In an experimental determination of principal stresses a cantilever of hollow circular cross section is subjected to a varying bending moment and torque; the internal and external diameters of the cantilever are 40 and 50 mm, respectively. For a given loading condition the bending moment and torque at a particular section of the cantilever are 100 and 50 Nm, respectively. Calculate the maximum and minimum principal stresses ata point on the outer surface of the cantileverat this section where the direct stress produced by the bending moment is tensile. Determine also the maximum shear stress at the point and the inclination of the principal stresses to the axis of the cantilever.

In an experimental determination of principal stresses a cantilever of hollow circular cross section is subjected to a varying bending moment and torque; the internal and external diameters of the cantilever are 40 and 50 mm, respectively. For a given loading condition the bending moment and torque at a particular section of the cantilever are 100 and 50 Nm, respectively. Calculate the maximum and minimum principal stresses ata point on the outer surface of the cantileverat this section where the direct stress produced by the bending moment is tensile. Determine also the maximum shear stress at the point and the inclination of the principal stresses to the axis of the cantilever.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Pressure Vessels

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Question

In an experimental determination of principal stresses a cantilever of hollow circular cross section is
subjected to a varying bending moment and torque; the internal and external diameters of the cantilever
are 40 and 50 mm, respectively. For a given loading condition the bending moment and torque at a
particular section of the cantilever are 100 and 50 Nm, respectively. Calculate the maximum and
minimum principal stresses ata point on the outer surface of the cantilever at this section where the direct
stress produced by the bending moment is tensile. Determine also the maximum shear stress at the point
and the inclination of the principal stresses to the axis of the cantilever.
The experimental values of principal stress are estimated from readings obtained from a 45°
strain gauge rosette aligned so that one of its three arms is parallel to and another perpendicular to
the axis of the cantilever. For the loading condition of zero torque and varying bending moment,
comment on the ratio of these strain gauge readings.
Ans. o1= 14.6 N/mm², ơ1=-0.8 N/mm2
Tmax =7.7 N/mm², 0=-13.3° and –103.3°.

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