Derive the torsion equation for circular shaft
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Torsion is twisting moment or couple or torque, which tend to rotate the plane perpendicular to the longitudinal axis.
Thus, shafts are usually cylindrical in section, solid or hollow and may be steel or copper alloys.a
They may be subjected to following loads:-
1. Torsion only
2. Torsion with axial loads
3. Torsion with bending or transverse load
4. Torsion with axial and bending loads
In case of a shaft if the force is applied tangentially and in the plane of transverse cross-section the torque or twisting moment may be calculated by multiplying force with the radius of the shaft.
Assumptions for the derivation of Torsional equation:
1. The material of the shaft is uniform throughout.
2. The shaft, circular in cross-section remains circular even after loading.
3. A plane section of the shaft normal to its axis before loading remains plane even after the torque has been applied.
4. The twist along the length of the shaft is uniform.
5. The distance between any two normal cross-sections remains same even after application of torque.
6. The maximum shear stress induced in the shaft due to application of torque does not exceed its elastic limit value.
Derivation of Torsion Fromula:
Let us consider,
L = length of shaft
R = radius of shaft
J = polar moment of inertia
a= maximum shear stress induced
G = modulus of rigidity
4= shear strain at the outer surface of the shaft
a= angle of twist
A shaft is fixed at one end and torque is being applied at the another. If a line PQ is drawn on the shaft, it will be distorted to PQ’ on the application of torque. The cross-section will be twisted through an angle
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Home Engineering Civil Engineering Torsion INTRODUCTION TO TORSION, DERIVATION OF TORSIONAL FORMULA,HOLLOW AND SOLID SHAFT
Note on INTRODUCTION TO TORSION, DERIVATION OF TORSIONAL FORMULA,HOLLOW AND SOLID SHAFT
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Note Things to remember
Introduction:
Torsion is twisting moment or couple or torque, which tend to rotate the plane perpendicular to the longitudinal axis.
Thus, shafts are usually cylindrical in section, solid or hollow and may be steel or copper alloys.a
They may be subjected to following loads:-
1. Torsion only
2. Torsion with axial loads
3. Torsion with bending or transverse load
4. Torsion with axial and bending loads
In case of a shaft if the force is applied tangentially and in the plane of transverse cross-section the torque or twisting moment may be calculated by multiplying force with the radius of the shaft.
Assumptions for the derivation of Torsional equation:
1. The material of the shaft is uniform throughout.
2. The shaft, circular in cross-section remains circular even after loading.
3. A plane section of the shaft normal to its axis before loading remains plane even after the torque has been applied.
4. The twist along the length of the shaft is uniform.
5. The distance between any two normal cross-sections remains same even after application of torque.
6. The maximum shear stress induced in the shaft due to application of torque does not exceed its elastic limit value.
Derivation of Torsion Fromula:
Let us consider,
L = length of shaft
R = radius of shaft
J = polar moment of inertia
a= maximum shear stress induced
G = modulus of rigidity
4= shear strain at the outer surface of the shaft
a= angle of twist
A shaft is fixed at one end and torque is being applied at the another. If a line PQ is drawn on the shaft, it will be distorted to PQ’ on the application of torque. The cross-section will be twisted through an angle φ and surface by an angle of a.a
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