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HW1 TorsionThinSections

This document contains 4 problems about torsion of thin-walled sections. Problem 1 asks to determine shearing stresses at points on a hollow shaft under a given torque. Problem 2 asks to determine the minimum dimension of a hollow member under a given torque. Problem 3 asks to determine ratios of maximum shearing stresses and angles of twist in two thin-walled tubes with different cross sections under equal torques. Problem 4 asks to calculate shear flow, maximum shear stress, and angle of twist for an idealized airfoil cross section under a given torque. The problems are to be completed and submitted by January 21, 2016.

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Ajay Kotwal
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427 views1 page

HW1 TorsionThinSections

This document contains 4 problems about torsion of thin-walled sections. Problem 1 asks to determine shearing stresses at points on a hollow shaft under a given torque. Problem 2 asks to determine the minimum dimension of a hollow member under a given torque. Problem 3 asks to determine ratios of maximum shearing stresses and angles of twist in two thin-walled tubes with different cross sections under equal torques. Problem 4 asks to calculate shear flow, maximum shear stress, and angle of twist for an idealized airfoil cross section under a given torque. The problems are to be completed and submitted by January 21, 2016.

Uploaded by

Ajay Kotwal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Homework# 1: Torsion of thin-walled sections

[Due on 21/1/2016]

Figure 1 Figure 2 Figure 3

Figure 4

1. A 90-N-m torque is applied to a hollow shaft having the cross-section as shown in Figure 1. Neglecting
the effect of stress concentrations, determine the shearing stress at points a and b.

2.A hollow member having the cross section as shownin Figure 2 is to be formed from sheet metal of 1.5
mm thickness. Knowing that a 140 N-m torque will be applied to the member, determine the smallest
dimension d that can be used if the shearing stress is not to exceed 5 MPa.

3. Equal torques are applied to thin-walled tubes of the same length L, same thickness t, and same radius c
as shown in Figure 3. The tube in Figure 3(b) has been slit lengthwise. Determine (a) the ratio τb/τa of the
maximum shearing stresses in the tubes, (b) the ratio φb/φa of the angles of twist of the tubes.

4. The thin-walled cross-section shown in Figure 4 represents a highly idealized air-foil structure for
which the curved portion is the leading edge, the thicker vertical web is the spar, and the trailing straight
segmentsform the aft portion of the airfoil. If the cross-section is subjectedto a torque T, calculate (a) the
shear flow in each portion (b) maximum shear stress (c) angle of twist. Assume linear elastic material
response with G as the shear modulus.

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