No Slide TitleTORSION
FG05_00CO.TIF
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Torsional stress developed within the drive shaft of this condensation fan depends upon the output of the motor.
OBJECTIVES
You can calculate the stress distribution and angle of twist in a long slender bar subjected to torsional loading.
You can calculate support reaction for a statically indeterminate torsional problems
You can estimate the maximum stress and angle of twist in members having noncircular cross section.
Figure: 04-01a
plane (simply rotate)
FG05_01a.TIF
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FG05_27R.TIF
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FG05_28b.TIF
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Warping of cross- sectional as shown in Fig. 5–28b .
Geometry of Deformation of Circular Bars
• Circumferential lines remain plane after deformation
• Longitudinal lines become helical
Strain - Displacement Analysis
Two fundamental assumptions :
2. every cross section remains plane, remains
perpendicular to the axis, and remains undistorted as
it rotates about the axis
FG05_01-01UN.TIF
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Notice the deformation of the rectangular element when this rubber bar is subjected to a torque.
FG05_01-02UN.TIF
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Notice the deformation of the rectangular element when this rubber bar is subjected to a torque.
FG05_02.TIF
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FG05_03.TIF
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5.2 The Torsion Formula
Develop an equation relating internal torque to stress distribution on the cross section
Linear variation in shear strain leads to linear variation in shear stress.
FG05_05.TIF
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Shear stress varies linearly along each radial line of the cross section
FG05_06.TIF
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Differential ring or annulus having a thickness dr and circumference 2p
FG05_07a.TIF
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Shear stress varies linearly along each radial line of the cross section
FG05_07b.TIF
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Shear stress varies linearly along each radial line of the cross section
FG05_0801.TIF
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FG05_0802.TIF
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FG05_08-01UN.TIF
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Tubular drive shaft for a truck subjected to an overload resulting in failure
FG05_09a_b.TIF
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The shear stress distributed over the tube’s cross- sectional area varies linearly along any radial line
FG05_11a.TIF
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FG05_13-01UN.TIF
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Drive shaft of this cutting machine must be designed to meet the power requirements of its motor.
FG05_14.TIF
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FG05_14-25UN.TIF
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Oil wells are commonly drilled to depths exceeding a thousand meters.
FG05_15a.TIF
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The shaft is assumed to have a circular cross section that can gradually vary along its length, Fig. 5–15a
FG05_15b.TIF
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A differential disk of thickness dx, located at position x, is isolated from the shaft, Fig. 5–15b.
FG05_15-01UN.TIF
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When computing both the stress and the angle of twist of this soil auger, it is necessary to consider the variable loading which acts along its length.
FG05_16.TIF
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The shaft’s cross-sectional area and the applied torque are constant along the length of the shaft, Fig. 5–16.
FG05_17.TIF
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A specimen of known length and diameter is placed in a torsion testing machine like the one shown in Fig. 5–17
FG05_18.TIF
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FG05_19a.TIF
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FG05_19b.TIF
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FG05_19c.TIF
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These results are also shown on the torque diagram for the shaft
FG05_20a-1.TIF
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FG05_26-11UN01.TIF
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Notice the deformation that occurs to the square element when this rubber bar is subjected to a torque.
FG05_26-11UN02.TIF
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Notice the deformation that occurs to the square element when this rubber bar is subjected to a torque.
FG05_27L.TIF
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FG05_27R.TIF
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FG05_28a.TIF
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FG05_28b.TIF
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Warping of cross- sectional as shown in Fig. 5–28b .
FG05_28c.TIF
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Reason for this can be shown by considering an element of material located at one of these points
FG05_28-01UNT01.TIF
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Results of analysis for square cross sections, along with other results from the theory of elasticity, for shafts having triangular and elliptical cross sections
FG05_29.TIF
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FG05_35a-c.TIF
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Three common discontinuities of the cross section that occur in practice
FG05_36.TIF
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FG05_36-01UN.TIF
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Stress concentrations can arise at the coupling of these shafts, and this must be taken into account when the coupling is designed.
FG05_37a.TIF
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