4
13.4 11 13.42 8 13.41 2 13.416 2 OTHER 3
Matched Acceptable Value: 0, Within Range: 24 Acceptable Value: 13, Acceptable Range: {12.5, 13.5}
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What is the radius of a cylinder with an equivalent cross-section area in mm ?
Shear Stress in Beams I 5
Shear Stress in Beams I 6
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Shear Stress in Beams I 7
Shear Stress in Beams I 8
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Shear Stress in Beams I 9
Shear Stress in Beams I 10
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Shear Stress in Beams I 11
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
9.1 For the following problems, a beam segment subjected to internal bending moments at sections A and B is shown along with a sketch of the cross-sectional dimensions. For each problem: (a) Sketch a side view of the beam segment and plot the distribution of bending stresses acting at sections A and B. Indicate the magnitude of key bending stresses on the sketch. (b) Determine the resultant forces acting in the x direction on the specified area at sections A and B and show these resultant forces on the sketch. (c) Is the specified area in equilibrium with respect to forces acting in the x direction? If not, determine the horizontal force required to satisfy equilibrium for the specified area and show the location and direction of this force on the sketch. Consider area (1) of the 20-in.-long beam segment, which is subjected to internal bending moments of MA = 24 kip-ft and MB = 28 kip-ft.
Fig. P9.1a Beam segment Fig. P9.1b Cross-sectional dimensions
Solution Moment of inertia about the z axis:
Shape IC d = yi – y d²A IC + d²A (in.4) (in.) (in.4) (in.4)
left web 864.000 0.000 0.000 864.000 top flange 12.505 10.250 1,287.016 1,299.521 bottom flange 12.505 –10.250 1,287.016 1,299.521 right web 864.000 0.000 0.000 864.000
Moment of inertia about the z axis (in.4) = 4,327.042
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
9.1 For the following problems, a beam segment subjected to internal bending moments at sections A and B is shown along with a sketch of the cross-sectional dimensions. For each problem: (a) Sketch a side view of the beam segment and plot the distribution of bending stresses acting at sections A and B. Indicate the magnitude of key bending stresses on the sketch. (b) Determine the resultant forces acting in the x direction on the specified area at sections A and B and show these resultant forces on the sketch. (c) Is the specified area in equilibrium with respect to forces acting in the x direction? If not, determine the horizontal force required to satisfy equilibrium for the specified area and show the location and direction of this force on the sketch. Consider area (1) of the 20-in.-long beam segment, which is subjected to internal bending moments of MA = 24 kip-ft and MB = 28 kip-ft.
Fig. P9.1a Beam segment Fig. P9.1b Cross-sectional dimensions
Solution Moment of inertia about the z axis:
Shape IC d = yi – y d²A IC + d²A (in.4) (in.) (in.4) (in.4)
left web 864.000 0.000 0.000 864.000 top flange 12.505 10.250 1,287.016 1,299.521 bottom flange 12.505 –10.250 1,287.016 1,299.521 right web 864.000 0.000 0.000 864.000
Moment of inertia about the z axis (in.4) = 4,327.042
Problem 8.45
Shear Stress in Beams I 12
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Homework
¢ Problem P9.2 ¢ Problem P9.3 ¢ Problem P9.7
Shear Stress in Beams I 13
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